0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.17/0.42 % Computer : n028.cluster.edu 0.17/0.42 % Model : x86_64 x86_64 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.17/0.42 % Memory : 8046.5625MB 0.17/0.42 % OS : Linux 6.8.0-71-generic 0.17/0.42 % CPULimit : 1440 0.17/0.42 % WCLimit : 180 0.17/0.42 % DateTime : Mon Jul 27 14:20:17 UTC 2026 0.17/0.43 % CPUTime : 0.17/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.17/0.48 Running higher-order theorem proving 0.23/0.54 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox/benchmark/theBenchmark.p 0.73/0.73 % (2882974)Detected a higher-order problem, will run a greedy HOL sequence. 0.73/0.73 % (2882983)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1590261343:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi) 0.73/0.73 % (2882985)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 0.73/0.73 % (2882985)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 0.73/0.73 % (2882983)Instruction limit reached! 0.73/0.73 % (2882983)------------------------------ 0.73/0.73 % (2882983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.73/0.73 % (2882983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.73/0.73 % (2882983)CaDiCaL version: 2.1.3 0.73/0.73 % (2882983)Termination reason: Instruction limit 0.73/0.73 % (2882983)Termination phase: Preprocessing 2 0.73/0.73 % (2882983)Time elapsed: 0.010 s 0.73/0.73 % (2882983)Peak memory usage: 10 MB 0.73/0.73 % (2882983)Instructions burned: 25 (million) 0.73/0.73 % (2882979)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2474799967:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi) 0.73/0.73 % (2882984)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3951407694:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi) 0.73/0.73 % (2882982)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=206556626: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) 0.73/0.73 % (2882981)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1719627286:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi) 0.73/0.73 % (2882980)lrs+10_16_si=on:nwc=1.5:random_seed=765278751:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi) 0.73/0.73 % (2882985)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=2150129502:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi) 0.73/0.73 % (2882981)Instruction limit reached! 0.73/0.73 % (2882981)------------------------------ 0.73/0.73 % (2882981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.73/0.73 % (2882981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.73/0.73 % (2882981)CaDiCaL version: 2.1.3 0.73/0.73 % (2882981)Termination reason: Instruction limit 0.73/0.73 % (2882981)Termination phase: shuffling 0.73/0.73 % (2882981)Time elapsed: 0.004 s 0.73/0.73 % (2882981)Peak memory usage: 10 MB 0.73/0.73 % (2882981)Instructions burned: 4 (million) 0.73/0.73 % (2882980)Instruction limit reached! 0.73/0.73 % (2882980)------------------------------ 0.73/0.73 % (2882980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.73/0.73 % (2882980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.73/0.73 % (2882980)CaDiCaL version: 2.1.3 0.73/0.73 % (2882980)Termination reason: Instruction limit 0.73/0.73 % (2882980)Termination phase: Property scanning 0.73/0.73 % (2882980)Time elapsed: 0.015 s 0.73/0.73 % (2882980)Peak memory usage: 10 MB 0.73/0.73 % (2882980)Instructions burned: 18 (million) 0.73/0.73 % (2882988)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3056775142:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 0.73/0.73 % (2882988)Instruction limit reached! 0.73/0.73 % (2882988)------------------------------ 0.73/0.73 % (2882988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.73/0.73 % (2882988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.73/0.73 % (2882988)CaDiCaL version: 2.1.3 0.73/0.73 % (2882988)Termination reason: Instruction limit 0.73/0.73 % (2882988)Termination phase: shuffling 0.73/0.73 % (2882988)Time elapsed: 0.002 s 0.73/0.73 % (2882988)Peak memory usage: 10 MB 0.73/0.73 % (2882988)Instructions burned: 4 (million) 0.73/0.73 % (2882997)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1084988634:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_1799 on theBenchmark for (1799ds/12Mi) 0.73/0.79 % (2882994)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3523323764:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1799 on theBenchmark for (1799ds/5Mi) 0.73/0.79 % (2882994)Instruction limit reached! 0.73/0.79 % (2882994)------------------------------ 0.73/0.79 % (2882994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.73/0.79 % (2882994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.73/0.79 % (2882994)CaDiCaL version: 2.1.3 0.73/0.79 % (2882994)Termination reason: Instruction limit 0.73/0.79 % (2882994)Termination phase: shuffling 0.73/0.79 % (2882994)Time elapsed: 0.004 s 0.73/0.79 % (2882994)Peak memory usage: 10 MB 0.73/0.79 % (2882994)Instructions burned: 5 (million) 0.73/0.79 % (2882997)Instruction limit reached! 0.73/0.79 % (2882997)------------------------------ 0.73/0.79 % (2882997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.73/0.79 % (2882997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.73/0.79 % (2882997)CaDiCaL version: 2.1.3 0.73/0.79 % (2882997)Termination reason: Instruction limit 0.73/0.79 % (2882997)Termination phase: shuffling 0.73/0.79 % (2882997)Time elapsed: 0.006 s 0.73/0.79 % (2882997)Peak memory usage: 10 MB 0.73/0.79 % (2882997)Instructions burned: 14 (million) 0.73/0.79 % (2882995)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 0.73/0.79 % (2882995)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2654984881:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1799 on theBenchmark for (1799ds/7Mi) 0.73/0.79 % (2882984)Instruction limit reached! 0.73/0.79 % (2882984)------------------------------ 0.73/0.79 % (2882984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.73/0.79 % (2882984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.73/0.79 % (2882984)CaDiCaL version: 2.1.3 0.73/0.79 % (2882984)Termination reason: Instruction limit 0.73/0.79 % (2882984)Termination phase: Function definition elimination 0.73/0.79 % (2882984)Time elapsed: 0.053 s 0.73/0.79 % (2882984)Peak memory usage: 11 MB 0.73/0.79 % (2882984)Instructions burned: 75 (million) 0.73/0.79 % (2882979)Instruction limit reached! 0.73/0.79 % (2882979)------------------------------ 0.73/0.79 % (2882979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.73/0.79 % (2882979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.73/0.79 % (2882979)CaDiCaL version: 2.1.3 0.73/0.79 % (2882979)Termination reason: Instruction limit 0.73/0.79 % (2882979)Termination phase: Property scanning 0.73/0.79 % (2882979)Time elapsed: 0.057 s 0.73/0.79 % (2882979)Peak memory usage: 11 MB 0.73/0.79 % (2882979)Instructions burned: 88 (million) 0.73/0.79 % (2882995)Instruction limit reached! 0.73/0.79 % (2882995)------------------------------ 0.73/0.79 % (2882995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.73/0.79 % (2882995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.73/0.79 % (2882995)CaDiCaL version: 2.1.3 0.73/0.79 % (2882995)Termination reason: Instruction limit 0.73/0.79 % (2882995)Termination phase: shuffling 0.73/0.79 % (2882995)Time elapsed: 0.006 s 0.73/0.79 % (2882995)Peak memory usage: 10 MB 0.73/0.79 % (2882995)Instructions burned: 7 (million) 0.73/0.79 % (2883001)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=2837345824:i=86:piset=equals:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/86Mi) 0.73/0.79 % (2883000)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 0.73/0.79 % (2883000)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 0.73/0.79 % (2883000)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=937010439:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1799 on theBenchmark for (1799ds/28Mi) 0.73/0.79 % (2883004)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on 1.40/0.83 % (2883004)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=3910147164:i=2:add=on:rtra=on_1798 on theBenchmark for (1798ds/2Mi) 1.40/0.83 % (2883003)lrs+10_1_si=on:cs=on:random_seed=2009199679:i=8:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/8Mi) 1.40/0.83 % (2883004)Instruction limit reached! 