0.00/0.02 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.08/0.36 % Computer : n024.cluster.edu 0.08/0.36 % Model : x86_64 x86_64 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.36 % Memory : 8046.5625MB 0.08/0.36 % OS : Linux 6.8.0-71-generic 0.08/0.36 % CPULimit : 1440 0.08/0.36 % WCLimit : 180 0.08/0.36 % DateTime : Mon Jul 27 06:55:45 UTC 2026 0.08/0.36 % CPUTime : 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.08/0.39 Running higher-order theorem proving 0.08/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.19/0.56 % (2964843)Detected a higher-order problem, will run a greedy HOL sequence. 0.19/0.56 % (2964854)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 0.19/0.56 % (2964854)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 0.19/0.56 % (2964850)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2667559502:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi) 0.19/0.56 % (2964853)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3279823663:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi) 0.19/0.56 % (2964854)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=248282082:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi) 0.19/0.56 % (2964848)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3405857999:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi) 0.19/0.56 % (2964849)lrs+10_16_si=on:nwc=1.5:random_seed=2438825079:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi) 0.19/0.56 % (2964852)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1388578060:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi) 0.19/0.56 % (2964851)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=470840764:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1799 on theBenchmark for (1799ds/634Mi) 0.19/0.56 % (2964850)Instruction limit reached! 0.19/0.56 % (2964850)------------------------------ 0.19/0.56 % (2964850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.19/0.56 % (2964850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.19/0.56 % (2964850)CaDiCaL version: 2.1.3 0.19/0.56 % (2964850)Termination reason: Instruction limit 0.19/0.56 % (2964850)Termination phase: shuffling 0.19/0.56 % (2964850)Time elapsed: 0.002 s 0.19/0.56 % (2964850)Peak memory usage: 10 MB 0.19/0.56 % (2964850)Instructions burned: 5 (million) 0.19/0.56 % (2964849)Instruction limit reached! 0.19/0.56 % (2964849)------------------------------ 0.19/0.56 % (2964849)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.19/0.56 % (2964849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.19/0.56 % (2964849)CaDiCaL version: 2.1.3 0.19/0.56 % (2964849)Termination reason: Instruction limit 0.19/0.56 % (2964849)Termination phase: Property scanning 0.19/0.56 % (2964849)Time elapsed: 0.009 s 0.19/0.56 % (2964849)Peak memory usage: 10 MB 0.19/0.56 % (2964849)Instructions burned: 20 (million) 0.19/0.56 % (2964852)Instruction limit reached! 0.19/0.56 % (2964852)------------------------------ 0.19/0.56 % (2964852)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.19/0.56 % (2964852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.19/0.56 % (2964852)CaDiCaL version: 2.1.3 0.19/0.56 % (2964852)Termination reason: Instruction limit 0.19/0.56 % (2964852)Termination phase: Preprocessing 3 0.19/0.56 % (2964852)Time elapsed: 0.012 s 0.19/0.56 % (2964852)Peak memory usage: 11 MB 0.19/0.56 % (2964852)Instructions burned: 26 (million) 0.19/0.56 % (2964864)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=661220467:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 0.19/0.56 % (2964864)Instruction limit reached! 0.19/0.56 % (2964864)------------------------------ 0.19/0.56 % (2964864)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.19/0.56 % (2964864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.19/0.56 % (2964864)CaDiCaL version: 2.1.3 0.19/0.56 % (2964864)Termination reason: Instruction limit 0.19/0.56 % (2964864)Termination phase: shuffling 0.19/0.56 % (2964864)Time elapsed: 0.002 s 0.19/0.56 % (2964864)Peak memory usage: 10 MB 0.19/0.56 % (2964864)Instructions burned: 4 (million) 0.19/0.56 % (2964853)Instruction limit reached! 0.19/0.56 % (2964853)------------------------------ 0.19/0.56 % (2964853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.99/0.61 % (2964853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.99/0.61 % (2964853)CaDiCaL version: 2.1.3 0.99/0.61 % (2964853)Termination reason: Instruction limit 0.99/0.61 % (2964853)Termination phase: Property scanning 0.99/0.61 % (2964853)Time elapsed: 0.030 s 0.99/0.61 % (2964853)Peak memory usage: 12 MB 0.99/0.61 % (2964853)Instructions burned: 75 (million) 0.99/0.61 % (2964866)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 0.99/0.61 % (2964865)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=522556037:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1799 on theBenchmark for (1799ds/5Mi) 0.99/0.61 % (2964865)Instruction limit reached! 0.99/0.61 % (2964865)------------------------------ 0.99/0.61 % (2964865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.99/0.61 % (2964865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.99/0.61 % (2964865)CaDiCaL version: 2.1.3 0.99/0.61 % (2964865)Termination reason: Instruction limit 0.99/0.61 % (2964865)Termination phase: shuffling 0.99/0.61 % (2964865)Time elapsed: 0.003 s 0.99/0.61 % (2964865)Peak memory usage: 10 MB 0.99/0.61 % (2964865)Instructions burned: 6 (million) 0.99/0.61 % (2964866)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2031896276:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1799 on theBenchmark for (1799ds/7Mi) 0.99/0.61 % (2964848)Instruction limit reached! 0.99/0.61 % (2964848)------------------------------ 0.99/0.61 % (2964848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.99/0.61 % (2964848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.99/0.61 % (2964848)CaDiCaL version: 2.1.3 0.99/0.61 % (2964848)Termination reason: Instruction limit 0.99/0.61 % (2964848)Termination phase: Property scanning 0.99/0.61 % (2964848)Time elapsed: 0.038 s 0.99/0.61 % (2964848)Peak memory usage: 12 MB 0.99/0.61 % (2964848)Instructions burned: 88 (million) 0.99/0.61 % (2964866)Instruction limit reached! 0.99/0.61 % (2964866)------------------------------ 0.99/0.61 % (2964866)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.99/0.61 % (2964866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.99/0.61 % (2964866)CaDiCaL version: 2.1.3 0.99/0.61 % (2964866)Termination reason: Instruction limit 0.99/0.61 % (2964866)Termination phase: shuffling 0.99/0.61 % (2964866)Time elapsed: 0.003 s 0.99/0.61 % (2964866)Peak memory usage: 10 MB 0.99/0.61 % (2964866)Instructions burned: 7 (million) 0.99/0.61 % (2964869)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 0.99/0.61 % (2964869)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 0.99/0.61 % (2964869)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2104033730:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1799 on theBenchmark for (1799ds/28Mi) 0.99/0.61 % (2964868)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2839565505:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_1799 on theBenchmark for (1799ds/12Mi) 0.99/0.61 % (2964868)Instruction limit reached! 0.99/0.61 % (2964868)------------------------------ 0.99/0.61 % (2964868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.99/0.61 % (2964868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.99/0.61 % (2964868)CaDiCaL version: 2.1.3 0.99/0.61 % (2964868)Termination reason: Instruction limit 0.99/0.61 % (2964868)Termination phase: shuffling 0.99/0.61 % (2964868)Time elapsed: 0.006 s 0.99/0.61 % (2964868)Peak memory usage: 10 MB 0.99/0.61 % (2964868)Instructions burned: 14 (million) 0.99/0.61 % (2964854)Instruction limit reached! 0.99/0.61 % (2964854)------------------------------ 0.99/0.61 % (2964854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.99/0.61 % (2964854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.99/0.61 % (2964854)CaDiCaL version: 2.1.3 0.99/0.61 % (2964854)Termination reason: Instruction limit 1.33/0.66 % (2964854)Termination phase: Saturation 1.33/0.66 % (2964854)Time elapsed: 0.056 s 1.33/0.66 % (2964854)Peak memory usage: 14 MB 1.33/0.66 % (2964854)Instructions burned: 157 (million) 1.33/0.66 % (2964872)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3117854134:i=86:piset=equals:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/86Mi) 1.33/0.66 % (2964874)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on 1.33/0.66 % (2964869)Instruction limit reached! 1.33/0.66 % (2964869)------------------------------ 1.33/0.66 % (2964869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.33/0.66 % (2964869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.33/0.66 % (2964869)CaDiCaL version: 2.1.3 1.33/0.66 % (2964869)Termination reason: Instruction limit 1.33/0.66 % (2964869)Termination phase: Property scanning 1.33/0.66 % (2964869)Time elapsed: 0.012 s 1.33/0.66 % (2964869)Peak memory usage: 10 MB 1.33/0.66 % (2964869)Instructions burned: 30 (million) 1.33/0.66 % (2964873)lrs+10_1_si=on:cs=on:random_seed=193079066:i=8:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/8Mi) 1.33/0.66 % (2964874)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2309655403:i=2:add=on:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 1.33/0.66 % (2964874)Instruction limit reached! 1.33/0.66 % (2964874)------------------------------ 1.33/0.66 % (2964874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.33/0.66 % (2964874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.33/0.66 % (2964874)CaDiCaL version: 2.1.3 1.33/0.66 % (2964874)Termination reason: Instruction limit 1.33/0.66 % (2964874)Termination phase: shuffling 1.33/0.66 % (2964874)Time elapsed: 0.002 s 1.33/0.66 % (2964874)Peak memory usage: 9 MB 1.33/0.66 % (2964874)Instructions burned: 4 (million) 1.33/0.66 % (2964873)Instruction limit reached! 1.33/0.66 % (2964873)------------------------------ 1.33/0.66 % (2964873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.33/0.66 % (2964873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.33/0.66 % (2964873)CaDiCaL version: 2.1.3 1.33/0.66 % (2964873)Termination reason: Instruction limit 1.33/0.66 % (2964873)Termination phase: shuffling 1.33/0.66 % (2964873)Time elapsed: 0.004 s 1.33/0.66 % (2964873)Peak memory usage: 10 MB 1.33/0.66 % (2964873)Instructions burned: 9 (million) 1.33/0.66 % (2964879)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3463445370:st=2:i=249:sd=1:rtra=on:ss=axioms_1799 on theBenchmark for (1799ds/249Mi) 1.33/0.66 % (2964880)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1863222002:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1799 on theBenchmark for (1799ds/25Mi) 1.33/0.66 % (2964883)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=757398336:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_1798 on theBenchmark for (1798ds/14Mi) 1.33/0.66 % (2964884)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3080477977:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/327Mi) 1.33/0.66 % (2964878)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=926593720:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_1799 on theBenchmark for (1799ds/38Mi) 1.33/0.66 % (2964872)Instruction limit reached! 1.33/0.66 % (2964872)------------------------------ 1.33/0.66 % (2964872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.33/0.66 % (2964872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.33/0.66 % (2964872)CaDiCaL version: 2.1.3 1.33/0.66 % (2964872)Termination reason: Instruction limit 1.33/0.66 % (2964872)Termination phase: Saturation 1.33/0.66 % (2964872)Time elapsed: 0.033 s 1.33/0.66 % (2964872)Peak memory usage: 12 MB 1.33/0.66 % (2964872)Instructions burned: 88 (million) 1.33/0.66 % (2964883)Instruction limit reached! 1.33/0.66 % (2964883)------------------------------ 1.33/0.66 % (2964883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.33/0.66 % (2964880)Instruction limit reached! 1.33/0.66 % (2964880)------------------------------ 1.61/0.72 % (2964880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.61/0.72 % (2964880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.61/0.72 % (2964883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.61/0.72 % (2964880)CaDiCaL version: 2.1.3 1.61/0.72 % (2964883)CaDiCaL version: 2.1.3 1.61/0.72 % (2964883)Termination reason: Instruction limit 1.61/0.72 % (2964883)Termination phase: shuffling 1.61/0.72 % (2964880)Termination reason: Instruction limit 1.61/0.72 % (2964880)Termination phase: Preprocessing 2 1.61/0.72 % (2964880)Time elapsed: 0.011 s 1.61/0.72 % (2964883)Time elapsed: 0.007 s 1.61/0.72 % (2964880)Peak memory usage: 10 MB 1.61/0.72 % (2964883)Peak memory usage: 10 MB 1.61/0.72 % (2964883)Instructions burned: 14 (million) 1.61/0.72 % (2964880)Instructions burned: 26 (million) 1.61/0.72 % (2964878)Instruction limit reached! 1.61/0.72 % (2964878)------------------------------ 1.61/0.72 % (2964878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.61/0.72 % (2964878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.61/0.72 % (2964878)CaDiCaL version: 2.1.3 1.61/0.72 % (2964878)Termination reason: Instruction limit 1.61/0.72 % (2964878)Termination phase: Preprocessing 3 1.61/0.72 % (2964878)Time elapsed: 0.018 s 1.61/0.72 % (2964878)Peak memory usage: 11 MB 1.61/0.72 % (2964878)Instructions burned: 39 (million) 1.61/0.72 % (2964890)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3119023544:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_1798 on theBenchmark for (1798ds/14Mi) 1.61/0.72 % (2964891)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3978149194:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_1798 on theBenchmark for (1798ds/2Mi) 1.61/0.72 % (2964892)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1719192002:i=26:ep=R:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/26Mi) 1.61/0.72 % (2964891)Instruction limit reached! 