1.40/0.83 % (2883004)------------------------------ 1.40/0.83 % (2883004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.40/0.83 % (2883004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.40/0.83 % (2883004)CaDiCaL version: 2.1.3 1.40/0.83 % (2883004)Termination reason: Instruction limit 1.40/0.83 % (2883004)Termination phase: shuffling 1.40/0.83 % (2883004)Time elapsed: 0.002 s 1.40/0.83 % (2883004)Peak memory usage: 10 MB 1.40/0.83 % (2883004)Instructions burned: 2 (million) 1.40/0.83 % (2883005)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1479756400:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_1798 on theBenchmark for (1798ds/38Mi) 1.40/0.83 % (2883003)Instruction limit reached! 1.40/0.83 % (2883003)------------------------------ 1.40/0.83 % (2883003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.40/0.83 % (2883003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.40/0.83 % (2883003)CaDiCaL version: 2.1.3 1.40/0.83 % (2883003)Termination reason: Instruction limit 1.40/0.83 % (2883003)Termination phase: shuffling 1.40/0.83 % (2883003)Time elapsed: 0.008 s 1.40/0.83 % (2883003)Peak memory usage: 10 MB 1.40/0.83 % (2883003)Instructions burned: 9 (million) 1.40/0.83 % (2883001)Instruction limit reached! 1.40/0.83 % (2883001)------------------------------ 1.40/0.83 % (2883001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.40/0.83 % (2883001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.40/0.83 % (2883001)CaDiCaL version: 2.1.3 1.40/0.83 % (2883001)Termination reason: Instruction limit 1.40/0.83 % (2883001)Termination phase: Property scanning 1.40/0.83 % (2883001)Time elapsed: 0.031 s 1.40/0.83 % (2883001)Peak memory usage: 11 MB 1.40/0.83 % (2883001)Instructions burned: 86 (million) 1.40/0.83 % (2883000)Instruction limit reached! 1.40/0.83 % (2883000)------------------------------ 1.40/0.83 % (2883000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.40/0.83 % (2883000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.40/0.83 % (2883000)CaDiCaL version: 2.1.3 1.40/0.83 % (2883000)Termination reason: Instruction limit 1.40/0.83 % (2883000)Termination phase: Property scanning 1.40/0.83 % (2883000)Time elapsed: 0.025 s 1.40/0.83 % (2883000)Peak memory usage: 10 MB 1.40/0.83 % (2883000)Instructions burned: 29 (million) 1.40/0.83 % (2883012)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2411733838:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1798 on theBenchmark for (1798ds/25Mi) 1.40/0.83 % (2882985)Instruction limit reached! 1.40/0.83 % (2882985)------------------------------ 1.40/0.83 % (2882985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.40/0.83 % (2882985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.40/0.83 % (2882985)CaDiCaL version: 2.1.3 1.40/0.83 % (2882985)Termination reason: Instruction limit 1.40/0.83 % (2882985)Termination phase: Saturation 1.40/0.83 % (2882985)Time elapsed: 0.110 s 1.40/0.83 % (2882985)Peak memory usage: 13 MB 1.40/0.83 % (2882985)Instructions burned: 157 (million) 1.40/0.83 % (2883010)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=196282471:st=2:i=249:sd=1:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/249Mi) 1.40/0.83 % (2883012)Instruction limit reached! 1.40/0.83 % (2883012)------------------------------ 1.40/0.83 % (2883012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.40/0.83 % (2883012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.40/0.83 % (2883012)CaDiCaL version: 2.1.3 1.40/0.83 % (2883012)Termination reason: Instruction limit 1.40/0.83 % (2883012)Termination phase: SInE selection 1.40/0.83 % (2883012)Time elapsed: 0.011 s 1.40/0.83 % (2883012)Peak memory usage: 10 MB 1.40/0.83 % (2883012)Instructions burned: 25 (million) 1.40/0.83 % (2883005)Instruction limit reached! 1.40/0.83 % (2883005)------------------------------ 1.77/0.92 % (2883005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.77/0.92 % (2883005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.77/0.92 % (2883005)CaDiCaL version: 2.1.3 1.77/0.92 % (2883005)Termination reason: Instruction limit 1.77/0.92 % (2883005)Termination phase: Saturation 1.77/0.92 % (2883005)Time elapsed: 0.032 s 1.77/0.92 % (2883005)Peak memory usage: 12 MB 1.77/0.92 % (2883005)Instructions burned: 39 (million) 1.77/0.92 % (2883013)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2015465151:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_1798 on theBenchmark for (1798ds/14Mi) 1.77/0.92 % (2883013)Instruction limit reached! 1.77/0.92 % (2883013)------------------------------ 1.77/0.92 % (2883013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.77/0.92 % (2883013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.77/0.92 % (2883013)CaDiCaL version: 2.1.3 1.77/0.92 % (2883013)Termination reason: Instruction limit 1.77/0.92 % (2883013)Termination phase: shuffling 1.77/0.92 % (2883013)Time elapsed: 0.012 s 1.77/0.92 % (2883013)Peak memory usage: 10 MB 1.77/0.92 % (2883013)Instructions burned: 14 (million) 1.77/0.92 % (2883018)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=69563884: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) 1.77/0.92 % (2883014)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1601995377:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/327Mi) 1.77/0.92 % (2883018)Instruction limit reached! 1.77/0.92 % (2883018)------------------------------ 1.77/0.92 % (2883018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.77/0.92 % (2883018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.77/0.92 % (2883018)CaDiCaL version: 2.1.3 1.77/0.92 % (2883018)Termination reason: Instruction limit 1.77/0.92 % (2883018)Termination phase: shuffling 1.77/0.92 % (2883018)Time elapsed: 0.002 s 1.77/0.92 % (2883018)Peak memory usage: 10 MB 1.77/0.92 % (2883018)Instructions burned: 4 (million) 1.77/0.92 % (2883016)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1361890157:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_1798 on theBenchmark for (1798ds/14Mi) 1.77/0.92 % (2883016)Instruction limit reached! 1.77/0.92 % (2883016)------------------------------ 1.77/0.92 % (2883016)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.77/0.92 % (2883016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.77/0.92 % (2883016)CaDiCaL version: 2.1.3 1.77/0.92 % (2883016)Termination reason: Instruction limit 1.77/0.92 % (2883016)Termination phase: shuffling 1.77/0.92 % (2883016)Time elapsed: 0.012 s 1.77/0.92 % (2883016)Peak memory usage: 10 MB 1.77/0.92 % (2883016)Instructions burned: 15 (million) 1.77/0.92 % (2883019)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2877614519:i=26:ep=R:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/26Mi) 1.77/0.92 % (2883024)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1250948116:cond=on:i=60:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/60Mi) 1.77/0.92 % (2883023)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1429729089:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_1798 on theBenchmark for (1798ds/23Mi) 1.77/0.92 % (2883019)Instruction limit reached! 1.77/0.92 % (2883019)------------------------------ 1.77/0.92 % (2883019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.77/0.92 % (2883019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.77/0.92 % (2883019)CaDiCaL version: 2.1.3 1.77/0.92 % (2883019)Termination reason: Instruction limit 1.77/0.92 % (2883019)Termination phase: Property scanning 1.77/0.92 % (2883019)Time elapsed: 0.021 s 1.77/0.92 % (2883019)Peak memory usage: 10 MB 1.77/0.92 % (2883019)Instructions burned: 26 (million) 1.77/0.92 % (2883024)Instruction limit reached! 1.77/0.92 % (2883024)------------------------------ 1.77/0.92 % (2883024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.77/0.92 % (2883024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.77/1.03 % (2883024)CaDiCaL version: 2.1.3 1.77/1.03 % (2883024)Termination reason: Instruction limit 1.77/1.03 % (2883024)Termination phase: Saturation 1.77/1.03 % (2883024)Time elapsed: 0.027 s 1.77/1.03 % (2883024)Peak memory usage: 13 MB 1.77/1.03 % (2883024)Instructions burned: 61 (million) 1.77/1.03 % (2883026)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 1.77/1.03 % (2883026)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs 1.77/1.03 % (2883023)Instruction limit reached! 1.77/1.03 % (2883023)------------------------------ 1.77/1.03 % (2883023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.77/1.03 % (2883026)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=781602077:i=14:add=off:nm=40:rtra=on:rawr=on_1797 on theBenchmark for (1797ds/14Mi) 1.77/1.03 % (2883023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.77/1.03 % (2883023)CaDiCaL version: 2.1.3 1.77/1.03 % (2883023)Termination reason: Instruction limit 1.77/1.03 % (2883023)Termination phase: Property scanning 1.77/1.03 % (2883023)Time elapsed: 0.020 s 1.77/1.03 % (2883023)Peak memory usage: 10 MB 1.77/1.03 % (2883023)Instructions burned: 24 (million) 1.77/1.03 % (2883031)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=2809696256:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_1797 on theBenchmark for (1797ds/31Mi) 1.77/1.03 % (2883026)Instruction limit reached! 1.77/1.03 % (2883026)------------------------------ 1.77/1.03 % (2883026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.77/1.03 % (2883026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.77/1.03 % (2883026)CaDiCaL version: 2.1.3 1.77/1.03 % (2883026)Termination reason: Instruction limit 1.77/1.03 % (2883026)Termination phase: shuffling 1.77/1.03 % (2883026)Time elapsed: 0.012 s 1.77/1.03 % (2883026)Peak memory usage: 10 MB 1.77/1.03 % (2883026)Instructions burned: 14 (million) 1.77/1.03 % (2883010)Refutation not found, incomplete strategy 1.77/1.03 % (2883010)------------------------------ 1.77/1.03 % (2883010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.77/1.03 % (2883010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.77/1.03 % (2883010)CaDiCaL version: 2.1.3 1.77/1.03 % (2883010)Termination reason: Refutation not found, incomplete strategy 1.77/1.03 % (2883010)Time elapsed: 0.087 s 1.77/1.03 % (2883010)Peak memory usage: 13 MB 1.77/1.03 % (2883010)Instructions burned: 119 (million) 1.77/1.03 % (2883030)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off 1.77/1.03 % (2883010)------------------------------ 1.77/1.03 % (2883010)------------------------------ 1.77/1.03 % (2883030)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=3733478506:i=8:nm=2:rtra=on:fe=abstraction:inj=on_1797 on theBenchmark for (1797ds/8Mi) 1.77/1.03 % (2883031)Instruction limit reached! 1.77/1.03 % (2883031)------------------------------ 1.77/1.03 % (2883031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.77/1.03 % (2883031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.77/1.03 % (2883031)CaDiCaL version: 2.1.3 1.77/1.03 % (2883031)Termination reason: Instruction limit 1.77/1.03 % (2883031)Termination phase: Property scanning 1.77/1.03 % (2883031)Time elapsed: 0.013 s 1.77/1.03 % (2883031)Peak memory usage: 10 MB 1.77/1.03 % (2883031)Instructions burned: 32 (million) 1.77/1.03 % (2883030)Instruction limit reached! 1.77/1.03 % (2883030)------------------------------ 1.77/1.03 % (2883030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.77/1.03 % (2883030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.77/1.03 % (2883030)CaDiCaL version: 2.1.3 1.77/1.03 % (2883030)Termination reason: Instruction limit 1.77/1.03 % (2883030)Termination phase: shuffling 1.77/1.03 % (2883030)Time elapsed: 0.008 s 1.77/1.03 % (2883030)Peak memory usage: 10 MB 1.77/1.03 % (2883030)Instructions burned: 9 (million) 3.58/1.16 % (2883033)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1562920365:i=7:hud=5:bd=preordered:rtra=on:bet=on_1797 on theBenchmark for (1797ds/7Mi) 3.58/1.16 % (2883033)Instruction limit reached! 3.58/1.16 % (2883033)------------------------------ 3.58/1.16 % (2883033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.58/1.16 % (2883033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.58/1.16 % (2883033)CaDiCaL version: 2.1.3 3.58/1.16 % (2883033)Termination reason: Instruction limit 3.58/1.16 % (2883033)Termination phase: shuffling 3.58/1.16 % (2883033)Time elapsed: 0.005 s 3.58/1.16 % (2883033)Peak memory usage: 10 MB 3.58/1.16 % (2883033)Instructions burned: 7 (million) 3.58/1.16 % (2883038)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1045970113:i=1240:rtra=on:ixr=off_1797 on theBenchmark for (1797ds/1240Mi) 3.58/1.16 % (2883035)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3718059168:i=23:rtra=on:ntd=on_1797 on theBenchmark for (1797ds/23Mi) 3.58/1.16 % (2883036)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1196271396:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_1797 on theBenchmark for (1797ds/20Mi) 3.58/1.16 % (2883036)Instruction limit reached! 3.58/1.16 % (2883036)------------------------------ 3.58/1.16 % (2883036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.58/1.16 % (2883036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.58/1.16 % (2883036)CaDiCaL version: 2.1.3 3.58/1.16 % (2883036)Termination reason: Instruction limit 3.58/1.16 % (2883036)Termination phase: Property scanning 3.58/1.16 % (2883036)Time elapsed: 0.015 s 3.58/1.16 % (2883036)Peak memory usage: 10 MB 3.58/1.16 % (2883036)Instructions burned: 21 (million) 3.58/1.16 % (2883039)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2372378932:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1797 on theBenchmark for (1797ds/143Mi) 3.58/1.16 % (2883035)Instruction limit reached! 3.58/1.16 % (2883035)------------------------------ 3.58/1.16 % (2883035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.58/1.16 % (2883035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.58/1.16 % (2883035)CaDiCaL version: 2.1.3 3.58/1.16 % (2883035)Termination reason: Instruction limit 3.58/1.16 % (2883035)Termination phase: Property scanning 3.58/1.16 % (2883035)Time elapsed: 0.019 s 3.58/1.16 % (2883035)Peak memory usage: 10 MB 3.58/1.16 % (2883035)Instructions burned: 23 (million) 3.58/1.16 % (2883041)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=384870212:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_1797 on theBenchmark for (1797ds/193Mi) 3.58/1.16 % (2883045)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4097217105:i=42:hud=10:rtra=on_1796 on theBenchmark for (1796ds/42Mi) 3.58/1.16 % (2883047)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 3.58/1.16 % (2883047)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=311969412:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1796 on theBenchmark for (1796ds/7Mi) 3.58/1.16 % (2883047)Instruction limit reached! 3.58/1.16 % (2883047)------------------------------ 3.58/1.16 % (2883047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.58/1.16 % (2883047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.58/1.16 % (2883047)CaDiCaL version: 2.1.3 3.58/1.16 % (2883047)Termination reason: Instruction limit 3.58/1.16 % (2883047)Termination phase: shuffling 3.58/1.16 % (2883047)Time elapsed: 0.007 s 3.58/1.16 % (2883047)Peak memory usage: 10 MB 3.58/1.16 % (2883047)Instructions burned: 8 (million) 3.58/1.16 % (2883045)Instruction limit reached! 