1.61/0.72 % (2964891)------------------------------ 1.61/0.72 % (2964891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.61/0.72 % (2964891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.61/0.72 % (2964891)CaDiCaL version: 2.1.3 1.61/0.72 % (2964891)Termination reason: Instruction limit 1.61/0.72 % (2964891)Termination phase: shuffling 1.61/0.72 % (2964891)Time elapsed: 0.002 s 1.61/0.72 % (2964891)Peak memory usage: 10 MB 1.61/0.72 % (2964891)Instructions burned: 4 (million) 1.61/0.72 % (2964890)Instruction limit reached! 1.61/0.72 % (2964890)------------------------------ 1.61/0.72 % (2964890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.61/0.72 % (2964890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.61/0.72 % (2964890)CaDiCaL version: 2.1.3 1.61/0.72 % (2964890)Termination reason: Instruction limit 1.61/0.72 % (2964890)Termination phase: shuffling 1.61/0.72 % (2964890)Time elapsed: 0.006 s 1.61/0.72 % (2964890)Peak memory usage: 10 MB 1.61/0.72 % (2964890)Instructions burned: 14 (million) 1.61/0.72 % (2964892)Instruction limit reached! 1.61/0.72 % (2964892)------------------------------ 1.61/0.72 % (2964892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.61/0.72 % (2964892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.61/0.72 % (2964892)CaDiCaL version: 2.1.3 1.61/0.72 % (2964892)Termination reason: Instruction limit 1.61/0.72 % (2964892)Termination phase: Property scanning 1.61/0.72 % (2964892)Time elapsed: 0.012 s 1.61/0.72 % (2964892)Peak memory usage: 10 MB 1.61/0.72 % (2964892)Instructions burned: 27 (million) 1.61/0.72 % (2964895)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=4023216601:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_1798 on theBenchmark for (1798ds/23Mi) 1.61/0.72 % (2964900)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 1.61/0.72 % (2964900)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs 1.61/0.72 % (2964899)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4126989794:cond=on:i=60:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/60Mi) 1.61/0.79 % (2964900)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3108020684:i=14:add=off:nm=40:rtra=on:rawr=on_1798 on theBenchmark for (1798ds/14Mi) 1.61/0.79 % (2964895)Instruction limit reached! 1.61/0.79 % (2964895)------------------------------ 1.61/0.79 % (2964895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.61/0.79 % (2964895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.61/0.79 % (2964895)CaDiCaL version: 2.1.3 1.61/0.79 % (2964895)Termination reason: Instruction limit 1.61/0.79 % (2964895)Termination phase: Property scanning 1.61/0.79 % (2964895)Time elapsed: 0.010 s 1.61/0.79 % (2964895)Peak memory usage: 10 MB 1.61/0.79 % (2964895)Instructions burned: 24 (million) 1.61/0.79 % (2964901)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off 1.61/0.79 % (2964900)Instruction limit reached! 1.61/0.79 % (2964900)------------------------------ 1.61/0.79 % (2964900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.61/0.79 % (2964900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.61/0.79 % (2964900)CaDiCaL version: 2.1.3 1.61/0.79 % (2964900)Termination reason: Instruction limit 1.61/0.79 % (2964900)Termination phase: shuffling 1.61/0.79 % (2964900)Time elapsed: 0.006 s 1.61/0.79 % (2964900)Peak memory usage: 10 MB 1.61/0.79 % (2964900)Instructions burned: 14 (million) 1.61/0.79 % (2964901)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=2766571404:i=8:nm=2:rtra=on:fe=abstraction:inj=on_1798 on theBenchmark for (1798ds/8Mi) 1.61/0.79 % (2964901)Instruction limit reached! 1.61/0.79 % (2964901)------------------------------ 1.61/0.79 % (2964901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.61/0.79 % (2964901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.61/0.79 % (2964901)CaDiCaL version: 2.1.3 1.61/0.79 % (2964901)Termination reason: Instruction limit 1.61/0.79 % (2964901)Termination phase: shuffling 1.61/0.79 % (2964901)Time elapsed: 0.003 s 1.61/0.79 % (2964901)Peak memory usage: 10 MB 1.61/0.79 % (2964901)Instructions burned: 8 (million) 1.61/0.79 % (2964899)Instruction limit reached! 1.61/0.79 % (2964899)------------------------------ 1.61/0.79 % (2964899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.61/0.79 % (2964899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.61/0.79 % (2964899)CaDiCaL version: 2.1.3 1.61/0.79 % (2964899)Termination reason: Instruction limit 1.61/0.79 % (2964899)Termination phase: Property scanning 1.61/0.79 % (2964899)Time elapsed: 0.028 s 1.61/0.79 % (2964899)Peak memory usage: 12 MB 1.61/0.79 % (2964899)Instructions burned: 62 (million) 1.61/0.79 % (2964905)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=34338320:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_1798 on theBenchmark for (1798ds/31Mi) 1.61/0.79 % (2964906)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=4017776889:i=7:hud=5:bd=preordered:rtra=on:bet=on_1798 on theBenchmark for (1798ds/7Mi) 1.61/0.79 % (2964906)Instruction limit reached! 1.61/0.79 % (2964906)------------------------------ 1.61/0.79 % (2964906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.61/0.79 % (2964906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.61/0.79 % (2964906)CaDiCaL version: 2.1.3 1.61/0.79 % (2964906)Termination reason: Instruction limit 1.61/0.79 % (2964906)Termination phase: shuffling 1.61/0.79 % (2964906)Time elapsed: 0.004 s 1.61/0.79 % (2964906)Peak memory usage: 10 MB 1.61/0.79 % (2964906)Instructions burned: 8 (million) 1.61/0.79 % (2964908)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2077044469:i=23:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/23Mi) 1.61/0.79 % (2964905)Instruction limit reached! 1.61/0.79 % (2964905)------------------------------ 1.61/0.79 % (2964905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.61/0.79 % (2964905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.90/0.85 % (2964905)CaDiCaL version: 2.1.3 1.90/0.85 % (2964905)Termination reason: Instruction limit 1.90/0.85 % (2964905)Termination phase: Property scanning 1.90/0.85 % (2964905)Time elapsed: 0.014 s 1.90/0.85 % (2964905)Peak memory usage: 10 MB 1.90/0.85 % (2964905)Instructions burned: 32 (million) 1.90/0.85 % (2964908)Instruction limit reached! 1.90/0.85 % (2964908)------------------------------ 1.90/0.85 % (2964908)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.90/0.85 % (2964908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.90/0.85 % (2964908)CaDiCaL version: 2.1.3 1.90/0.85 % (2964908)Termination reason: Instruction limit 1.90/0.85 % (2964908)Termination phase: Property scanning 1.90/0.85 % (2964908)Time elapsed: 0.009 s 1.90/0.85 % (2964908)Peak memory usage: 10 MB 1.90/0.85 % (2964908)Instructions burned: 25 (million) 1.90/0.85 % (2964879)Instruction limit reached! 1.90/0.85 % (2964879)------------------------------ 1.90/0.85 % (2964879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.90/0.85 % (2964879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.90/0.85 % (2964879)CaDiCaL version: 2.1.3 1.90/0.85 % (2964879)Termination reason: Instruction limit 1.90/0.85 % (2964879)Termination phase: Saturation 1.90/0.85 % (2964879)Time elapsed: 0.113 s 1.90/0.85 % (2964879)Peak memory usage: 14 MB 1.90/0.85 % (2964879)Instructions burned: 250 (million) 1.90/0.85 % (2964909)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=978846445:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_1797 on theBenchmark for (1797ds/20Mi) 1.90/0.85 % (2964913)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=4196383262:i=1240:rtra=on:ixr=off_1797 on theBenchmark for (1797ds/1240Mi) 1.90/0.85 % (2964909)Instruction limit reached! 1.90/0.85 % (2964909)------------------------------ 1.90/0.85 % (2964909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.90/0.85 % (2964909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.90/0.85 % (2964909)CaDiCaL version: 2.1.3 1.90/0.85 % (2964909)Termination reason: Instruction limit 1.90/0.85 % (2964909)Termination phase: Property scanning 1.90/0.85 % (2964909)Time elapsed: 0.009 s 1.90/0.85 % (2964909)Peak memory usage: 10 MB 1.90/0.85 % (2964909)Instructions burned: 21 (million) 1.90/0.85 % (2964914)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=950136077:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1797 on theBenchmark for (1797ds/143Mi) 1.90/0.85 % (2964915)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3842003905:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_1797 on theBenchmark for (1797ds/193Mi) 1.90/0.85 % (2964916)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3726376884:i=42:hud=10:rtra=on_1797 on theBenchmark for (1797ds/42Mi) 1.90/0.85 % (2964916)Instruction limit reached! 1.90/0.85 % (2964916)------------------------------ 1.90/0.85 % (2964916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.90/0.85 % (2964916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.90/0.85 % (2964916)CaDiCaL version: 2.1.3 1.90/0.85 % (2964916)Termination reason: Instruction limit 1.90/0.85 % (2964916)Termination phase: Property scanning 1.90/0.85 % (2964916)Time elapsed: 0.017 s 1.90/0.85 % (2964916)Peak memory usage: 10 MB 1.90/0.85 % (2964916)Instructions burned: 43 (million) 1.90/0.85 % (2964884)Instruction limit reached! 1.90/0.85 % (2964884)------------------------------ 1.90/0.85 % (2964884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.90/0.85 % (2964884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.90/0.85 % (2964884)CaDiCaL version: 2.1.3 1.90/0.85 % (2964884)Termination reason: Instruction limit 1.90/0.85 % (2964884)Termination phase: Saturation 1.90/0.85 % (2964884)Time elapsed: 0.148 s 1.90/0.85 % (2964884)Peak memory usage: 14 MB 1.90/0.85 % (2964884)Instructions burned: 327 (million) 1.90/0.85 % (2964921)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 1.90/0.85 % (2964921)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3544950244:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1797 on theBenchmark for (1797ds/7Mi) 1.90/0.85 % (2964921)Instruction limit reached! 2.65/0.94 % (2964921)------------------------------ 2.65/0.94 % (2964921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.65/0.94 % (2964921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.65/0.94 % (2964921)CaDiCaL version: 2.1.3 2.65/0.94 % (2964921)Termination reason: Instruction limit 2.65/0.94 % (2964921)Termination phase: shuffling 2.65/0.94 % (2964921)Time elapsed: 0.004 s 2.65/0.94 % (2964921)Peak memory usage: 10 MB 2.65/0.94 % (2964921)Instructions burned: 9 (million) 2.65/0.94 % (2964925)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=44454584:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_1797 on theBenchmark for (1797ds/181Mi) 2.65/0.94 % (2964926)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=1271463631:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1797 on theBenchmark for (1797ds/169Mi) 2.65/0.94 % (2964928)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on 2.65/0.94 % (2964914)Instruction limit reached! 2.65/0.94 % (2964914)------------------------------ 2.65/0.94 % (2964914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.65/0.94 % (2964914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.65/0.94 % (2964914)CaDiCaL version: 2.1.3 2.65/0.94 % (2964914)Termination reason: Instruction limit 2.65/0.94 % (2964914)Termination phase: Saturation 2.65/0.94 % (2964914)Time elapsed: 0.062 s 2.65/0.94 % (2964914)Peak memory usage: 14 MB 2.65/0.94 % (2964914)Instructions burned: 144 (million) 2.65/0.94 % (2964928)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=891147341:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_1797 on theBenchmark for (1797ds/6Mi) 2.65/0.94 % (2964928)Instruction limit reached! 2.65/0.94 % (2964928)------------------------------ 2.65/0.94 % (2964928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.65/0.94 % (2964928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.65/0.94 % (2964928)CaDiCaL version: 2.1.3 2.65/0.94 % (2964928)Termination reason: Instruction limit 2.65/0.94 % (2964928)Termination phase: shuffling 2.65/0.94 % (2964928)Time elapsed: 0.003 s 2.65/0.94 % (2964928)Peak memory usage: 10 MB 2.65/0.94 % (2964928)Instructions burned: 6 (million) 2.65/0.94 % (2964915)Instruction limit reached! 2.65/0.94 % (2964915)------------------------------ 2.65/0.94 % (2964915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.65/0.94 % (2964915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.65/0.94 % (2964915)CaDiCaL version: 2.1.3 2.65/0.94 % (2964915)Termination reason: Instruction limit 2.65/0.94 % (2964915)Termination phase: Saturation 2.65/0.94 % (2964915)Time elapsed: 0.082 s 2.65/0.94 % (2964915)Peak memory usage: 14 MB 2.65/0.94 % (2964915)Instructions burned: 195 (million) 2.65/0.94 % (2964931)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=4106558043:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1796 on theBenchmark for (1796ds/22Mi) 2.65/0.94 % (2964933)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2435516706:i=19:add=on:rtra=on_1796 on theBenchmark for (1796ds/19Mi) 2.65/0.94 % (2964931)Instruction limit reached! 2.65/0.94 % (2964931)------------------------------ 2.65/0.94 % (2964931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.65/0.94 % (2964931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.65/0.94 % (2964931)CaDiCaL version: 2.1.3 2.65/0.94 % (2964931)Termination reason: Instruction limit 2.65/0.94 % (2964931)Termination phase: Property scanning 2.65/0.94 % (2964931)Time elapsed: 0.009 s 2.65/0.94 % (2964931)Peak memory usage: 10 MB 2.65/0.94 % (2964931)Instructions burned: 22 (million) 2.65/0.94 % (2964933)Instruction limit reached! 2.65/0.94 % (2964933)------------------------------ 2.65/0.94 % (2964933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.65/0.94 % (2964933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.65/0.94 % (2964933)CaDiCaL version: 2.1.3 2.65/0.94 % (2964933)Termination reason: Instruction limit 2.65/0.94 % (2964933)Termination phase: shuffling 4.15/1.05 % (2964933)Time elapsed: 0.008 s 4.15/1.05 % (2964933)Peak memory usage: 10 MB 4.15/1.05 % (2964933)Instructions burned: 19 (million) 4.15/1.05 % (2964934)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2385673038:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_1796 on theBenchmark for (1796ds/316Mi) 4.15/1.05 % (2964851)Instruction limit reached! 4.15/1.05 % (2964851)------------------------------ 4.15/1.05 % (2964851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.15/1.05 % (2964851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.15/1.05 % (2964851)CaDiCaL version: 2.1.3 4.15/1.05 % (2964851)Termination reason: Instruction limit 4.15/1.05 % (2964851)Termination phase: Saturation 4.15/1.05 % (2964851)Time elapsed: 0.327 s 4.15/1.05 % (2964851)Peak memory usage: 19 MB 4.15/1.05 % (2964851)Instructions burned: 635 (million) 4.15/1.05 % (2964926)Instruction limit reached! 4.15/1.05 % (2964926)------------------------------ 4.15/1.05 % (2964926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.15/1.05 % (2964926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.15/1.05 % (2964926)CaDiCaL version: 2.1.3 4.15/1.05 % (2964926)Termination reason: Instruction limit 4.15/1.05 % (2964926)Termination phase: Saturation 4.15/1.05 % (2964926)Time elapsed: 0.070 s 4.15/1.05 % (2964926)Peak memory usage: 14 MB 4.15/1.05 % (2964926)Instructions burned: 171 (million) 4.15/1.05 % (2964937)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=1898919826:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_1796 on theBenchmark for (1796ds/853Mi) 4.15/1.05 % (2964938)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=1917716401:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_1796 on theBenchmark for (1796ds/45Mi) 4.15/1.05 % (2964925)Instruction limit reached! 4.15/1.05 % (2964925)------------------------------ 4.15/1.05 % (2964925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.15/1.05 % (2964925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.15/1.05 % (2964925)CaDiCaL version: 2.1.3 4.15/1.05 % (2964925)Termination reason: Instruction limit 4.15/1.05 % (2964925)Termination phase: Saturation 4.15/1.05 % (2964925)Time elapsed: 0.083 s 4.15/1.05 % (2964925)Peak memory usage: 14 MB 4.15/1.05 % (2964925)Instructions burned: 181 (million) 4.15/1.05 % (2964942)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2450644341:i=480:rtra=on_1796 on theBenchmark for (1796ds/480Mi) 4.15/1.05 % (2964943)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=847816030:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_1796 on theBenchmark for (1796ds/21Mi) 4.15/1.05 % (2964938)Instruction limit reached! 4.15/1.05 % (2964938)------------------------------ 4.15/1.05 % (2964938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.15/1.05 % (2964938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.15/1.05 % (2964938)CaDiCaL version: 2.1.3 4.15/1.05 % (2964938)Termination reason: Instruction limit 4.15/1.05 % (2964938)Termination phase: Preprocessing 3 4.15/1.05 % (2964938)Time elapsed: 0.020 s 4.15/1.05 % (2964938)Peak memory usage: 11 MB 4.15/1.05 % (2964938)Instructions burned: 45 (million) 4.15/1.05 % (2964943)Instruction limit reached! 4.15/1.05 % (2964943)------------------------------ 4.15/1.05 % (2964943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.15/1.05 % (2964943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.15/1.05 % (2964943)CaDiCaL version: 2.1.3 4.15/1.05 % (2964943)Termination reason: Instruction limit 4.15/1.05 % (2964943)Termination phase: Property scanning 4.15/1.05 % (2964943)Time elapsed: 0.009 s 4.15/1.05 % (2964943)Peak memory usage: 10 MB 4.15/1.05 % (2964943)Instructions burned: 22 (million) 4.15/1.05 % (2964947)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on 4.15/1.05 % (2964947)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2757703406:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_1796 on theBenchmark for (1796ds/200Mi) 4.87/1.23 % (2964949)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3594129337:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_1796 on theBenchmark for (1796ds/13Mi) 4.87/1.23 % (2964950)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=321573487:i=66:s2at=3:nm=2:rtra=on:rawr=on_1795 on theBenchmark for (1795ds/66Mi) 4.87/1.23 % (2964949)Instruction limit reached! 4.87/1.23 % (2964949)------------------------------ 4.87/1.23 % (2964949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.87/1.23 % (2964949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.87/1.23 % (2964949)CaDiCaL version: 2.1.3 4.87/1.23 % (2964949)Termination reason: Instruction limit 4.87/1.23 % (2964949)Termination phase: shuffling 4.87/1.23 % (2964949)Time elapsed: 0.007 s 4.87/1.23 % (2964949)Peak memory usage: 10 MB 4.87/1.23 % (2964949)Instructions burned: 15 (million) 4.87/1.23 % (2964950)Instruction limit reached! 4.87/1.23 % (2964950)------------------------------ 4.87/1.23 % (2964950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.87/1.23 % (2964950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.87/1.23 % (2964950)CaDiCaL version: 2.1.3 4.87/1.23 % (2964950)Termination reason: Instruction limit 4.87/1.23 % (2964950)Termination phase: Property scanning 4.87/1.23 % (2964950)Time elapsed: 0.027 s 4.87/1.23 % (2964950)Peak memory usage: 11 MB 4.87/1.23 % (2964950)Instructions burned: 67 (million) 4.87/1.23 % (2964954)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=3288212772:i=51:fsr=off:rtra=on_1795 on theBenchmark for (1795ds/51Mi) 4.87/1.23 % (2964954)Instruction limit reached! 4.87/1.23 % (2964954)------------------------------ 4.87/1.23 % (2964954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.87/1.23 % (2964954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.87/1.23 % (2964954)CaDiCaL version: 2.1.3 4.87/1.23 % (2964954)Termination reason: Instruction limit 4.87/1.23 % (2964954)Termination phase: Property scanning 4.87/1.23 % (2964954)Time elapsed: 0.021 s 4.87/1.23 % (2964954)Peak memory usage: 12 MB 4.87/1.23 % (2964954)Instructions burned: 53 (million) 4.87/1.23 % (2964934)Instruction limit reached! 4.87/1.23 % (2964934)------------------------------ 4.87/1.23 % (2964934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.87/1.23 % (2964934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.87/1.23 % (2964934)CaDiCaL version: 2.1.3 4.87/1.23 % (2964934)Termination reason: Instruction limit 4.87/1.23 % (2964934)Termination phase: Saturation 4.87/1.23 % (2964934)Time elapsed: 0.124 s 4.87/1.23 % (2964934)Peak memory usage: 15 MB 4.87/1.23 % (2964934)Instructions burned: 316 (million) 4.87/1.23 % (2964955)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3321295898:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1795 on theBenchmark for (1795ds/31Mi) 4.87/1.23 % (2964947)Instruction limit reached! 4.87/1.23 % (2964947)------------------------------ 4.87/1.23 % (2964947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.87/1.23 % (2964947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.87/1.23 % (2964947)CaDiCaL version: 2.1.3 4.87/1.23 % (2964947)Termination reason: Instruction limit 4.87/1.23 % (2964947)Termination phase: Saturation 4.87/1.23 % (2964947)Time elapsed: 0.088 s 4.87/1.23 % (2964947)Peak memory usage: 13 MB 4.87/1.23 % (2964947)Instructions burned: 202 (million) 4.87/1.23 % (2964955)Instruction limit reached! 4.87/1.23 % (2964955)------------------------------ 4.87/1.23 % (2964955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.87/1.23 % (2964955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.87/1.23 % (2964955)CaDiCaL version: 2.1.3 4.87/1.23 % (2964955)Termination reason: Instruction limit 4.87/1.23 % (2964955)Termination phase: Property scanning 4.87/1.23 % (2964955)Time elapsed: 0.014 s 4.87/1.23 % (2964955)Peak memory usage: 10 MB 4.87/1.23 % (2964955)Instructions burned: 33 (million) 4.87/1.23 % (2964959)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=157617524:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_1795 on theBenchmark for (1795ds/137Mi) 5.45/1.31 % (2964960)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=3873829654:cond=on:i=34:hud=10:nm=10:rtra=on_1795 on theBenchmark for (1795ds/34Mi) 5.45/1.31 % (2964962)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3918592416:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_1794 on theBenchmark for (1794ds/67Mi) 5.45/1.31 % (2964960)Instruction limit reached! 5.45/1.31 % (2964960)------------------------------ 5.45/1.31 % (2964960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.45/1.31 % (2964960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.45/1.31 % (2964960)CaDiCaL version: 2.1.3 5.45/1.31 % (2964960)Termination reason: Instruction limit 5.45/1.31 % (2964960)Termination phase: Property scanning 5.45/1.31 % (2964960)Time elapsed: 0.015 s 5.45/1.31 % (2964960)Peak memory usage: 10 MB 5.45/1.31 % (2964960)Instructions burned: 35 (million) 5.45/1.31 % (2964963)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off 5.45/1.31 % (2964963)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=377018274:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_1794 on theBenchmark for (1794ds/180Mi) 5.45/1.31 % (2964942)Instruction limit reached! 5.45/1.31 % (2964942)------------------------------ 5.45/1.31 % (2964942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.45/1.31 % (2964942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.45/1.31 % (2964942)CaDiCaL version: 2.1.3 5.45/1.31 % (2964942)Termination reason: Instruction limit 5.45/1.31 % (2964942)Termination phase: Saturation 5.45/1.31 % (2964942)Time elapsed: 0.158 s 5.45/1.31 % (2964942)Peak memory usage: 16 MB 5.45/1.31 % (2964942)Instructions burned: 481 (million) 5.45/1.31 % (2964967)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=4252380167:st=2:i=246:sd=3:rtra=on:ss=axioms_1794 on theBenchmark for (1794ds/246Mi) 5.45/1.31 % (2964962)Instruction limit reached! 5.45/1.31 % (2964962)------------------------------ 5.45/1.31 % (2964962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.45/1.31 % (2964962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.45/1.31 % (2964962)CaDiCaL version: 2.1.3 5.45/1.31 % (2964962)Termination reason: Instruction limit 5.45/1.31 % (2964962)Termination phase: Property scanning 5.45/1.31 % (2964962)Time elapsed: 0.027 s 5.45/1.31 % (2964962)Peak memory usage: 11 MB 5.45/1.31 % (2964962)Instructions burned: 68 (million) 5.45/1.31 % (2964959)Instruction limit reached! 5.45/1.31 % (2964959)------------------------------ 5.45/1.31 % (2964959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.45/1.31 % (2964959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.45/1.31 % (2964959)CaDiCaL version: 2.1.3 5.45/1.31 % (2964959)Termination reason: Instruction limit 5.45/1.31 % (2964959)Termination phase: Saturation 5.45/1.31 % (2964959)Time elapsed: 0.056 s 5.45/1.31 % (2964959)Peak memory usage: 13 MB 5.45/1.31 % (2964959)Instructions burned: 139 (million) 5.45/1.31 % (2964969)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=612430690:cond=on:i=96:bd=all:rtra=on_1794 on theBenchmark for (1794ds/96Mi) 5.45/1.31 % (2964971)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2842986036:i=427:sd=1:rtra=on:ss=axioms_1794 on theBenchmark for (1794ds/427Mi) 5.45/1.31 % (2964972)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2002930965:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_1794 on theBenchmark for (1794ds/874Mi) 5.45/1.31 % (2964963)Instruction limit reached! 5.45/1.31 % (2964963)------------------------------ 5.45/1.31 % (2964963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.45/1.31 % (2964963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.45/1.31 % (2964963)CaDiCaL version: 2.1.3 5.45/1.31 % (2964963)Termination reason: Instruction limit 5.45/1.31 % (2964963)Termination phase: Saturation 5.45/1.31 % (2964963)Time elapsed: 0.076 s 5.45/1.31 % (2964963)Peak memory usage: 13 MB 5.45/1.31 % (2964963)Instructions burned: 181 (million) 5.45/1.31 % (2964969)Instruction limit reached! 6.08/1.42 % (2964969)------------------------------ 6.08/1.42 % (2964969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.08/1.42 % (2964969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.08/1.42 % (2964969)CaDiCaL version: 2.1.3 6.08/1.42 % (2964969)Termination reason: Instruction limit 6.08/1.42 % (2964969)Termination phase: Saturation 6.08/1.42 % (2964969)Time elapsed: 0.043 s 6.08/1.42 % (2964969)Peak memory usage: 13 MB 6.08/1.42 % (2964969)Instructions burned: 99 (million) 6.08/1.42 % (2964967)Instruction limit reached! 6.08/1.42 % (2964967)------------------------------ 6.08/1.42 % (2964967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.08/1.42 % (2964967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.08/1.42 % (2964967)CaDiCaL version: 2.1.3 6.08/1.42 % (2964967)Termination reason: Instruction limit 6.08/1.42 % (2964967)Termination phase: Saturation 6.08/1.42 % (2964967)Time elapsed: 0.078 s 6.08/1.42 % (2964967)Peak memory usage: 14 MB 6.08/1.42 % (2964967)Instructions burned: 249 (million) 6.08/1.42 % (2964978)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=1847227878:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_1793 on theBenchmark for (1793ds/515Mi) 6.08/1.42 % (2964979)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3294703941:st=1.5:i=130:rtra=on:ss=axioms_1793 on theBenchmark for (1793ds/130Mi) 6.08/1.42 % (2964980)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=358420934:i=44:ep=R:rtra=on:ntd=on_1793 on theBenchmark for (1793ds/44Mi) 6.08/1.42 % (2964980)Instruction limit reached! 6.08/1.42 % (2964980)------------------------------ 6.08/1.42 % (2964980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.08/1.42 % (2964980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.08/1.42 % (2964980)CaDiCaL version: 2.1.3 6.08/1.42 % (2964980)Termination reason: Instruction limit 6.08/1.42 % (2964980)Termination phase: Property scanning 6.08/1.42 % (2964980)Time elapsed: 0.019 s 6.08/1.42 % (2964980)Peak memory usage: 10 MB 6.08/1.42 % (2964980)Instructions burned: 46 (million) 6.08/1.42 % (2964979)Instruction limit reached! 