3.58/1.16 % (2883045)------------------------------ 3.58/1.16 % (2883045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.58/1.16 % (2883045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.58/1.16 % (2883045)CaDiCaL version: 2.1.3 3.58/1.16 % (2883045)Termination reason: Instruction limit 3.58/1.16 % (2883045)Termination phase: Function definition elimination 3.58/1.16 % (2883045)Time elapsed: 0.029 s 3.53/1.27 % (2883045)Peak memory usage: 11 MB 3.53/1.27 % (2883045)Instructions burned: 42 (million) 3.53/1.27 % (2883051)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2698646874:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_1796 on theBenchmark for (1796ds/181Mi) 3.53/1.27 % (2883052)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=1980009177:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1796 on theBenchmark for (1796ds/169Mi) 3.53/1.27 % (2883039)Instruction limit reached! 3.53/1.27 % (2883039)------------------------------ 3.53/1.27 % (2883039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.53/1.27 % (2883039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.53/1.27 % (2883039)CaDiCaL version: 2.1.3 3.53/1.27 % (2883039)Termination reason: Instruction limit 3.53/1.27 % (2883039)Termination phase: Saturation 3.53/1.27 % (2883039)Time elapsed: 0.115 s 3.53/1.27 % (2883039)Peak memory usage: 13 MB 3.53/1.27 % (2883039)Instructions burned: 143 (million) 3.53/1.27 % (2883014)Instruction limit reached! 3.53/1.27 % (2883014)------------------------------ 3.53/1.27 % (2883014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.53/1.27 % (2883014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.53/1.27 % (2883014)CaDiCaL version: 2.1.3 3.53/1.27 % (2883014)Termination reason: Instruction limit 3.53/1.27 % (2883014)Termination phase: Saturation 3.53/1.27 % (2883014)Time elapsed: 0.232 s 3.53/1.27 % (2883014)Peak memory usage: 16 MB 3.53/1.27 % (2883014)Instructions burned: 327 (million) 3.53/1.27 % (2883055)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on 3.53/1.27 % (2883041)Instruction limit reached! 3.53/1.27 % (2883041)------------------------------ 3.53/1.27 % (2883041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.53/1.27 % (2883041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.53/1.27 % (2883041)CaDiCaL version: 2.1.3 3.53/1.27 % (2883041)Termination reason: Instruction limit 3.53/1.27 % (2883041)Termination phase: Saturation 3.53/1.27 % (2883041)Time elapsed: 0.138 s 3.53/1.27 % (2883041)Peak memory usage: 14 MB 3.53/1.27 % (2883041)Instructions burned: 193 (million) 3.53/1.27 % (2883055)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=598332992:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_1795 on theBenchmark for (1795ds/6Mi) 3.53/1.27 % (2883056)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=527994351:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1795 on theBenchmark for (1795ds/22Mi) 3.53/1.27 % (2883055)Instruction limit reached! 3.53/1.27 % (2883055)------------------------------ 3.53/1.27 % (2883055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.53/1.27 % (2883055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.53/1.27 % (2883055)CaDiCaL version: 2.1.3 3.53/1.27 % (2883055)Termination reason: Instruction limit 3.53/1.27 % (2883055)Termination phase: shuffling 3.53/1.27 % (2883055)Time elapsed: 0.006 s 3.53/1.27 % (2883055)Peak memory usage: 10 MB 3.53/1.27 % (2883055)Instructions burned: 7 (million) 3.53/1.27 % (2883052)Refutation not found, incomplete strategy 3.53/1.27 % (2883052)------------------------------ 3.53/1.27 % (2883052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.53/1.27 % (2883052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.53/1.27 % (2883052)CaDiCaL version: 2.1.3 3.53/1.27 % (2883052)Termination reason: Refutation not found, incomplete strategy 3.53/1.27 % (2883052)Time elapsed: 0.066 s 3.53/1.27 % (2883052)Peak memory usage: 14 MB 3.53/1.27 % (2883052)Instructions burned: 80 (million) 3.53/1.27 % (2883052)------------------------------ 3.53/1.27 % (2883052)------------------------------ 3.53/1.27 % (2883056)Instruction limit reached! 3.53/1.27 % (2883056)------------------------------ 3.53/1.27 % (2883056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.53/1.27 % (2883056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.53/1.27 % (2883056)CaDiCaL version: 2.1.3 3.53/1.27 % (2883056)Termination reason: Instruction limit 3.53/1.27 % (2883056)Termination phase: Property scanning 4.93/1.35 % (2883056)Time elapsed: 0.018 s 4.93/1.35 % (2883056)Peak memory usage: 10 MB 4.93/1.35 % (2883056)Instructions burned: 22 (million) 4.93/1.35 % (2883060)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=4076335002:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_1795 on theBenchmark for (1795ds/316Mi) 4.93/1.35 % (2883061)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=2798364725:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_1795 on theBenchmark for (1795ds/853Mi) 4.93/1.35 % (2883057)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2025061710:i=19:add=on:rtra=on_1795 on theBenchmark for (1795ds/19Mi) 4.93/1.35 % (2883062)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=346050911:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_1795 on theBenchmark for (1795ds/45Mi) 4.93/1.35 % (2883057)Instruction limit reached! 4.93/1.35 % (2883057)------------------------------ 4.93/1.35 % (2883057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.93/1.35 % (2883057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.93/1.35 % (2883057)CaDiCaL version: 2.1.3 4.93/1.35 % (2883057)Termination reason: Instruction limit 4.93/1.35 % (2883057)Termination phase: Property scanning 4.93/1.35 % (2883057)Time elapsed: 0.015 s 4.93/1.35 % (2883057)Peak memory usage: 10 MB 4.93/1.35 % (2883057)Instructions burned: 19 (million) 4.93/1.35 % (2883051)Instruction limit reached! 4.93/1.35 % (2883051)------------------------------ 4.93/1.35 % (2883051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.93/1.35 % (2883051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.93/1.35 % (2883051)CaDiCaL version: 2.1.3 4.93/1.35 % (2883051)Termination reason: Instruction limit 4.93/1.35 % (2883051)Termination phase: Saturation 4.93/1.35 % (2883051)Time elapsed: 0.149 s 4.93/1.35 % (2883051)Peak memory usage: 14 MB 4.93/1.35 % (2883051)Instructions burned: 181 (million) 4.93/1.35 % (2883062)Instruction limit reached! 4.93/1.35 % (2883062)------------------------------ 4.93/1.35 % (2883062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.93/1.35 % (2883062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.93/1.35 % (2883062)CaDiCaL version: 2.1.3 4.93/1.35 % (2883062)Termination reason: Instruction limit 4.93/1.35 % (2883062)Termination phase: Property scanning 4.93/1.35 % (2883062)Time elapsed: 0.037 s 4.93/1.35 % (2883062)Peak memory usage: 11 MB 4.93/1.35 % (2883062)Instructions burned: 45 (million) 4.93/1.35 % (2883067)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2833317251:i=480:rtra=on_1794 on theBenchmark for (1794ds/480Mi) 4.93/1.35 % (2883068)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=980480519:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_1794 on theBenchmark for (1794ds/21Mi) 4.93/1.35 % (2883069)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on 4.93/1.35 % (2883069)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3806951219:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_1794 on theBenchmark for (1794ds/200Mi) 4.93/1.35 % (2883068)Instruction limit reached! 4.93/1.35 % (2883068)------------------------------ 4.93/1.35 % (2883068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.93/1.35 % (2883068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.93/1.35 % (2883068)CaDiCaL version: 2.1.3 4.93/1.35 % (2883068)Termination reason: Instruction limit 4.93/1.35 % (2883068)Termination phase: Property scanning 4.93/1.35 % (2883068)Time elapsed: 0.017 s 4.93/1.35 % (2883068)Peak memory usage: 10 MB 4.93/1.35 % (2883068)Instructions burned: 22 (million) 4.93/1.35 % (2883067)Refutation not found, incomplete strategy 4.93/1.35 % (2883067)------------------------------ 4.93/1.35 % (2883067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.85/1.53 % (2883067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.85/1.53 % (2883067)CaDiCaL version: 2.1.3 5.85/1.53 % (2883067)Termination reason: Refutation not found, incomplete strategy 5.85/1.53 % (2883067)Time elapsed: 0.044 s 5.85/1.53 % (2883067)Peak memory usage: 13 MB 5.85/1.53 % (2883067)Instructions burned: 53 (million) 5.85/1.53 % (2883067)------------------------------ 5.85/1.53 % (2883067)------------------------------ 5.85/1.53 % (2883073)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1313426793:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_1794 on theBenchmark for (1794ds/13Mi) 5.85/1.53 % (2883073)Instruction limit reached! 5.85/1.53 % (2883073)------------------------------ 5.85/1.53 % (2883073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.85/1.53 % (2883073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.85/1.53 % (2883073)CaDiCaL version: 2.1.3 5.85/1.53 % (2883073)Termination reason: Instruction limit 5.85/1.53 % (2883073)Termination phase: shuffling 5.85/1.53 % (2883073)Time elapsed: 0.012 s 5.85/1.53 % (2883073)Peak memory usage: 10 MB 5.85/1.53 % (2883073)Instructions burned: 14 (million) 5.85/1.53 % (2882982)Instruction limit reached! 5.85/1.53 % (2882982)------------------------------ 5.85/1.53 % (2882982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.85/1.53 % (2882982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.85/1.53 % (2882982)CaDiCaL version: 2.1.3 5.85/1.53 % (2882982)Termination reason: Instruction limit 5.85/1.53 % (2882982)Termination phase: Saturation 5.85/1.53 % (2882982)Time elapsed: 0.593 s 5.85/1.53 % (2882982)Peak memory usage: 17 MB 5.85/1.53 % (2882982)Instructions burned: 634 (million) 5.85/1.53 % (2883074)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=2001054410:i=66:s2at=3:nm=2:rtra=on:rawr=on_1793 on theBenchmark for (1793ds/66Mi) 5.85/1.53 % (2883076)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=4264603545:i=51:fsr=off:rtra=on_1793 on theBenchmark for (1793ds/51Mi) 5.85/1.53 % (2883077)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2753161613:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1793 on theBenchmark for (1793ds/31Mi) 5.85/1.53 % (2883074)Instruction limit reached! 5.85/1.53 % (2883074)------------------------------ 5.85/1.53 % (2883074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.85/1.53 % (2883074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.85/1.53 % (2883074)CaDiCaL version: 2.1.3 5.85/1.53 % (2883074)Termination reason: Instruction limit 5.85/1.53 % (2883074)Termination phase: Function definition elimination 5.85/1.53 % (2883074)Time elapsed: 0.046 s 5.85/1.53 % (2883074)Peak memory usage: 11 MB 5.85/1.53 % (2883074)Instructions burned: 66 (million) 5.85/1.53 % (2883077)Instruction limit reached! 5.85/1.53 % (2883077)------------------------------ 5.85/1.53 % (2883077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.85/1.53 % (2883077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.85/1.53 % (2883077)CaDiCaL version: 2.1.3 5.85/1.53 % (2883077)Termination reason: Instruction limit 5.85/1.53 % (2883077)Termination phase: Property scanning 5.85/1.53 % (2883077)Time elapsed: 0.025 s 5.85/1.53 % (2883077)Peak memory usage: 10 MB 5.85/1.53 % (2883077)Instructions burned: 32 (million) 5.85/1.53 % (2883076)Instruction limit reached! 5.85/1.53 % (2883076)------------------------------ 5.85/1.53 % (2883076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.85/1.53 % (2883076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.85/1.53 % (2883076)CaDiCaL version: 2.1.3 5.85/1.53 % (2883076)Termination reason: Instruction limit 5.85/1.53 % (2883076)Termination phase: Function definition elimination 5.85/1.53 % (2883076)Time elapsed: 0.039 s 5.85/1.53 % (2883076)Peak memory usage: 11 MB 5.85/1.53 % (2883076)Instructions burned: 53 (million) 5.85/1.53 % (2883060)Refutation not found, incomplete strategy 5.85/1.53 % (2883060)------------------------------ 5.85/1.53 % (2883060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.85/1.53 % (2883060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.52/1.75 % (2883060)CaDiCaL version: 2.1.3 6.52/1.75 % (2883060)Termination reason: Refutation not found, incomplete strategy 6.52/1.75 % (2883060)Time elapsed: 0.221 s 6.52/1.75 % (2883060)Peak memory usage: 16 MB 6.52/1.75 % (2883060)Instructions burned: 316 (million) 6.52/1.75 % (2883060)------------------------------ 6.52/1.75 % (2883060)------------------------------ 6.52/1.75 % (2883069)Instruction limit reached! 6.52/1.75 % (2883069)------------------------------ 6.52/1.75 % (2883069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.52/1.75 % (2883069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.52/1.75 % (2883069)CaDiCaL version: 2.1.3 6.52/1.75 % (2883069)Termination reason: Instruction limit 6.52/1.75 % (2883069)Termination phase: Saturation 6.52/1.75 % (2883069)Time elapsed: 0.142 s 6.52/1.75 % (2883069)Peak memory usage: 12 MB 6.52/1.75 % (2883069)Instructions burned: 200 (million) 6.52/1.75 % (2883038)Instruction limit reached! 6.52/1.75 % (2883038)------------------------------ 6.52/1.75 % (2883038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.52/1.75 % (2883081)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=691702885:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_1792 on theBenchmark for (1792ds/137Mi) 6.52/1.75 % (2883038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.52/1.75 % (2883038)CaDiCaL version: 2.1.3 6.52/1.75 % (2883038)Termination reason: Instruction limit 6.52/1.75 % (2883038)Termination phase: Saturation 6.52/1.75 % (2883038)Time elapsed: 0.445 s 6.52/1.75 % (2883038)Peak memory usage: 21 MB 6.52/1.75 % (2883038)Instructions burned: 1241 (million) 6.52/1.75 % (2883082)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=90834954:cond=on:i=34:hud=10:nm=10:rtra=on_1792 on theBenchmark for (1792ds/34Mi) 6.52/1.75 % (2883083)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=67911034:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_1792 on theBenchmark for (1792ds/67Mi) 6.52/1.75 % (2883084)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off 6.52/1.75 % (2883087)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=1989888783:cond=on:i=96:bd=all:rtra=on_1792 on theBenchmark for (1792ds/96Mi) 6.52/1.75 % (2883084)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=1357269936:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_1792 on theBenchmark for (1792ds/180Mi) 6.52/1.75 % (2883085)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=3622363451:st=2:i=246:sd=3:rtra=on:ss=axioms_1792 on theBenchmark for (1792ds/246Mi) 6.52/1.75 % (2883082)Instruction limit reached! 6.52/1.75 % (2883082)------------------------------ 6.52/1.75 % (2883082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.52/1.75 % (2883082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.52/1.75 % (2883082)CaDiCaL version: 2.1.3 6.52/1.75 % (2883082)Termination reason: Instruction limit 6.52/1.75 % (2883082)Termination phase: Property scanning 6.52/1.75 % (2883082)Time elapsed: 0.027 s 6.52/1.75 % (2883082)Peak memory usage: 10 MB 6.52/1.75 % (2883082)Instructions burned: 34 (million) 6.52/1.75 % (2883087)Instruction limit reached! 