6.08/1.42 % (2964979)------------------------------ 6.08/1.42 % (2964979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.08/1.42 % (2964979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.08/1.42 % (2964979)CaDiCaL version: 2.1.3 6.08/1.42 % (2964979)Termination reason: Instruction limit 6.08/1.42 % (2964979)Termination phase: Saturation 6.08/1.42 % (2964979)Time elapsed: 0.052 s 6.08/1.42 % (2964979)Peak memory usage: 13 MB 6.08/1.42 % (2964979)Instructions burned: 131 (million) 6.08/1.42 % (2964985)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=1910167823:s2a=on:i=571:nm=16:rtra=on_1793 on theBenchmark for (1793ds/571Mi) 6.08/1.42 % (2964987)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=3236643869:i=450:rtra=on:ixr=off:ntd=on_1793 on theBenchmark for (1793ds/450Mi) 6.08/1.42 % (2964971)Instruction limit reached! 6.08/1.42 % (2964971)------------------------------ 6.08/1.42 % (2964971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.08/1.42 % (2964971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.08/1.42 % (2964971)CaDiCaL version: 2.1.3 6.08/1.42 % (2964971)Termination reason: Instruction limit 6.08/1.42 % (2964971)Termination phase: Saturation 6.08/1.42 % (2964971)Time elapsed: 0.191 s 6.08/1.42 % (2964971)Peak memory usage: 15 MB 6.08/1.42 % (2964971)Instructions burned: 428 (million) 6.08/1.42 % (2964937)Instruction limit reached! 6.08/1.42 % (2964937)------------------------------ 6.08/1.42 % (2964937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.08/1.42 % (2964937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.08/1.42 % (2964937)CaDiCaL version: 2.1.3 6.08/1.42 % (2964937)Termination reason: Instruction limit 6.08/1.42 % (2964937)Termination phase: Saturation 6.08/1.42 % (2964937)Time elapsed: 0.412 s 6.08/1.42 % (2964937)Peak memory usage: 20 MB 6.08/1.42 % (2964937)Instructions burned: 853 (million) 6.08/1.42 % (2964913)Instruction limit reached! 6.08/1.42 % (2964913)------------------------------ 6.08/1.42 % (2964913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.72/1.54 % (2964913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.72/1.54 % (2964913)CaDiCaL version: 2.1.3 6.72/1.54 % (2964913)Termination reason: Instruction limit 6.72/1.54 % (2964913)Termination phase: Saturation 6.72/1.54 % (2964913)Time elapsed: 0.548 s 6.72/1.54 % (2964913)Peak memory usage: 19 MB 6.72/1.54 % (2964913)Instructions burned: 1241 (million) 6.72/1.54 % (2964990)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=246822960:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_1792 on theBenchmark for (1792ds/95Mi) 6.72/1.54 % (2964993)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=3374978900:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_1792 on theBenchmark for (1792ds/65Mi) 6.72/1.54 % (2964978)Instruction limit reached! 6.72/1.54 % (2964978)------------------------------ 6.72/1.54 % (2964978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.72/1.54 % (2964978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.72/1.54 % (2964994)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=1688909156:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_1792 on theBenchmark for (1792ds/105Mi) 6.72/1.54 % (2964978)CaDiCaL version: 2.1.3 6.72/1.54 % (2964978)Termination reason: Instruction limit 6.72/1.54 % (2964978)Termination phase: Saturation 6.72/1.54 % (2964978)Time elapsed: 0.199 s 6.72/1.54 % (2964978)Peak memory usage: 15 MB 6.72/1.54 % (2964978)Instructions burned: 515 (million) 6.72/1.54 % (2964987)Instruction limit reached! 6.72/1.54 % (2964987)------------------------------ 6.72/1.54 % (2964987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.72/1.54 % (2964987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.72/1.54 % (2964987)CaDiCaL version: 2.1.3 6.72/1.54 % (2964987)Termination reason: Instruction limit 6.72/1.54 % (2964987)Termination phase: Saturation 6.72/1.54 % (2964987)Time elapsed: 0.146 s 6.72/1.54 % (2964987)Peak memory usage: 19 MB 6.72/1.54 % (2964987)Instructions burned: 450 (million) 6.72/1.54 % (2964993)Instruction limit reached! 6.72/1.54 % (2964993)------------------------------ 6.72/1.54 % (2964993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.72/1.54 % (2964993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.72/1.54 % (2964993)CaDiCaL version: 2.1.3 6.72/1.54 % (2964993)Termination reason: Instruction limit 6.72/1.54 % (2964993)Termination phase: Property scanning 6.72/1.54 % (2964993)Time elapsed: 0.026 s 6.72/1.54 % (2964993)Peak memory usage: 11 MB 6.72/1.54 % (2964993)Instructions burned: 66 (million) 6.72/1.54 % (2964990)Instruction limit reached! 6.72/1.54 % (2964990)------------------------------ 6.72/1.54 % (2964990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.72/1.54 % (2964990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.72/1.54 % (2964990)CaDiCaL version: 2.1.3 6.72/1.54 % (2964990)Termination reason: Instruction limit 6.72/1.54 % (2964990)Termination phase: Saturation 6.72/1.54 % (2964990)Time elapsed: 0.039 s 6.72/1.54 % (2964990)Peak memory usage: 13 MB 6.72/1.54 % (2964990)Instructions burned: 97 (million) 6.72/1.54 % (2965000)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=3433387408:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_1791 on theBenchmark for (1791ds/5755Mi) 6.72/1.54 % (2965001)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=1179102584:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_1791 on theBenchmark for (1791ds/375Mi) 6.72/1.54 % (2964994)Instruction limit reached! 6.72/1.54 % (2964994)------------------------------ 6.72/1.54 % (2964994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.72/1.54 % (2965002)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=371931881:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1791 on theBenchmark for (1791ds/495Mi) 6.72/1.54 % (2964994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.49/1.67 % (2964994)CaDiCaL version: 2.1.3 7.49/1.67 % (2964994)Termination reason: Instruction limit 7.49/1.67 % (2964994)Termination phase: Saturation 7.49/1.67 % (2964994)Time elapsed: 0.044 s 7.49/1.67 % (2964994)Peak memory usage: 13 MB 7.49/1.67 % (2964994)Instructions burned: 105 (million) 7.49/1.67 % (2965003)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=943981990:cond=on:i=34:hud=10:nm=10:rtra=on_1791 on theBenchmark for (1791ds/34Mi) 7.49/1.67 % (2965003)Instruction limit reached! 7.49/1.67 % (2965003)------------------------------ 7.49/1.67 % (2965003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.49/1.67 % (2965003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.49/1.67 % (2965003)CaDiCaL version: 2.1.3 7.49/1.67 % (2965003)Termination reason: Instruction limit 7.49/1.67 % (2965003)Termination phase: Property scanning 7.49/1.67 % (2965003)Time elapsed: 0.014 s 7.49/1.67 % (2965003)Peak memory usage: 10 MB 7.49/1.67 % (2965003)Instructions burned: 36 (million) 7.49/1.67 % (2965008)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=725475131:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_1791 on theBenchmark for (1791ds/91Mi) 7.49/1.67 % (2965013)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=4138021456:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_1791 on theBenchmark for (1791ds/66Mi) 7.49/1.67 % (2965008)Instruction limit reached! 7.49/1.67 % (2965008)------------------------------ 7.49/1.67 % (2965008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.49/1.67 % (2965008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.49/1.67 % (2965008)CaDiCaL version: 2.1.3 7.49/1.67 % (2965008)Termination reason: Instruction limit 7.49/1.67 % (2965008)Termination phase: Saturation 7.49/1.67 % (2965008)Time elapsed: 0.038 s 7.49/1.67 % (2965008)Peak memory usage: 12 MB 7.49/1.67 % (2965008)Instructions burned: 91 (million) 7.49/1.67 % (2965013)Instruction limit reached! 7.49/1.67 % (2965013)------------------------------ 7.49/1.67 % (2965013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.49/1.67 % (2965013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.49/1.67 % (2965013)CaDiCaL version: 2.1.3 7.49/1.67 % (2965013)Termination reason: Instruction limit 7.49/1.67 % (2965013)Termination phase: Function definition elimination 7.49/1.67 % (2965013)Time elapsed: 0.028 s 7.49/1.67 % (2965013)Peak memory usage: 12 MB 7.49/1.67 % (2965013)Instructions burned: 68 (million) 7.49/1.67 % (2964972)Instruction limit reached! 7.49/1.67 % (2964972)------------------------------ 7.49/1.67 % (2964972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.49/1.67 % (2964972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.49/1.67 % (2964972)CaDiCaL version: 2.1.3 7.49/1.67 % (2964972)Termination reason: Instruction limit 7.49/1.67 % (2964972)Termination phase: Saturation 7.49/1.67 % (2964972)Time elapsed: 0.359 s 7.49/1.67 % (2964972)Peak memory usage: 16 MB 7.49/1.67 % (2964972)Instructions burned: 875 (million) 7.49/1.67 % (2964985)Instruction limit reached! 7.49/1.67 % (2964985)------------------------------ 7.49/1.67 % (2964985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.49/1.67 % (2964985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.49/1.67 % (2964985)CaDiCaL version: 2.1.3 7.49/1.67 % (2964985)Termination reason: Instruction limit 7.49/1.67 % (2964985)Termination phase: Saturation 7.49/1.67 % (2964985)Time elapsed: 0.264 s 7.49/1.67 % (2964985)Peak memory usage: 17 MB 7.49/1.67 % (2964985)Instructions burned: 572 (million) 7.49/1.67 % (2965016)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3553394402:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1790 on theBenchmark for (1790ds/22Mi) 7.49/1.67 % (2965018)lrs+10_1_sil=128000:si=on:urr=on:random_seed=1384700803:i=28:sd=1:rtra=on:ss=axioms:sgt=64_1790 on theBenchmark for (1790ds/28Mi) 7.49/1.67 % (2965017)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=3146370171:i=338:bd=all:ins=4:rtra=on_1790 on theBenchmark for (1790ds/338Mi) 7.49/1.67 % (2965016)Instruction limit reached! 8.22/1.81 % (2965016)------------------------------ 8.22/1.81 % (2965016)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.22/1.81 % (2965016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.22/1.81 % (2965016)CaDiCaL version: 2.1.3 8.22/1.81 % (2965016)Termination reason: Instruction limit 8.22/1.81 % (2965016)Termination phase: Property scanning 8.22/1.81 % (2965016)Time elapsed: 0.010 s 8.22/1.81 % (2965016)Peak memory usage: 10 MB 8.22/1.81 % (2965016)Instructions burned: 24 (million) 8.22/1.81 % (2965018)Instruction limit reached! 8.22/1.81 % (2965018)------------------------------ 8.22/1.81 % (2965018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.22/1.81 % (2965018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.22/1.81 % (2965018)CaDiCaL version: 2.1.3 8.22/1.81 % (2965018)Termination reason: Instruction limit 8.22/1.81 % (2965018)Termination phase: Property scanning 8.22/1.81 % (2965018)Time elapsed: 0.011 s 8.22/1.81 % (2965018)Peak memory usage: 10 MB 8.22/1.81 % (2965018)Instructions burned: 30 (million) 8.22/1.81 % (2965019)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on 8.22/1.81 % (2965019)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=1921261447:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_1790 on theBenchmark for (1790ds/137Mi) 8.22/1.81 % (2965024)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=1700353151:i=227:sd=1:bd=all:rtra=on:ss=axioms_1790 on theBenchmark for (1790ds/227Mi) 8.22/1.81 % (2965023)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=2215774105:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_1790 on theBenchmark for (1790ds/340Mi) 8.22/1.81 % (2965001)Instruction limit reached! 8.22/1.81 % (2965001)------------------------------ 8.22/1.81 % (2965001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.22/1.81 % (2965001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.22/1.81 % (2965001)CaDiCaL version: 2.1.3 8.22/1.81 % (2965001)Termination reason: Instruction limit 8.22/1.81 % (2965001)Termination phase: Saturation 8.22/1.81 % (2965001)Time elapsed: 0.176 s 8.22/1.81 % (2965001)Peak memory usage: 14 MB 8.22/1.81 % (2965001)Instructions burned: 375 (million) 8.22/1.81 % (2965019)Instruction limit reached! 8.22/1.81 % (2965019)------------------------------ 8.22/1.81 % (2965019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.22/1.81 % (2965019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.22/1.81 % (2965019)CaDiCaL version: 2.1.3 8.22/1.81 % (2965019)Termination reason: Instruction limit 8.22/1.81 % (2965019)Termination phase: Saturation 8.22/1.81 % (2965019)Time elapsed: 0.055 s 8.22/1.81 % (2965019)Peak memory usage: 13 MB 8.22/1.81 % (2965019)Instructions burned: 138 (million) 8.22/1.81 % (2965030)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on 8.22/1.81 % (2965030)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=152844768:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_1789 on theBenchmark for (1789ds/373Mi) 8.22/1.81 % (2965031)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=3375219793:i=116:ep=RSTC:rtra=on:ntd=on_1789 on theBenchmark for (1789ds/116Mi) 8.22/1.81 % (2965017)Instruction limit reached! 8.22/1.81 % (2965017)------------------------------ 8.22/1.81 % (2965017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.22/1.81 % (2965017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.22/1.81 % (2965017)CaDiCaL version: 2.1.3 8.22/1.81 % (2965017)Termination reason: Instruction limit 8.22/1.81 % (2965017)Termination phase: Saturation 8.22/1.81 % (2965017)Time elapsed: 0.128 s 8.22/1.81 % (2965017)Peak memory usage: 15 MB 8.22/1.81 % (2965017)Instructions burned: 339 (million) 8.22/1.81 % (2965024)Instruction limit reached! 8.22/1.81 % (2965024)------------------------------ 8.22/1.81 % (2965024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.22/1.81 % (2965024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.12/2.04 % (2965024)CaDiCaL version: 2.1.3 11.12/2.04 % (2965024)Termination reason: Instruction limit 11.12/2.04 % (2965024)Termination phase: Saturation 11.12/2.04 % (2965024)Time elapsed: 0.098 s 11.12/2.04 % (2965024)Peak memory usage: 14 MB 11.12/2.04 % (2965024)Instructions burned: 227 (million) 11.12/2.04 % (2965002)Instruction limit reached! 11.12/2.04 % (2965002)------------------------------ 11.12/2.04 % (2965002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.12/2.04 % (2965002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.12/2.04 % (2965002)CaDiCaL version: 2.1.3 11.12/2.04 % (2965002)Termination reason: Instruction limit 11.12/2.04 % (2965002)Termination phase: Saturation 11.12/2.04 % (2965002)Time elapsed: 0.232 s 11.12/2.04 % (2965002)Peak memory usage: 17 MB 11.12/2.04 % (2965002)Instructions burned: 495 (million) 11.12/2.04 % (2965036)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=2276901565:i=575:rtra=on_1788 on theBenchmark for (1788ds/575Mi) 11.12/2.04 % (2965037)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=3256512153:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_1788 on theBenchmark for (1788ds/270Mi) 11.12/2.04 % (2965031)Instruction limit reached! 11.12/2.04 % (2965031)------------------------------ 11.12/2.04 % (2965031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.12/2.04 % (2965031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.12/2.04 % (2965031)CaDiCaL version: 2.1.3 11.12/2.04 % (2965031)Termination reason: Instruction limit 11.12/2.04 % (2965031)Termination phase: Saturation 11.12/2.04 % (2965031)Time elapsed: 0.051 s 11.12/2.04 % (2965031)Peak memory usage: 13 MB 11.12/2.04 % (2965031)Instructions burned: 118 (million) 11.12/2.04 % (2965038)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3823428271:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1788 on theBenchmark for (1788ds/9840Mi) 11.12/2.04 % (2965023)Instruction limit reached! 11.12/2.04 % (2965023)------------------------------ 11.12/2.04 % (2965023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.12/2.04 % (2965023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.12/2.04 % (2965023)CaDiCaL version: 2.1.3 11.12/2.04 % (2965023)Termination reason: Instruction limit 11.12/2.04 % (2965023)Termination phase: Saturation 11.12/2.04 % (2965023)Time elapsed: 0.133 s 11.12/2.04 % (2965023)Peak memory usage: 13 MB 11.12/2.04 % (2965023)Instructions burned: 340 (million) 11.12/2.04 % (2965041)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=685771811:i=421:rtra=on:ss=axioms_1788 on theBenchmark for (1788ds/421Mi) 11.12/2.04 % (2965043)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 11.12/2.04 % (2965043)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=3889105505:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_1788 on theBenchmark for (1788ds/270Mi) 11.12/2.04 % (2965043)Refutation not found, incomplete strategy 11.12/2.04 % (2965043)------------------------------ 11.12/2.04 % (2965043)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.12/2.04 % (2965043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.12/2.04 % (2965043)CaDiCaL version: 2.1.3 11.12/2.04 % (2965043)Termination reason: Refutation not found, incomplete strategy 11.12/2.04 % (2965043)Time elapsed: 0.057 s 11.12/2.04 % (2965043)Peak memory usage: 14 MB 11.12/2.04 % (2965043)Instructions burned: 139 (million) 11.12/2.04 % (2965043)------------------------------ 11.12/2.04 % (2965043)------------------------------ 11.12/2.04 % (2965030)Instruction limit reached! 11.12/2.04 % (2965030)------------------------------ 11.12/2.04 % (2965030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.12/2.04 % (2965030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.12/2.04 % (2965030)CaDiCaL version: 2.1.3 11.12/2.04 % (2965030)Termination reason: Instruction limit 12.83/2.35 % (2965030)Termination phase: Saturation 12.83/2.35 % (2965030)Time elapsed: 0.148 s 12.83/2.35 % (2965030)Peak memory usage: 13 MB 12.83/2.35 % (2965030)Instructions burned: 373 (million) 12.83/2.35 % (2965037)Instruction limit reached! 12.83/2.35 % (2965037)------------------------------ 12.83/2.35 % (2965037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.83/2.35 % (2965037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.83/2.35 % (2965037)CaDiCaL version: 2.1.3 12.83/2.35 % (2965037)Termination reason: Instruction limit 12.83/2.35 % (2965037)Termination phase: Saturation 12.83/2.35 % (2965037)Time elapsed: 0.105 s 12.83/2.35 % (2965037)Peak memory usage: 14 MB 12.83/2.35 % (2965037)Instructions burned: 272 (million) 12.83/2.35 % (2965049)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 12.83/2.35 % (2965049)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 12.83/2.35 % (2965048)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2338826696:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1787 on theBenchmark for (1787ds/31Mi) 12.83/2.35 % (2965049)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3636153779:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_1787 on theBenchmark for (1787ds/1440Mi) 12.83/2.35 % (2965050)dis+10_2_sil=128000:si=on:random_seed=426103032:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_1787 on theBenchmark for (1787ds/339Mi) 12.83/2.35 % (2965048)Instruction limit reached! 12.83/2.35 % (2965048)------------------------------ 12.83/2.35 % (2965048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.83/2.35 % (2965048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.83/2.35 % (2965048)CaDiCaL version: 2.1.3 12.83/2.35 % (2965048)Termination reason: Instruction limit 12.83/2.35 % (2965048)Termination phase: Property scanning 12.83/2.35 % (2965048)Time elapsed: 0.013 s 12.83/2.35 % (2965048)Peak memory usage: 10 MB 12.83/2.35 % (2965048)Instructions burned: 33 (million) 12.83/2.35 % (2965054)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=639291587:i=111:add=on:fgj=on:rtra=on:fdi=1024_1787 on theBenchmark for (1787ds/111Mi) 12.83/2.35 % (2965054)Instruction limit reached! 12.83/2.35 % (2965054)------------------------------ 12.83/2.35 % (2965054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.83/2.35 % (2965054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.83/2.35 % (2965054)CaDiCaL version: 2.1.3 12.83/2.35 % (2965054)Termination reason: Instruction limit 12.83/2.35 % (2965054)Termination phase: Saturation 12.83/2.35 % (2965054)Time elapsed: 0.045 s 12.83/2.35 % (2965054)Peak memory usage: 13 MB 12.83/2.35 % (2965054)Instructions burned: 112 (million) 12.83/2.35 % (2965041)Instruction limit reached! 12.83/2.35 % (2965041)------------------------------ 12.83/2.35 % (2965041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.83/2.35 % (2965041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.83/2.35 % (2965041)CaDiCaL version: 2.1.3 12.83/2.35 % (2965041)Termination reason: Instruction limit 12.83/2.35 % (2965041)Termination phase: Saturation 12.83/2.35 % (2965041)Time elapsed: 0.188 s 12.83/2.35 % (2965041)Peak memory usage: 15 MB 12.83/2.35 % (2965041)Instructions burned: 423 (million) 12.83/2.35 % (2965036)Instruction limit reached! 12.83/2.35 % (2965036)------------------------------ 12.83/2.35 % (2965036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.83/2.35 % (2965036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.83/2.35 % (2965036)CaDiCaL version: 2.1.3 12.83/2.35 % (2965036)Termination reason: Instruction limit 12.83/2.35 % (2965036)Termination phase: Saturation 12.83/2.35 % (2965036)Time elapsed: 0.236 s 12.83/2.35 % (2965036)Peak memory usage: 15 MB 12.83/2.35 % (2965036)Instructions burned: 575 (million) 12.83/2.35 % (2965058)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=778794073:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1786 on theBenchmark for (1786ds/122Mi) 11.06/2.40 % (2965059)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=894634363:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_1786 on theBenchmark for (1786ds/136Mi) 11.06/2.40 % (2965060)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3034590194:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1786 on theBenchmark for (1786ds/232Mi) 11.06/2.40 % (2965050)Instruction limit reached! 11.06/2.40 % (2965050)------------------------------ 11.06/2.40 % (2965050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.40 % (2965050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.40 % (2965050)CaDiCaL version: 2.1.3 11.06/2.40 % (2965050)Termination reason: Instruction limit 11.06/2.40 % (2965050)Termination phase: Saturation 11.06/2.40 % (2965050)Time elapsed: 0.138 s 11.06/2.40 % (2965050)Peak memory usage: 14 MB 11.06/2.40 % (2965050)Instructions burned: 341 (million) 11.06/2.40 % (2965058)Instruction limit reached! 11.06/2.40 % (2965058)------------------------------ 11.06/2.40 % (2965058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.40 % (2965058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.40 % (2965058)CaDiCaL version: 2.1.3 11.06/2.40 % (2965058)Termination reason: Instruction limit 11.06/2.40 % (2965058)Termination phase: Saturation 11.06/2.40 % (2965058)Time elapsed: 0.049 s 11.06/2.40 % (2965058)Peak memory usage: 13 MB 11.06/2.40 % (2965058)Instructions burned: 123 (million) 11.06/2.40 % (2965064)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=925550026:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_1786 on theBenchmark for (1786ds/1254Mi) 11.06/2.40 % (2965059)Instruction limit reached! 11.06/2.40 % (2965059)------------------------------ 11.06/2.40 % (2965059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.40 % (2965059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.40 % (2965059)CaDiCaL version: 2.1.3 11.06/2.40 % (2965059)Termination reason: Instruction limit 11.06/2.40 % (2965059)Termination phase: Saturation 11.06/2.40 % (2965059)Time elapsed: 0.059 s 11.06/2.40 % (2965059)Peak memory usage: 14 MB 11.06/2.40 % (2965059)Instructions burned: 136 (million) 11.06/2.40 % (2965065)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs 11.06/2.40 % (2965065)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=2815801559:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_1785 on theBenchmark for (1785ds/281Mi) 11.06/2.40 % (2965069)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2875121520:i=619:add=on:rtra=on_1785 on theBenchmark for (1785ds/619Mi) 11.06/2.40 % (2965060)Instruction limit reached! 11.06/2.40 % (2965060)------------------------------ 11.06/2.40 % (2965060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.40 % (2965060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.40 % (2965060)CaDiCaL version: 2.1.3 11.06/2.40 % (2965060)Termination reason: Instruction limit 11.06/2.40 % (2965060)Termination phase: Saturation 11.06/2.40 % (2965060)Time elapsed: 0.112 s 11.06/2.40 % (2965060)Peak memory usage: 16 MB 11.06/2.40 % (2965060)Instructions burned: 233 (million) 11.06/2.40 % (2965072)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3108844533:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_1784 on theBenchmark for (1784ds/865Mi) 11.06/2.40 % (2965065)Instruction limit reached! 11.06/2.40 % (2965065)------------------------------ 11.06/2.40 % (2965065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.40 % (2965065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.40 % (2965065)CaDiCaL version: 2.1.3 11.06/2.40 % (2965065)Termination reason: Instruction limit 11.06/2.40 % (2965065)Termination phase: Saturation 11.06/2.40 % (2965065)Time elapsed: 0.116 s 11.06/2.40 % (2965065)Peak memory usage: 15 MB 11.06/2.40 % (2965065)Instructions burned: 283 (million) 11.06/2.40 % (2965076)lrs+10_1_sil=128000:si=on:urr=on:random_seed=256690858:i=212:sd=1:rtra=on:ss=axioms:sgt=64_1784 on theBenchmark for (1784ds/212Mi) 11.06/2.41 % (2965076)Instruction limit reached! 11.06/2.41 % (2965076)------------------------------ 11.06/2.41 % (2965076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.41 % (2965076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.41 % (2965076)CaDiCaL version: 2.1.3 11.06/2.41 % (2965076)Termination reason: Instruction limit 11.06/2.41 % (2965076)Termination phase: Saturation 11.06/2.41 % (2965076)Time elapsed: 0.094 s 11.06/2.41 % (2965076)Peak memory usage: 14 MB 11.06/2.41 % (2965076)Instructions burned: 214 (million) 11.06/2.41 % (2965069)Instruction limit reached! 11.06/2.41 % (2965069)------------------------------ 11.06/2.41 % (2965069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.41 % (2965069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.41 % (2965069)CaDiCaL version: 2.1.3 11.06/2.41 % (2965069)Termination reason: Instruction limit 11.06/2.41 % (2965069)Termination phase: Saturation 11.06/2.41 % (2965069)Time elapsed: 0.256 s 11.06/2.41 % (2965069)Peak memory usage: 15 MB 11.06/2.41 % (2965069)Instructions burned: 620 (million) 11.06/2.41 % (2965080)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=1332090230:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_1782 on theBenchmark for (1782ds/130Mi) 11.06/2.41 % (2965081)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3287024008:st=1.5:i=346:rtra=on:ss=axioms_1782 on theBenchmark for (1782ds/346Mi) 11.06/2.41 % (2965080)Instruction limit reached! 11.06/2.41 % (2965080)------------------------------ 11.06/2.41 % (2965080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.41 % (2965080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.41 % (2965080)CaDiCaL version: 2.1.3 11.06/2.41 % (2965080)Termination reason: Instruction limit 11.06/2.41 % (2965080)Termination phase: Saturation 11.06/2.41 % (2965080)Time elapsed: 0.055 s 11.06/2.41 % (2965080)Peak memory usage: 13 MB 11.06/2.41 % (2965080)Instructions burned: 132 (million) 11.06/2.41 % (2965086)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=3033115366:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_1782 on theBenchmark for (1782ds/152Mi) 11.06/2.41 % (2965049)Instruction limit reached! 