6.52/1.75 % (2883087)------------------------------ 6.52/1.75 % (2883087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.52/1.75 % (2883087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.52/1.75 % (2883087)CaDiCaL version: 2.1.3 6.52/1.75 % (2883087)Termination reason: Instruction limit 6.52/1.75 % (2883087)Termination phase: Property scanning 6.52/1.75 % (2883087)Time elapsed: 0.035 s 6.52/1.75 % (2883087)Peak memory usage: 11 MB 6.52/1.75 % (2883087)Instructions burned: 98 (million) 6.52/1.75 % (2883083)Instruction limit reached! 6.52/1.75 % (2883083)------------------------------ 6.52/1.75 % (2883083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.52/1.75 % (2883083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.52/1.75 % (2883083)CaDiCaL version: 2.1.3 6.52/1.75 % (2883083)Termination reason: Instruction limit 6.52/1.75 % (2883083)Termination phase: Function definition elimination 6.52/1.75 % (2883083)Time elapsed: 0.048 s 7.05/1.90 % (2883083)Peak memory usage: 11 MB 7.05/1.90 % (2883083)Instructions burned: 68 (million) 7.05/1.90 % (2883094)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1693639820:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_1792 on theBenchmark for (1792ds/874Mi) 7.05/1.90 % (2883093)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=3591006470:i=427:sd=1:rtra=on:ss=axioms_1792 on theBenchmark for (1792ds/427Mi) 7.05/1.90 % (2883095)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=976051082:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_1792 on theBenchmark for (1792ds/515Mi) 7.05/1.90 % (2883084)Instruction limit reached! 7.05/1.90 % (2883084)------------------------------ 7.05/1.90 % (2883084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.05/1.90 % (2883084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.05/1.90 % (2883084)CaDiCaL version: 2.1.3 7.05/1.90 % (2883084)Termination reason: Instruction limit 7.05/1.90 % (2883084)Termination phase: Saturation 7.05/1.90 % (2883084)Time elapsed: 0.110 s 7.05/1.90 % (2883084)Peak memory usage: 12 MB 7.05/1.90 % (2883084)Instructions burned: 181 (million) 7.05/1.90 % (2883081)Instruction limit reached! 7.05/1.90 % (2883081)------------------------------ 7.05/1.90 % (2883081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.05/1.90 % (2883081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.05/1.90 % (2883081)CaDiCaL version: 2.1.3 7.05/1.90 % (2883081)Termination reason: Instruction limit 7.05/1.90 % (2883081)Termination phase: Saturation 7.05/1.90 % (2883081)Time elapsed: 0.129 s 7.05/1.90 % (2883081)Peak memory usage: 13 MB 7.05/1.90 % (2883081)Instructions burned: 137 (million) 7.05/1.90 % (2883100)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1846377601:i=44:ep=R:rtra=on:ntd=on_1791 on theBenchmark for (1791ds/44Mi) 7.05/1.90 % (2883099)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3863658782:st=1.5:i=130:rtra=on:ss=axioms_1791 on theBenchmark for (1791ds/130Mi) 7.05/1.90 % (2883093)Refutation not found, incomplete strategy 7.05/1.90 % (2883093)------------------------------ 7.05/1.90 % (2883093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.05/1.90 % (2883093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.05/1.90 % (2883093)CaDiCaL version: 2.1.3 7.05/1.90 % (2883093)Termination reason: Refutation not found, incomplete strategy 7.05/1.90 % (2883093)Time elapsed: 0.093 s 7.05/1.90 % (2883093)Peak memory usage: 14 MB 7.05/1.90 % (2883093)Instructions burned: 117 (million) 7.05/1.90 % (2883093)------------------------------ 7.05/1.90 % (2883093)------------------------------ 7.05/1.90 % (2883100)Instruction limit reached! 7.05/1.90 % (2883100)------------------------------ 7.05/1.90 % (2883100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.05/1.90 % (2883100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.05/1.90 % (2883100)CaDiCaL version: 2.1.3 7.05/1.90 % (2883100)Termination reason: Instruction limit 7.05/1.90 % (2883100)Termination phase: Function definition elimination 7.05/1.90 % (2883100)Time elapsed: 0.030 s 7.05/1.90 % (2883100)Peak memory usage: 11 MB 7.05/1.90 % (2883100)Instructions burned: 44 (million) 7.05/1.90 % (2883085)Instruction limit reached! 7.05/1.90 % (2883085)------------------------------ 7.05/1.90 % (2883085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.05/1.90 % (2883085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.05/1.90 % (2883085)CaDiCaL version: 2.1.3 7.05/1.90 % (2883085)Termination reason: Instruction limit 7.05/1.90 % (2883085)Termination phase: Saturation 7.05/1.90 % (2883085)Time elapsed: 0.181 s 7.05/1.90 % (2883085)Peak memory usage: 15 MB 7.05/1.90 % (2883085)Instructions burned: 246 (million) 7.05/1.90 % (2883103)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=3752293494:s2a=on:i=571:nm=16:rtra=on_1790 on theBenchmark for (1790ds/571Mi) 7.05/1.90 % (2883104)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=917475381:i=450:rtra=on:ixr=off:ntd=on_1790 on theBenchmark for (1790ds/450Mi) 7.05/1.90 % (2883106)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1322559161:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_1790 on theBenchmark for (1790ds/95Mi) 8.56/2.02 % (2883099)Instruction limit reached! 8.56/2.02 % (2883099)------------------------------ 8.56/2.02 % (2883099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.56/2.02 % (2883099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.56/2.02 % (2883099)CaDiCaL version: 2.1.3 8.56/2.02 % (2883099)Termination reason: Instruction limit 8.56/2.02 % (2883099)Termination phase: Saturation 8.56/2.02 % (2883099)Time elapsed: 0.104 s 8.56/2.02 % (2883099)Peak memory usage: 13 MB 8.56/2.02 % (2883099)Instructions burned: 130 (million) 8.56/2.02 % (2883106)Instruction limit reached! 8.56/2.02 % (2883106)------------------------------ 8.56/2.02 % (2883106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.56/2.02 % (2883106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.56/2.02 % (2883106)CaDiCaL version: 2.1.3 8.56/2.02 % (2883106)Termination reason: Instruction limit 8.56/2.02 % (2883106)Termination phase: Saturation 8.56/2.02 % (2883106)Time elapsed: 0.068 s 8.56/2.02 % (2883106)Peak memory usage: 12 MB 8.56/2.02 % (2883106)Instructions burned: 95 (million) 8.56/2.02 % (2883109)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=404199328:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_1789 on theBenchmark for (1789ds/65Mi) 8.56/2.02 % (2883110)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=609108190: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_1789 on theBenchmark for (1789ds/105Mi) 8.56/2.02 % (2883109)Instruction limit reached! 8.56/2.02 % (2883109)------------------------------ 8.56/2.02 % (2883109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.56/2.02 % (2883109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.56/2.02 % (2883109)CaDiCaL version: 2.1.3 8.56/2.02 % (2883109)Termination reason: Instruction limit 8.56/2.02 % (2883109)Termination phase: Function definition elimination 8.56/2.02 % (2883109)Time elapsed: 0.050 s 8.56/2.02 % (2883109)Peak memory usage: 11 MB 8.56/2.02 % (2883109)Instructions burned: 65 (million) 8.56/2.02 % (2883094)Instruction limit reached! 8.56/2.02 % (2883094)------------------------------ 8.56/2.02 % (2883094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.56/2.02 % (2883094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.56/2.02 % (2883094)CaDiCaL version: 2.1.3 8.56/2.02 % (2883094)Termination reason: Instruction limit 8.56/2.02 % (2883094)Termination phase: Saturation 8.56/2.02 % (2883094)Time elapsed: 0.303 s 8.56/2.02 % (2883094)Peak memory usage: 16 MB 8.56/2.02 % (2883094)Instructions burned: 875 (million) 8.56/2.02 % (2883114)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=2250922450:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_1788 on theBenchmark for (1788ds/375Mi) 8.56/2.02 % (2883113)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=1425850593:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_1788 on theBenchmark for (1788ds/5755Mi) 8.56/2.03 % (2883110)Instruction limit reached! 8.56/2.03 % (2883110)------------------------------ 8.56/2.03 % (2883110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.56/2.03 % (2883110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.56/2.03 % (2883110)CaDiCaL version: 2.1.3 8.56/2.03 % (2883110)Termination reason: Instruction limit 8.56/2.03 % (2883110)Termination phase: Saturation 8.56/2.03 % (2883110)Time elapsed: 0.075 s 8.56/2.03 % (2883110)Peak memory usage: 12 MB 8.56/2.03 % (2883110)Instructions burned: 105 (million) 8.56/2.03 % (2883095)Instruction limit reached! 8.56/2.03 % (2883095)------------------------------ 8.56/2.03 % (2883095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.56/2.03 % (2883095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.56/2.03 % (2883095)CaDiCaL version: 2.1.3 8.56/2.03 % (2883095)Termination reason: Instruction limit 8.56/2.03 % (2883095)Termination phase: Saturation 8.56/2.03 % (2883095)Time elapsed: 0.354 s 11.06/2.25 % (2883095)Peak memory usage: 16 MB 11.06/2.25 % (2883095)Instructions burned: 517 (million) 11.06/2.25 % (2883117)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3297586832:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1788 on theBenchmark for (1788ds/495Mi) 11.06/2.25 % (2883118)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=1217119563:cond=on:i=34:hud=10:nm=10:rtra=on_1788 on theBenchmark for (1788ds/34Mi) 11.06/2.25 % (2883061)Instruction limit reached! 11.06/2.25 % (2883061)------------------------------ 11.06/2.25 % (2883061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.25 % (2883061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.25 % (2883061)CaDiCaL version: 2.1.3 11.06/2.25 % (2883061)Termination reason: Instruction limit 11.06/2.25 % (2883061)Termination phase: Saturation 11.06/2.25 % (2883061)Time elapsed: 0.745 s 11.06/2.25 % (2883061)Peak memory usage: 17 MB 11.06/2.25 % (2883061)Instructions burned: 853 (million) 11.06/2.25 % (2883104)Instruction limit reached! 11.06/2.25 % (2883104)------------------------------ 11.06/2.25 % (2883104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.25 % (2883104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.25 % (2883104)CaDiCaL version: 2.1.3 11.06/2.25 % (2883104)Termination reason: Instruction limit 11.06/2.25 % (2883104)Termination phase: Saturation 11.06/2.25 % (2883104)Time elapsed: 0.296 s 11.06/2.25 % (2883104)Peak memory usage: 13 MB 11.06/2.25 % (2883104)Instructions burned: 450 (million) 11.06/2.25 % (2883118)Instruction limit reached! 11.06/2.25 % (2883118)------------------------------ 11.06/2.25 % (2883118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.25 % (2883118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.25 % (2883118)CaDiCaL version: 2.1.3 11.06/2.25 % (2883118)Termination reason: Instruction limit 11.06/2.25 % (2883118)Termination phase: Property scanning 11.06/2.25 % (2883118)Time elapsed: 0.026 s 11.06/2.25 % (2883118)Peak memory usage: 10 MB 11.06/2.25 % (2883118)Instructions burned: 34 (million) 11.06/2.25 % (2883114)Instruction limit reached! 11.06/2.25 % (2883114)------------------------------ 11.06/2.25 % (2883114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.25 % (2883114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.25 % (2883114)CaDiCaL version: 2.1.3 11.06/2.25 % (2883114)Termination reason: Instruction limit 11.06/2.25 % (2883114)Termination phase: Saturation 11.06/2.25 % (2883114)Time elapsed: 0.147 s 11.06/2.25 % (2883114)Peak memory usage: 14 MB 11.06/2.25 % (2883114)Instructions burned: 375 (million) 11.06/2.25 % (2883121)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=2182185172:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_1787 on theBenchmark for (1787ds/91Mi) 11.06/2.25 % (2883124)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=3077067240:i=338:bd=all:ins=4:rtra=on_1787 on theBenchmark for (1787ds/338Mi) 11.06/2.25 % (2883122)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=2507626370:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_1787 on theBenchmark for (1787ds/66Mi) 11.06/2.25 % (2883123)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2928842080:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1787 on theBenchmark for (1787ds/22Mi) 11.06/2.25 % (2883123)Instruction limit reached! 11.06/2.25 % (2883123)------------------------------ 11.06/2.25 % (2883123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.25 % (2883123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.06/2.25 % (2883123)CaDiCaL version: 2.1.3 11.06/2.25 % (2883123)Termination reason: Instruction limit 11.06/2.25 % (2883123)Termination phase: Property scanning 11.06/2.25 % (2883123)Time elapsed: 0.017 s 11.06/2.25 % (2883123)Peak memory usage: 10 MB 11.06/2.25 % (2883123)Instructions burned: 22 (million) 11.06/2.25 % (2883122)Instruction limit reached! 11.06/2.25 % (2883122)------------------------------ 11.06/2.25 % (2883122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.06/2.25 % (2883122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.65/2.50 % (2883122)CaDiCaL version: 2.1.3 11.65/2.50 % (2883122)Termination reason: Instruction limit 11.65/2.50 % (2883122)Termination phase: Saturation 11.65/2.50 % (2883122)Time elapsed: 0.052 s 11.65/2.50 % (2883122)Peak memory usage: 13 MB 11.65/2.50 % (2883122)Instructions burned: 66 (million) 11.65/2.50 % (2883129)lrs+10_1_sil=128000:si=on:urr=on:random_seed=446167903:i=28:sd=1:rtra=on:ss=axioms:sgt=64_1786 on theBenchmark for (1786ds/28Mi) 11.65/2.50 % (2883121)Instruction limit reached! 11.65/2.50 % (2883121)------------------------------ 11.65/2.50 % (2883121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.65/2.50 % (2883121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.65/2.50 % (2883121)CaDiCaL version: 2.1.3 11.65/2.50 % (2883121)Termination reason: Instruction limit 11.65/2.50 % (2883121)Termination phase: Saturation 11.65/2.50 % (2883121)Time elapsed: 0.067 s 11.65/2.50 % (2883121)Peak memory usage: 12 MB 11.65/2.50 % (2883121)Instructions burned: 92 (million) 11.65/2.50 % (2883103)Instruction limit reached! 11.65/2.50 % (2883103)------------------------------ 11.65/2.50 % (2883103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.65/2.50 % (2883103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.65/2.50 % (2883103)CaDiCaL version: 2.1.3 11.65/2.50 % (2883103)Termination reason: Instruction limit 11.65/2.50 % (2883103)Termination phase: Saturation 11.65/2.50 % (2883103)Time elapsed: 0.413 s 11.65/2.50 % (2883103)Peak memory usage: 14 MB 11.65/2.50 % (2883103)Instructions burned: 571 (million) 11.65/2.50 % (2883130)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on 11.65/2.50 % (2883129)Instruction limit reached! 11.65/2.50 % (2883129)------------------------------ 11.65/2.50 % (2883129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.65/2.50 % (2883129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.65/2.50 % (2883129)CaDiCaL version: 2.1.3 11.65/2.50 % (2883129)Termination reason: Instruction limit 11.65/2.50 % (2883129)Termination phase: SInE selection 11.65/2.50 % (2883129)Time elapsed: 0.023 s 11.65/2.50 % (2883129)Peak memory usage: 10 MB 11.65/2.50 % (2883129)Instructions burned: 28 (million) 11.65/2.50 % (2883130)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=265276023:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_1786 on theBenchmark for (1786ds/137Mi) 11.65/2.50 % (2883132)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=2916816581:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_1786 on theBenchmark for (1786ds/340Mi) 11.65/2.50 % (2883133)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=155577919:i=227:sd=1:bd=all:rtra=on:ss=axioms_1786 on theBenchmark for (1786ds/227Mi) 11.65/2.50 % (2883134)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on 11.65/2.50 % (2883134)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=460598439:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_1786 on theBenchmark for (1786ds/373Mi) 11.65/2.50 % (2883124)Instruction limit reached! 