11.06/2.41 % (2965049)------------------------------ 11.06/2.41 % (2965049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.41 % (2965049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.41 % (2965049)CaDiCaL version: 2.1.3 11.06/2.41 % (2965049)Termination reason: Instruction limit 11.06/2.41 % (2965049)Termination phase: Saturation 11.06/2.41 % (2965049)Time elapsed: 0.615 s 11.06/2.41 % (2965049)Peak memory usage: 23 MB 11.06/2.41 % (2965049)Instructions burned: 1443 (million) 11.06/2.41 % (2965072)Instruction limit reached! 11.06/2.41 % (2965072)------------------------------ 11.06/2.41 % (2965072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.41 % (2965072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.41 % (2965072)CaDiCaL version: 2.1.3 11.06/2.41 % (2965072)Termination reason: Instruction limit 11.06/2.41 % (2965072)Termination phase: Saturation 11.06/2.41 % (2965072)Time elapsed: 0.340 s 11.06/2.41 % (2965072)Peak memory usage: 19 MB 11.06/2.41 % (2965072)Instructions burned: 865 (million) 11.06/2.41 % (2965081) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2964843-2965081"... 11.06/2.41 % (2965086)Instruction limit reached! 11.06/2.41 % (2965086)------------------------------ 11.06/2.41 % (2965086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.41 % (2965086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.41 % (2965086)CaDiCaL version: 2.1.3 11.06/2.41 % (2965086)Termination reason: Instruction limit 11.06/2.41 % (2965086)Termination phase: Saturation 11.06/2.41 % (2965086)Time elapsed: 0.069 s 11.06/2.41 % (2965086)Peak memory usage: 14 MB 11.06/2.41 % (2965086)Instructions burned: 152 (million) 11.06/2.41 % (2965088)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2260230598:i=75:ep=R:rtra=on:ntd=on_1781 on theBenchmark for (1781ds/75Mi) 11.06/2.41 % (2965091)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=851069588:st=2.5:i=387:sd=2:rtra=on:ss=axioms_1781 on theBenchmark for (1781ds/387Mi) 11.06/2.41 % (2965088)Instruction limit reached! 11.06/2.41 % (2965088)------------------------------ 11.06/2.41 % (2965088)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.41 % (2965088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.41 % (2965088)CaDiCaL version: 2.1.3 11.06/2.41 % (2965088)Termination reason: Instruction limit 11.06/2.41 % (2965088)Termination phase: Saturation 11.06/2.41 % (2965088)Time elapsed: 0.030 s 11.06/2.41 % (2965088)Peak memory usage: 12 MB 11.06/2.41 % (2965088)Instructions burned: 75 (million) 11.06/2.41 % (2965092)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1855730149:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_1781 on theBenchmark for (1781ds/148Mi) 11.06/2.41 % (2965081)...printing done. 11.06/2.41 % (2965081)Refutation found. Thanks to Tanya! 11.06/2.41 % SZS status Theorem for theBenchmark 11.06/2.41 % SZS output start Proof for theBenchmark 11.06/2.41 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType). 11.06/2.41 thf(func_def_0, type, in: ($i > $i > $o)). 11.06/2.41 thf(func_def_1, type, exu: (($i > $o) > $o)). 11.06/2.41 thf(func_def_3, type, setextAx: $o). 11.06/2.41 thf(func_def_5, type, emptysetAx: $o). 11.06/2.41 thf(func_def_6, type, setadjoin: ($i > $i > $i)). 11.06/2.41 thf(func_def_7, type, setadjoinAx: $o). 11.06/2.41 thf(func_def_8, type, powerset: ($i > $i)). 11.06/2.41 thf(func_def_9, type, powersetAx: $o). 11.06/2.41 thf(func_def_10, type, setunion: ($i > $i)). 11.06/2.41 thf(func_def_11, type, setunionAx: $o). 11.06/2.41 thf(func_def_13, type, omega0Ax: $o). 11.06/2.41 thf(func_def_14, type, omegaSAx: $o). 11.06/2.41 thf(func_def_15, type, omegaIndAx: $o). 11.06/2.41 thf(func_def_16, type, replAx: $o). 11.06/2.41 thf(func_def_17, type, foundationAx: $o). 11.06/2.41 thf(func_def_18, type, wellorderingAx: $o). 11.06/2.41 thf(func_def_19, type, descr: (($i > $o) > $i)). 11.06/2.41 thf(func_def_20, type, descrp: $o). 11.06/2.41 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)). 11.06/2.41 thf(func_def_22, type, dsetconstrI: $o). 11.06/2.41 thf(func_def_23, type, dsetconstrEL: $o). 11.06/2.41 thf(func_def_24, type, dsetconstrER: $o). 11.06/2.41 thf(func_def_25, type, exuE1: $o). 11.06/2.41 thf(func_def_26, type, prop2set: ($o > $i)). 11.06/2.41 thf(func_def_27, type, prop2setE: $o). 11.06/2.41 thf(func_def_28, type, emptysetE: $o). 11.06/2.41 thf(func_def_29, type, emptysetimpfalse: $o). 11.06/2.41 thf(func_def_30, type, notinemptyset: $o). 11.06/2.41 thf(func_def_31, type, exuE3e: $o). 11.06/2.41 thf(func_def_32, type, setext: $o). 11.06/2.41 thf(func_def_33, type, emptyI: $o). 11.06/2.41 thf(func_def_34, type, noeltsimpempty: $o). 11.06/2.41 thf(func_def_35, type, setbeta: $o). 11.06/2.41 thf(func_def_36, type, nonempty: ($i > $o)). 11.06/2.41 thf(func_def_37, type, nonemptyE1: $o). 11.06/2.41 thf(func_def_38, type, nonemptyI: $o). 11.06/2.41 thf(func_def_39, type, nonemptyI1: $o). 11.06/2.41 thf(func_def_40, type, setadjoinIL: $o). 11.06/2.41 thf(func_def_41, type, emptyinunitempty: $o). 11.06/2.41 thf(func_def_42, type, setadjoinIR: $o). 11.06/2.41 thf(func_def_43, type, setadjoinE: $o). 11.06/2.41 thf(func_def_44, type, setadjoinOr: $o). 11.06/2.41 thf(func_def_45, type, setoftrueEq: $o). 11.06/2.41 thf(func_def_46, type, powersetI: $o). 11.06/2.41 thf(func_def_47, type, emptyinPowerset: $o). 11.06/2.41 thf(func_def_48, type, emptyInPowerset: $o). 11.06/2.41 thf(func_def_49, type, powersetE: $o). 11.06/2.41 thf(func_def_50, type, setunionI: $o). 11.06/2.41 thf(func_def_51, type, setunionE: $o). 11.06/2.41 thf(func_def_52, type, subPowSU: $o). 11.06/2.41 thf(func_def_53, type, exuE2: $o). 11.06/2.41 thf(func_def_54, type, nonemptyImpWitness: $o). 11.06/2.41 thf(func_def_55, type, uniqinunit: $o). 11.06/2.41 thf(func_def_56, type, notinsingleton: $o). 11.06/2.41 thf(func_def_57, type, eqinunit: $o). 11.06/2.41 thf(func_def_58, type, singletonsswitch: $o). 11.06/2.41 thf(func_def_59, type, upairsetE: $o). 11.06/2.41 thf(func_def_60, type, upairsetIL: $o). 11.06/2.41 thf(func_def_61, type, upairsetIR: $o). 11.06/2.41 thf(func_def_62, type, emptyE1: $o). 11.06/2.41 thf(func_def_63, type, vacuousDall: $o). 11.06/2.41 thf(func_def_64, type, quantDeMorgan1: $o). 11.06/2.41 thf(func_def_65, type, quantDeMorgan2: $o). 11.06/2.41 thf(func_def_66, type, quantDeMorgan3: $o). 11.06/2.41 thf(func_def_67, type, quantDeMorgan4: $o). 11.06/2.41 thf(func_def_68, type, prop2setI: $o). 11.06/2.41 thf(func_def_69, type, set2prop: ($i > $o)). 11.06/2.41 thf(func_def_70, type, prop2set2propI: $o). 11.06/2.41 thf(func_def_71, type, notdexE: $o). 11.06/2.41 thf(func_def_72, type, notdallE: $o). 11.06/2.41 thf(func_def_73, type, exuI1: $o). 11.06/2.41 thf(func_def_74, type, exuI3: $o). 11.06/2.41 thf(func_def_75, type, exuI2: $o). 11.06/2.41 thf(func_def_76, type, inCongP: $o). 11.06/2.41 thf(func_def_77, type, in__Cong: $o). 11.06/2.41 thf(func_def_78, type, exuE3u: $o). 11.06/2.41 thf(func_def_79, type, exu__Cong: $o). 11.06/2.41 thf(func_def_80, type, emptyset__Cong: $o). 11.06/2.41 thf(func_def_81, type, setadjoin__Cong: $o). 11.06/2.41 thf(func_def_82, type, powerset__Cong: $o). 11.06/2.41 thf(func_def_83, type, setunion__Cong: $o). 11.06/2.41 thf(func_def_84, type, omega__Cong: $o). 11.06/2.41 thf(func_def_85, type, exuEu: $o). 11.06/2.41 thf(func_def_86, type, descr__Cong: $o). 11.06/2.41 thf(func_def_87, type, dsetconstr__Cong: $o). 11.06/2.41 thf(func_def_88, type, subset: ($i > $i > $o)). 11.06/2.41 thf(func_def_89, type, disjoint: ($i > $i > $o)). 11.06/2.41 thf(func_def_90, type, setsmeet: ($i > $i > $o)). 11.06/2.41 thf(func_def_91, type, subsetI1: $o). 11.06/2.41 thf(func_def_92, type, eqimpsubset2: $o). 11.06/2.41 thf(func_def_93, type, eqimpsubset1: $o). 11.06/2.41 thf(func_def_94, type, subsetI2: $o). 11.06/2.41 thf(func_def_95, type, emptysetsubset: $o). 11.06/2.41 thf(func_def_96, type, subsetE: $o). 11.06/2.41 thf(func_def_97, type, subsetE2: $o). 11.06/2.41 thf(func_def_98, type, notsubsetI: $o). 11.06/2.41 thf(func_def_99, type, notequalI1: $o). 11.06/2.41 thf(func_def_100, type, notequalI2: $o). 11.06/2.41 thf(func_def_101, type, subsetRefl: $o). 11.06/2.41 thf(func_def_102, type, subsetTrans: $o). 11.06/2.41 thf(func_def_103, type, setadjoinSub: $o). 11.06/2.41 thf(func_def_104, type, setadjoinSub2: $o). 11.06/2.41 thf(func_def_105, type, subset2powerset: $o). 11.06/2.41 thf(func_def_106, type, setextsub: $o). 11.06/2.41 thf(func_def_107, type, subsetemptysetimpeq: $o). 11.06/2.41 thf(func_def_108, type, powersetI1: $o). 11.06/2.41 thf(func_def_109, type, powersetE1: $o). 11.06/2.41 thf(func_def_110, type, inPowerset: $o). 11.06/2.41 thf(func_def_111, type, powersetsubset: $o). 11.06/2.41 thf(func_def_112, type, sepInPowerset: $o). 11.06/2.41 thf(func_def_113, type, sepSubset: $o). 11.06/2.41 thf(func_def_114, type, binunion: ($i > $i > $i)). 11.06/2.41 thf(func_def_115, type, binunionIL: $o). 11.06/2.41 thf(func_def_116, type, upairset2IR: $o). 11.06/2.41 thf(func_def_117, type, binunionIR: $o). 11.06/2.41 thf(func_def_118, type, binunionEcases: $o). 11.06/2.41 thf(func_def_119, type, binunionE: $o). 11.06/2.41 thf(func_def_120, type, binunionLsub: $o). 11.06/2.41 thf(func_def_121, type, binunionRsub: $o). 11.06/2.41 thf(func_def_122, type, binintersect: ($i > $i > $i)). 11.06/2.41 thf(func_def_123, type, binintersectI: $o). 11.06/2.41 thf(func_def_124, type, binintersectSubset5: $o). 11.06/2.41 thf(func_def_125, type, binintersectEL: $o). 11.06/2.41 thf(func_def_126, type, binintersectLsub: $o). 11.06/2.41 thf(func_def_127, type, binintersectSubset2: $o). 11.06/2.41 thf(func_def_128, type, binintersectSubset3: $o). 11.06/2.41 thf(func_def_129, type, binintersectER: $o). 11.06/2.41 thf(func_def_130, type, disjointsetsI1: $o). 11.06/2.41 thf(func_def_131, type, binintersectRsub: $o). 11.06/2.41 thf(func_def_132, type, binintersectSubset4: $o). 11.06/2.41 thf(func_def_133, type, binintersectSubset1: $o). 11.06/2.41 thf(func_def_134, type, bs114d: $o). 11.06/2.41 thf(func_def_135, type, regular: ($i > $o)). 11.06/2.41 thf(func_def_136, type, setminus: ($i > $i > $i)). 11.06/2.41 thf(func_def_137, type, setminusI: $o). 11.06/2.41 thf(func_def_138, type, setminusEL: $o). 11.06/2.41 thf(func_def_139, type, setminusER: $o). 11.06/2.41 thf(func_def_140, type, setminusSubset2: $o). 11.06/2.41 thf(func_def_141, type, setminusERneg: $o). 11.06/2.41 thf(func_def_142, type, setminusELneg: $o). 11.06/2.41 thf(func_def_143, type, setminusILneg: $o). 11.06/2.41 thf(func_def_144, type, setminusIRneg: $o). 11.06/2.41 thf(func_def_145, type, setminusLsub: $o). 11.06/2.41 thf(func_def_146, type, setminusSubset1: $o). 11.06/2.41 thf(func_def_147, type, symdiff: ($i > $i > $i)). 11.06/2.41 thf(func_def_148, type, symdiffE: $o). 11.06/2.41 thf(func_def_149, type, symdiffI1: $o). 11.06/2.41 thf(func_def_150, type, symdiffI2: $o). 11.06/2.41 thf(func_def_151, type, symdiffIneg1: $o). 11.06/2.41 thf(func_def_152, type, symdiffIneg2: $o). 11.06/2.41 thf(func_def_153, type, iskpair: ($i > $o)). 11.06/2.41 thf(func_def_154, type, secondinupair: $o). 11.06/2.41 thf(func_def_155, type, setukpairIL: $o). 11.06/2.41 thf(func_def_156, type, setukpairIR: $o). 11.06/2.41 thf(func_def_157, type, kpairiskpair: $o). 11.06/2.41 thf(func_def_158, type, kpair: ($i > $i > $i)). 11.06/2.41 thf(func_def_159, type, kpairp: $o). 11.06/2.41 thf(func_def_160, type, cartprod: ($i > $i > $i)). 11.06/2.41 thf(func_def_161, type, singletonsubset: $o). 11.06/2.41 thf(func_def_162, type, singletoninpowerset: $o). 11.06/2.41 thf(func_def_163, type, singletoninpowunion: $o). 11.06/2.41 thf(func_def_164, type, upairset2E: $o). 11.06/2.41 thf(func_def_165, type, upairsubunion: $o). 11.06/2.41 thf(func_def_166, type, upairinpowunion: $o). 11.06/2.41 thf(func_def_167, type, ubforcartprodlem1: $o). 11.06/2.41 thf(func_def_168, type, ubforcartprodlem2: $o). 11.06/2.41 thf(func_def_169, type, ubforcartprodlem3: $o). 11.06/2.41 thf(func_def_170, type, cartprodpairin: $o). 11.06/2.41 thf(func_def_171, type, cartprodmempair1: $o). 11.06/2.41 thf(func_def_172, type, cartprodmempair: $o). 11.06/2.41 thf(func_def_173, type, setunionE2: $o). 11.06/2.41 thf(func_def_174, type, setunionsingleton1: $o). 11.06/2.41 thf(func_def_175, type, setunionsingleton2: $o). 11.06/2.41 thf(func_def_176, type, setunionsingleton: $o). 11.06/2.41 thf(func_def_177, type, singleton: ($i > $o)). 11.06/2.41 thf(func_def_178, type, singletonprop: $o). 11.06/2.41 thf(func_def_179, type, ex1: ($i > ($i > $o) > $o)). 11.06/2.41 thf(func_def_180, type, ex1E1: $o). 11.06/2.41 thf(func_def_181, type, ex1I: $o). 11.06/2.41 thf(func_def_182, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))). 11.06/2.41 thf(func_def_183, type, vIMP: ($o > $o > $o)). 11.06/2.41 thf(func_def_184, type, db0: !>[X0: $tType]:(X0)). 11.06/2.41 thf(func_def_185, type, db1: !>[X0: $tType]:(X0)). 11.06/2.41 thf(func_def_186, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))). 11.06/2.41 thf(func_def_187, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))). 11.06/2.41 thf(func_def_188, type, vNOT: ($o > $o)). 11.06/2.41 thf(func_def_189, type, db2: !>[X0: $tType]:(X0)). 11.06/2.41 thf(func_def_190, type, db3: !>[X0: $tType]:(X0)). 11.06/2.41 thf(func_def_191, type, vIFF: ($o > $o > $o)). 11.06/2.41 thf(func_def_192, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))). 11.06/2.41 thf(func_def_193, type, vAND: ($o > $o > $o)). 11.06/2.41 thf(func_def_196, type, vOR: ($o > $o > $o)). 11.06/2.41 thf(func_def_197, type, db4: !>[X0: $tType]:(X0)). 11.06/2.41 thf(func_def_198, type, db5: !>[X0: $tType]:(X0)). 11.06/2.41 thf(f70,axiom,( 11.06/2.41 (emptyset__Cong = (emptyset = emptyset))), 11.06/2.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong)). 11.06/2.41 thf(f74,axiom,( 11.06/2.41 (omega__Cong = (omega = omega))), 11.06/2.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong)). 11.06/2.41 thf(f158,axiom,( 11.06/2.41 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & (X0 = ((setadjoin @ X1 @ emptyset)))))) = singleton)), 11.06/2.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)). 11.06/2.41 thf(f159,axiom,( 11.06/2.41 (singletonprop = ! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))), 11.06/2.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop)). 11.06/2.41 thf(f160,axiom,( 11.06/2.41 (ex1 = (^[X0 : $i, X1 : ($i > $o)] : ((singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))), 11.06/2.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1)). 11.06/2.41 thf(f163,conjecture,( 11.06/2.41 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => ! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => (ex1 @ X0 @ (^[X2 : $i] : ((X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2)). 11.06/2.41 thf(f164,negated_conjecture,( 11.06/2.41 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => ! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => (ex1 @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(negated_conjecture,[status(cth)],[f163])). 11.06/2.41 thf(f185,plain,( 11.06/2.41 (ex1 = (^[X0 : $i, X1 : ($i > $o)] : ((singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))), 11.06/2.41 inference(rectify,[],[f160])). 11.06/2.41 thf(f186,plain,( 11.06/2.41 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))), 11.06/2.41 inference(fool_elimination,[],[f185])). 11.06/2.41 thf(f287,plain,( 11.06/2.41 (emptyset__Cong = ((emptyset = emptyset)))), 11.06/2.41 inference(fool_elimination,[],[f70])). 11.06/2.41 thf(f310,plain,( 11.06/2.41 (omega__Cong = ((omega = omega)))), 11.06/2.41 inference(fool_elimination,[],[f74])). 11.06/2.41 thf(f336,plain,( 11.06/2.41 (singletonprop = ! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X4 : $i] : ((X1 @ X4) & (in @ X4 @ X0)) => (singleton @ (dsetconstr @ X0 @ (^[X5 : $i] : ((X1 @ X5))))))))), 11.06/2.41 inference(rectify,[],[f159])). 11.06/2.41 thf(f337,plain,( 11.06/2.41 (singletonprop = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (singleton @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))))))))))))), 11.06/2.41 inference(fool_elimination,[],[f336])). 11.06/2.41 thf(f432,plain,( 11.06/2.41 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => ! [X0 : $i,X1 : ($i > $o)] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X4 : $i] : ((X1 @ X4) & (in @ X4 @ X0)) => (ex1 @ X0 @ (^[X5 : $i] : ((X1 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(rectify,[],[f164])). 11.06/2.41 thf(f433,plain,( 11.06/2.41 (((~ (setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (ex1 @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 11.06/2.41 inference(fool_elimination,[],[f432])). 11.06/2.41 thf(f456,plain,( 11.06/2.41 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & (X0 = ((setadjoin @ X1 @ emptyset)))))) = singleton)), 11.06/2.41 inference(rectify,[],[f158])). 11.06/2.41 thf(f457,plain,( 11.06/2.41 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))), 11.06/2.41 inference(fool_elimination,[],[f456])). 11.06/2.41 thf(f501,plain,( 11.06/2.41 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))), 11.06/2.41 inference(cnf_transformation,[],[f186])). 11.06/2.41 thf(f528,plain,( 11.06/2.41 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))), 11.06/2.41 inference(cnf_transformation,[],[f457])). 11.06/2.41 thf(f546,plain,( 11.06/2.41 (((~ (setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (ex1 @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 11.06/2.41 inference(cnf_transformation,[],[f433])). 11.06/2.41 thf(f550,plain,( 11.06/2.41 (emptyset__Cong = ((emptyset = emptyset)))), 11.06/2.41 inference(cnf_transformation,[],[f287])). 11.06/2.41 thf(f574,plain,( 11.06/2.41 (omega__Cong = ((omega = omega)))), 11.06/2.41 inference(cnf_transformation,[],[f310])). 11.06/2.41 thf(f586,plain,( 11.06/2.41 (singletonprop = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (singleton @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))))))))))))), 11.06/2.41 inference(cnf_transformation,[],[f337])). 11.06/2.41 thf(f646,plain,( 11.06/2.41 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))), 11.06/2.41 inference(definition_unfolding,[],[f501,f528])). 11.06/2.41 thf(f659,plain,( 11.06/2.41 (((~ (setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((setadjoin @ Y5 @ emptyset) = Y4) & (in @ Y5 @ Y4))))) @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 11.06/2.41 inference(definition_unfolding,[],[f546,f646])). 11.06/2.41 thf(f665,plain,( 11.06/2.41 (singletonprop = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))))))))))))), 11.06/2.41 inference(definition_unfolding,[],[f586,f528])). 11.06/2.41 thf(f685,plain,( 11.06/2.41 ($true = ((~ (setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(beta-eta_normalization,[],[f659])). 11.06/2.41 thf(f690,plain,( 11.06/2.41 (singletonprop = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))), 11.06/2.41 inference(beta-eta_normalization,[],[f665])). 11.06/2.41 thf(f698,plain,( 11.06/2.41 (omega__Cong = $true)), 11.06/2.41 inference(boolean_simplification,[],[f574])). 11.06/2.41 thf(f699,plain,( 11.06/2.41 (emptyset__Cong = $true)), 11.06/2.41 inference(boolean_simplification,[],[f550])). 11.06/2.41 thf(f802,plain,( 11.06/2.41 ($false = ((setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(not_proxy_clausification,[],[f685])). 11.06/2.41 thf(f858,plain,( 11.06/2.41 (singletonprop = $false) | (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))) = $true)), 11.06/2.41 inference(iff_proxy_clausification,[],[f690])). 11.06/2.41 thf(f1813,plain,( 11.06/2.41 ($false = ((setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => ($true => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(forward_demodulation,[],[f802,f699])). 11.06/2.41 thf(f1814,plain,( 11.06/2.41 ($false = ((setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(boolean_simplification,[],[f1813])). 11.06/2.41 thf(f2294,definition,( 11.06/2.41 spl0_283 <=> (singletonprop = $true)), 11.06/2.41 introduced(definition,[new_symbols(definition,[spl0_283])],[avatar_definition])). 11.06/2.41 thf(f2296,plain,( 11.06/2.41 (singletonprop = $true) | ~spl0_283), 11.06/2.41 inference(avatar_component_clause,[],[f2294])). 11.06/2.41 thf(f2298,definition,( 11.06/2.41 spl0_284 <=> (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))) = $false)), 11.06/2.41 introduced(definition,[new_symbols(definition,[spl0_284])],[avatar_definition])). 11.06/2.41 thf(f2300,plain,( 11.06/2.41 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))) = $false) | ~spl0_284), 11.06/2.41 inference(avatar_component_clause,[],[f2298])). 11.06/2.41 thf(f2303,definition,( 11.06/2.41 spl0_285 <=> (singletonprop = $false)), 11.06/2.41 introduced(definition,[new_symbols(definition,[spl0_285])],[avatar_definition])). 11.06/2.41 thf(f2305,plain,( 11.06/2.41 (singletonprop = $false) | ~spl0_285), 11.06/2.41 inference(avatar_component_clause,[],[f2303])). 11.06/2.41 thf(f2307,definition,( 11.06/2.41 spl0_286 <=> (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))) = $true)), 11.06/2.41 introduced(definition,[new_symbols(definition,[spl0_286])],[avatar_definition])). 11.06/2.41 thf(f2309,plain,( 11.06/2.41 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))) = $true) | ~spl0_286), 11.06/2.41 inference(avatar_component_clause,[],[f2307])). 11.06/2.41 thf(f2310,plain,( 11.06/2.41 spl0_285 | spl0_286), 11.06/2.41 inference(avatar_split_clause,[],[f858,f2307,f2303])). 11.06/2.41 thf(f3713,plain,( 11.06/2.41 ($false = ((setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => ($true => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(forward_demodulation,[],[f1814,f698])). 11.06/2.41 thf(f3714,plain,( 11.06/2.41 ($false = ((setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(boolean_simplification,[],[f3713])). 11.06/2.41 thf(f3715,plain,( 11.06/2.41 ($false = ((emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3714])). 11.06/2.41 thf(f3717,plain,( 11.06/2.41 ($false = ((setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3715])). 11.06/2.41 thf(f3721,plain,( 11.06/2.41 (((powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f3717])). 11.06/2.41 thf(f3723,plain,( 11.06/2.41 (((setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f3721])). 11.06/2.41 thf(f3727,plain,( 11.06/2.41 ($false = ((omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3723])). 11.06/2.41 thf(f3730,plain,( 11.06/2.41 ($false = ((omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3727])). 11.06/2.41 thf(f3732,plain,( 11.06/2.41 ($false = ((omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3730])). 11.06/2.41 thf(f3736,plain,( 11.06/2.41 ($false = ((replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3732])). 11.06/2.41 thf(f3738,plain,( 11.06/2.41 ($false = ((foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3736])). 11.06/2.41 thf(f3741,plain,( 11.06/2.41 ($false = ((wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3738])). 11.06/2.41 thf(f3745,plain,( 11.06/2.41 ($false = ((descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3741])). 11.06/2.41 thf(f3747,plain,( 11.06/2.41 ($false = ((dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3745])). 11.06/2.41 thf(f3750,plain,( 11.06/2.41 ($false = ((dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3747])). 11.06/2.41 thf(f3753,plain,( 11.06/2.41 ($false = ((dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3750])). 11.06/2.41 thf(f3757,plain,( 11.06/2.41 ($false = ((exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3753])). 11.06/2.41 thf(f3760,plain,( 11.06/2.41 ($false = ((prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3757])). 11.06/2.41 thf(f3762,plain,( 11.06/2.41 (((emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f3760])). 11.06/2.41 thf(f3766,plain,( 11.06/2.41 ($false = ((emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3762])). 11.06/2.41 thf(f3768,plain,( 11.06/2.41 ($false = ((notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3766])). 11.06/2.41 thf(f3772,plain,( 11.06/2.41 ($false = ((exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3768])). 11.06/2.41 thf(f3774,plain,( 11.06/2.41 ($false = ((setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3772])). 11.06/2.41 thf(f3778,plain,( 11.06/2.41 ($false = ((emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3774])). 11.06/2.41 thf(f3781,plain,( 11.06/2.41 ($false = ((noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3778])). 11.06/2.41 thf(f3784,plain,( 11.06/2.41 ($false = ((setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3781])). 11.06/2.41 thf(f3786,plain,( 11.06/2.41 ($false = ((nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3784])). 11.06/2.41 thf(f3790,plain,( 11.06/2.41 ($false = ((nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3786])). 11.06/2.41 thf(f3793,plain,( 11.06/2.41 (((nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f3790])). 11.06/2.41 thf(f3795,plain,( 11.06/2.41 ($false = ((setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3793])). 11.06/2.41 thf(f3798,plain,( 11.06/2.41 ($false = ((emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3795])). 11.06/2.41 thf(f3802,plain,( 11.06/2.41 ($false = ((setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3798])). 11.06/2.41 thf(f3804,plain,( 11.06/2.41 ($false = ((setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3802])). 11.06/2.41 thf(f3808,plain,( 11.06/2.41 ($false = ((setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3804])). 11.06/2.41 thf(f3810,plain,( 11.06/2.41 ($false = ((setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3808])). 11.06/2.41 thf(f3814,plain,( 11.06/2.41 ($false = ((powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3810])). 11.06/2.41 thf(f3816,plain,( 11.06/2.41 ($false = ((emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3814])). 11.06/2.41 thf(f3820,plain,( 11.06/2.41 ($false = ((emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3816])). 11.06/2.41 thf(f3823,plain,( 11.06/2.41 ($false = ((powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3820])). 11.06/2.41 thf(f3826,plain,( 11.06/2.41 ($false = ((setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3823])). 11.06/2.41 thf(f3829,plain,( 11.06/2.41 ($false = ((setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3826])). 11.06/2.41 thf(f3831,plain,( 11.06/2.41 ($false = ((subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3829])). 11.06/2.41 thf(f3834,plain,( 11.06/2.41 ($false = ((exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3831])). 11.06/2.41 thf(f3837,plain,( 11.06/2.41 ($false = ((nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3834])). 11.06/2.41 thf(f3841,plain,( 11.06/2.41 ($false = ((uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3837])). 11.06/2.41 thf(f3843,plain,( 11.06/2.41 ($false = ((notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3841])). 11.06/2.41 thf(f3846,plain,( 11.06/2.41 ($false = ((eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3843])). 11.06/2.41 thf(f3849,plain,( 11.06/2.41 ($false = ((singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3846])). 11.06/2.41 thf(f3852,plain,( 11.06/2.41 ($false = ((upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3849])). 11.06/2.41 thf(f3855,plain,( 11.06/2.41 ($false = ((upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3852])). 11.06/2.41 thf(f3858,plain,( 11.06/2.41 ($false = ((upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3855])). 11.06/2.41 thf(f3862,plain,( 11.06/2.41 ($false = ((emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3858])). 11.06/2.41 thf(f3864,plain,( 11.06/2.41 ($false = ((vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3862])). 11.06/2.41 thf(f3867,plain,( 11.06/2.41 ($false = ((quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3864])). 11.06/2.41 thf(f3871,plain,( 11.06/2.41 (((quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f3867])). 11.06/2.41 thf(f3874,plain,( 11.06/2.41 ($false = ((quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3871])). 11.06/2.41 thf(f3876,plain,( 11.06/2.41 ($false = ((quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3874])). 11.06/2.41 thf(f3880,plain,( 11.06/2.41 ($false = ((prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3876])). 11.06/2.41 thf(f3883,plain,( 11.06/2.41 (((prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f3880])). 11.06/2.41 thf(f3886,plain,( 11.06/2.41 ($false = ((notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3883])). 11.06/2.41 thf(f3888,plain,( 11.06/2.41 ($false = ((notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3886])). 11.06/2.41 thf(f3891,plain,( 11.06/2.41 ($false = ((exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3888])). 11.06/2.41 thf(f3894,plain,( 11.06/2.41 ($false = ((exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3891])). 11.06/2.41 thf(f3896,plain,( 11.06/2.41 ($false = ((exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3894])). 11.06/2.41 thf(f3900,plain,( 11.06/2.41 ($false = ((inCongP => (in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3896])). 11.06/2.41 thf(f3902,plain,( 11.06/2.41 (((in__Cong => (exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f3900])). 11.06/2.41 thf(f3905,plain,( 11.06/2.41 ($false = ((exuE3u => (exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3902])). 11.06/2.41 thf(f3909,plain,( 11.06/2.41 ($false = ((exu__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3905])). 11.06/2.41 thf(f3911,plain,( 11.06/2.41 (((setadjoin__Cong => (powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f3909])). 11.06/2.41 thf(f3914,plain,( 11.06/2.41 ($false = ((powerset__Cong => (setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3911])). 11.06/2.41 thf(f3918,plain,( 11.06/2.41 ($false = ((setunion__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3914])). 11.06/2.41 thf(f3920,plain,( 11.06/2.41 ($false = ((exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3918])). 11.06/2.41 thf(f3924,plain,( 11.06/2.41 ($false = ((descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3920])). 11.06/2.41 thf(f3927,plain,( 11.06/2.41 (((dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f3924])). 11.06/2.41 thf(f3930,plain,( 11.06/2.41 ($false = ((subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3927])). 11.06/2.41 thf(f3933,plain,( 11.06/2.41 ($false = ((eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3930])). 11.06/2.41 thf(f3935,plain,( 11.06/2.41 ($false = ((eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3933])). 11.06/2.41 thf(f3939,plain,( 11.06/2.41 ($false = ((subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3935])). 11.06/2.41 thf(f3941,plain,( 11.06/2.41 (((emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f3939])). 11.06/2.41 thf(f3944,plain,( 11.06/2.41 (((subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f3941])). 11.06/2.41 thf(f3948,plain,( 11.06/2.41 ($false = ((subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3944])). 11.06/2.41 thf(f3950,plain,( 11.06/2.41 ($false = ((notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3948])). 11.06/2.41 thf(f3954,plain,( 11.06/2.41 ($false = ((notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3950])). 11.06/2.41 thf(f3957,plain,( 11.06/2.41 ($false = ((notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3954])). 11.06/2.41 thf(f3959,plain,( 11.06/2.41 ($false = ((subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3957])). 11.06/2.41 thf(f3962,plain,( 11.06/2.41 ($false = ((subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3959])). 11.06/2.41 thf(f3966,plain,( 11.06/2.41 ($false = ((setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3962])). 11.06/2.41 thf(f3969,plain,( 11.06/2.41 ($false = ((setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3966])). 11.06/2.41 thf(f3972,plain,( 11.06/2.41 ($false = ((subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3969])). 11.06/2.41 thf(f3974,plain,( 11.06/2.41 ($false = ((setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3972])). 11.06/2.41 thf(f3978,plain,( 11.06/2.41 ($false = ((subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3974])). 11.06/2.41 thf(f3981,plain,( 11.06/2.41 ($false = ((powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3978])). 11.06/2.41 thf(f3984,plain,( 11.06/2.41 ($false = ((powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3981])). 11.06/2.41 thf(f3987,plain,( 11.06/2.41 ($false = ((inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3984])). 11.06/2.41 thf(f3989,plain,( 11.06/2.41 ($false = ((powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3987])). 11.06/2.41 thf(f3992,plain,( 11.06/2.41 ($false = ((sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3989])). 11.06/2.41 thf(f3996,plain,( 11.06/2.41 ($false = ((sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3992])). 11.06/2.41 thf(f3998,plain,( 11.06/2.41 ($false = ((binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f3996])). 11.06/2.41 thf(f4001,plain,( 11.06/2.41 (((upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f3998])). 11.06/2.41 thf(f4005,plain,( 11.06/2.41 ($false = ((binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4001])). 11.06/2.41 thf(f4007,plain,( 11.06/2.41 ($false = ((binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4005])). 11.06/2.41 thf(f4011,plain,( 11.06/2.41 ($false = ((binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4007])). 11.06/2.41 thf(f4014,plain,( 11.06/2.41 ($false = ((binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4011])). 11.06/2.41 thf(f4017,plain,( 11.06/2.41 ($false = ((binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4014])). 11.06/2.41 thf(f4019,plain,( 11.06/2.41 ($false = ((binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4017])). 11.06/2.41 thf(f4022,plain,( 11.06/2.41 ($false = ((binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4019])). 11.06/2.41 thf(f4026,plain,( 11.06/2.41 ($false = ((binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4022])). 11.06/2.41 thf(f4029,plain,( 11.06/2.41 ($false = ((binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4026])). 11.06/2.41 thf(f4031,plain,( 11.06/2.41 ($false = ((binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4029])). 11.06/2.41 thf(f4034,plain,( 11.06/2.41 (((binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f4031])). 11.06/2.41 thf(f4038,plain,( 11.06/2.41 ($false = ((binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4034])). 11.06/2.41 thf(f4041,plain,( 11.06/2.41 ($false = ((disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4038])). 11.06/2.41 thf(f4043,plain,( 11.06/2.41 ($false = ((binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4041])). 11.06/2.41 thf(f4046,plain,( 11.06/2.41 ($false = ((binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4043])). 11.06/2.41 thf(f4050,plain,( 11.06/2.41 ($false = ((binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4046])). 11.06/2.41 thf(f4052,plain,( 11.06/2.41 ($false = ((bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4050])). 11.06/2.41 thf(f4056,plain,( 11.06/2.41 ($false = ((setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4052])). 11.06/2.41 thf(f4058,plain,( 11.06/2.41 ($false = ((setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4056])). 11.06/2.41 thf(f4062,plain,( 11.06/2.41 ($false = ((setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4058])). 11.06/2.41 thf(f4065,plain,( 11.06/2.41 (((setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f4062])). 11.06/2.41 thf(f4068,plain,( 11.06/2.41 ($false = ((setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4065])). 11.06/2.41 thf(f4070,plain,( 11.06/2.41 ($false = ((setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4068])). 11.06/2.41 thf(f4074,plain,( 11.06/2.41 ($false = ((setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4070])). 11.06/2.41 thf(f4077,plain,( 11.06/2.41 ($false = ((setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4074])). 11.06/2.41 thf(f4080,plain,( 11.06/2.41 ($false = ((setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4077])). 11.06/2.41 thf(f4083,plain,( 11.06/2.41 ($false = ((setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4080])). 11.06/2.41 thf(f4085,plain,( 11.06/2.41 ($false = ((symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4083])). 11.06/2.41 thf(f4089,plain,( 11.06/2.41 ($false = ((symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4085])). 11.06/2.41 thf(f4092,plain,( 11.06/2.41 ($false = ((symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4089])). 11.06/2.41 thf(f4095,plain,( 11.06/2.41 ($false = ((symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4092])). 11.06/2.41 thf(f4098,plain,( 11.06/2.41 ($false = ((symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4095])). 11.06/2.41 thf(f4100,plain,( 11.06/2.41 ($false = ((secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4098])). 11.06/2.41 thf(f4104,plain,( 11.06/2.41 ($false = ((setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4100])). 11.06/2.41 thf(f4107,plain,( 11.06/2.41 (((setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f4104])). 11.06/2.41 thf(f4109,plain,( 11.06/2.41 ($false = ((kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4107])). 11.06/2.41 thf(f4112,plain,( 11.06/2.41 ($false = ((kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4109])). 11.06/2.41 thf(f4115,plain,( 11.06/2.41 ($false = ((singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4112])). 11.06/2.41 thf(f4118,plain,( 11.06/2.41 ($false = ((singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4115])). 11.06/2.41 thf(f4121,plain,( 11.06/2.41 ($false = ((singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4118])). 11.06/2.41 thf(f4125,plain,( 11.06/2.41 ($false = ((upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4121])). 11.06/2.41 thf(f4127,plain,( 11.06/2.41 ($false = ((upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4125])). 11.06/2.41 thf(f4130,plain,( 11.06/2.41 ($false = ((upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4127])). 11.06/2.41 thf(f4133,plain,( 11.06/2.41 ($false = ((ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4130])). 11.06/2.41 thf(f4137,plain,( 11.06/2.41 ($false = ((ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4133])). 11.06/2.41 thf(f4140,plain,( 11.06/2.41 ($false = ((ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4137])). 11.06/2.41 thf(f4142,plain,( 11.06/2.41 ($false = ((cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4140])). 11.06/2.41 thf(f4146,plain,( 11.06/2.41 ($false = ((cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4142])). 11.06/2.41 thf(f4148,plain,( 11.06/2.41 ($false = ((cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4146])). 11.06/2.41 thf(f4151,plain,( 11.06/2.41 ($false = ((setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4148])). 11.06/2.41 thf(f4155,plain,( 11.06/2.41 ($false = ((setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4151])). 11.06/2.41 thf(f4157,plain,( 11.06/2.41 ($false = ((setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4155])). 11.06/2.41 thf(f4160,plain,( 11.06/2.41 ($false = ((setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4157])). 11.06/2.41 thf(f4163,plain,( 11.06/2.41 ($false = ((singletonprop => (ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4160])). 11.06/2.41 thf(f4166,plain,( 11.06/2.41 ($false = ((ex1E1 => (ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4163])). 11.06/2.41 thf(f4167,plain,( 11.06/2.41 (singletonprop = $true)), 11.06/2.41 inference(imp_proxy_clausification,[],[f4163])). 11.06/2.41 thf(f4169,plain,( 11.06/2.41 ($false = ((ex1I => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))), 11.06/2.41 inference(imp_proxy_clausification,[],[f4166])). 11.06/2.41 thf(f4171,plain,( 11.06/2.41 spl0_283), 11.06/2.41 inference(avatar_split_clause,[],[f4167,f2294])). 11.06/2.41 thf(f4173,plain,( 11.06/2.41 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))) = $false)), 11.06/2.41 inference(imp_proxy_clausification,[],[f4169])). 11.06/2.41 thf(f4176,plain,( 11.06/2.41 spl0_284), 11.06/2.41 inference(avatar_split_clause,[],[f4173,f2298])). 11.06/2.41 thf(f4276,plain,( 11.06/2.41 ($false = $true) | (~spl0_283 | ~spl0_285)), 11.06/2.41 inference(forward_demodulation,[],[f2296,f2305])). 11.06/2.41 thf(f4277,plain,( 11.06/2.41 $false | (~spl0_283 | ~spl0_285)), 11.06/2.41 inference(trivial_inequality_removal,[],[f4276])). 11.06/2.41 thf(f4278,plain,( 11.06/2.41 ~spl0_283 | ~spl0_285), 11.06/2.41 inference(avatar_contradiction_clause,[],[f4277])). 11.06/2.41 thf(f4295,plain,( 11.06/2.41 ($false = $true) | (~spl0_284 | ~spl0_286)), 11.06/2.41 inference(forward_demodulation,[],[f2309,f2300])). 11.06/2.41 thf(f4296,plain,( 11.06/2.41 $false | (~spl0_284 | ~spl0_286)), 11.06/2.41 inference(trivial_inequality_removal,[],[f4295])). 11.06/2.41 thf(f4297,plain,( 11.06/2.41 ~spl0_284 | ~spl0_286), 11.06/2.41 inference(avatar_contradiction_clause,[],[f4296])). 11.06/2.41 cnf(s144, plain, spl0_285 | spl0_286, inference(sat_conversion,[],[f2310])). 11.06/2.41 cnf(s457, plain, spl0_283, inference(sat_conversion,[],[f4171])). 11.06/2.41 cnf(s460, plain, spl0_284, inference(sat_conversion,[],[f4176])). 11.06/2.41 cnf(s494, plain, ~spl0_283 | ~spl0_285, inference(sat_conversion,[],[f4278])). 11.06/2.41 cnf(s496, plain, ~spl0_284 | ~spl0_286, inference(sat_conversion,[],[f4297])). 11.06/2.41 cnf(s497, plain, ~spl0_286, inference(rat,[],[s496,s460])). 11.06/2.41 cnf(s498, plain, ~spl0_285, inference(rat,[],[s494,s457])). 11.06/2.41 cnf(s554, plain, $false, inference(rat,[],[s144,s497,s498])). 11.06/2.41 thf(f4305,plain,( 11.06/2.41 $false), 11.06/2.41 inference(avatar_sat_refutation,[],[s554])). 11.06/2.41 % SZS output end Proof for theBenchmark 11.06/2.41 % (2965081)------------------------------ 11.06/2.41 % (2965081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.41 % (2965081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.41 % (2965081)CaDiCaL version: 2.1.3 11.06/2.41 % (2965081)Termination reason: Refutation 11.06/2.41 % (2965081)Time elapsed: 0.202 s 11.06/2.41 % (2965081)Peak memory usage: 16 MB 11.06/2.41 % (2965081)Instructions burned: 484 (million) 11.06/2.41 % (2964843)Success in time 1.969 s 11.06/2.41 % Vampire exiting 11.06/2.41 EOF