11.65/2.50 % (2883124)------------------------------ 11.65/2.50 % (2883124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.65/2.50 % (2883124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.65/2.50 % (2883124)CaDiCaL version: 2.1.3 11.65/2.50 % (2883124)Termination reason: Instruction limit 11.65/2.50 % (2883124)Termination phase: Saturation 11.65/2.50 % (2883124)Time elapsed: 0.125 s 11.65/2.50 % (2883124)Peak memory usage: 16 MB 11.65/2.50 % (2883124)Instructions burned: 338 (million) 11.65/2.50 % (2883139)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=1835421620:i=116:ep=RSTC:rtra=on:ntd=on_1785 on theBenchmark for (1785ds/116Mi) 11.65/2.50 % (2883133)Refutation not found, incomplete strategy 11.65/2.50 % (2883133)------------------------------ 11.65/2.50 % (2883133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.65/2.50 % (2883133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.02/2.83 % (2883133)CaDiCaL version: 2.1.3 14.02/2.83 % (2883133)Termination reason: Refutation not found, incomplete strategy 14.02/2.83 % (2883133)Time elapsed: 0.081 s 14.02/2.83 % (2883133)Peak memory usage: 14 MB 14.02/2.83 % (2883133)Instructions burned: 101 (million) 14.02/2.83 % (2883133)------------------------------ 14.02/2.83 % (2883133)------------------------------ 14.02/2.83 % (2883130)Instruction limit reached! 14.02/2.83 % (2883130)------------------------------ 14.02/2.83 % (2883130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.02/2.83 % (2883130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.02/2.83 % (2883130)CaDiCaL version: 2.1.3 14.02/2.83 % (2883130)Termination reason: Instruction limit 14.02/2.83 % (2883130)Termination phase: Saturation 14.02/2.83 % (2883130)Time elapsed: 0.096 s 14.02/2.83 % (2883130)Peak memory usage: 12 MB 14.02/2.83 % (2883130)Instructions burned: 138 (million) 14.02/2.83 % (2883139)Instruction limit reached! 14.02/2.83 % (2883139)------------------------------ 14.02/2.83 % (2883139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.02/2.83 % (2883139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.02/2.83 % (2883139)CaDiCaL version: 2.1.3 14.02/2.83 % (2883139)Termination reason: Instruction limit 14.02/2.83 % (2883139)Termination phase: Saturation 14.02/2.83 % (2883139)Time elapsed: 0.044 s 14.02/2.83 % (2883139)Peak memory usage: 12 MB 14.02/2.83 % (2883139)Instructions burned: 118 (million) 14.02/2.83 % (2883143)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=723326515: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_1785 on theBenchmark for (1785ds/9840Mi) 14.02/2.83 % (2883142)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2796135219:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_1785 on theBenchmark for (1785ds/270Mi) 14.02/2.83 % (2883117)Instruction limit reached! 14.02/2.83 % (2883117)------------------------------ 14.02/2.83 % (2883117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.02/2.83 % (2883117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.02/2.83 % (2883117)CaDiCaL version: 2.1.3 14.02/2.83 % (2883117)Termination reason: Instruction limit 14.02/2.83 % (2883117)Termination phase: Saturation 14.02/2.83 % (2883141)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=3927527903:i=575:rtra=on_1785 on theBenchmark for (1785ds/575Mi) 14.02/2.83 % (2883117)Time elapsed: 0.332 s 14.02/2.83 % (2883117)Peak memory usage: 13 MB 14.02/2.83 % (2883117)Instructions burned: 496 (million) 14.02/2.83 % (2883147)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=2684579197:i=421:rtra=on:ss=axioms_1784 on theBenchmark for (1784ds/421Mi) 14.02/2.83 % (2883132)Instruction limit reached! 14.02/2.83 % (2883132)------------------------------ 14.02/2.83 % (2883132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.02/2.83 % (2883132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.02/2.83 % (2883132)CaDiCaL version: 2.1.3 14.02/2.83 % (2883132)Termination reason: Instruction limit 14.02/2.83 % (2883132)Termination phase: Saturation 14.02/2.83 % (2883132)Time elapsed: 0.272 s 14.02/2.83 % (2883132)Peak memory usage: 15 MB 14.02/2.83 % (2883132)Instructions burned: 341 (million) 14.02/2.83 % (2883134)Instruction limit reached! 14.02/2.83 % (2883134)------------------------------ 14.02/2.83 % (2883134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.02/2.83 % (2883134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.02/2.83 % (2883134)CaDiCaL version: 2.1.3 14.02/2.83 % (2883134)Termination reason: Instruction limit 14.02/2.83 % (2883134)Termination phase: Saturation 14.02/2.83 % (2883134)Time elapsed: 0.266 s 14.02/2.83 % (2883134)Peak memory usage: 14 MB 14.02/2.83 % (2883134)Instructions burned: 373 (million) 14.02/2.83 % (2883142)Instruction limit reached! 14.02/2.83 % (2883142)------------------------------ 14.02/2.83 % (2883142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.02/2.83 % (2883142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.02/2.83 % (2883142)CaDiCaL version: 2.1.3 18.46/3.23 % (2883142)Termination reason: Instruction limit 18.46/3.23 % (2883142)Termination phase: Saturation 18.46/3.23 % (2883142)Time elapsed: 0.185 s 18.46/3.23 % (2883142)Peak memory usage: 12 MB 18.46/3.23 % (2883142)Instructions burned: 273 (million) 18.46/3.23 % (2883149)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 18.46/3.23 % (2883149)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=1842479556:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_1783 on theBenchmark for (1783ds/270Mi) 18.46/3.23 % (2883150)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3536756841:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1783 on theBenchmark for (1783ds/31Mi) 18.46/3.23 % (2883151)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 18.46/3.23 % (2883151)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 18.46/3.23 % (2883151)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=566510128:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_1783 on theBenchmark for (1783ds/1440Mi) 18.46/3.23 % (2883150)Instruction limit reached! 18.46/3.23 % (2883150)------------------------------ 18.46/3.23 % (2883150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.23 % (2883150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.23 % (2883150)CaDiCaL version: 2.1.3 18.46/3.23 % (2883150)Termination reason: Instruction limit 18.46/3.23 % (2883150)Termination phase: Property scanning 18.46/3.23 % (2883150)Time elapsed: 0.025 s 18.46/3.23 % (2883150)Peak memory usage: 10 MB 18.46/3.23 % (2883150)Instructions burned: 32 (million) 18.46/3.23 % (2883155)dis+10_2_sil=128000:si=on:random_seed=4191410000:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_1782 on theBenchmark for (1782ds/339Mi) 18.46/3.23 % (2883149)Refutation not found, incomplete strategy 18.46/3.23 % (2883149)------------------------------ 18.46/3.23 % (2883149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.23 % (2883149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.23 % (2883149)CaDiCaL version: 2.1.3 18.46/3.23 % (2883149)Termination reason: Refutation not found, incomplete strategy 18.46/3.23 % (2883149)Time elapsed: 0.150 s 18.46/3.23 % (2883149)Peak memory usage: 14 MB 18.46/3.23 % (2883149)Instructions burned: 198 (million) 18.46/3.23 % (2883149)------------------------------ 18.46/3.23 % (2883149)------------------------------ 18.46/3.23 % (2883157)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=2786241627:i=111:add=on:fgj=on:rtra=on:fdi=1024_1781 on theBenchmark for (1781ds/111Mi) 18.46/3.23 % (2883147)Instruction limit reached! 18.46/3.23 % (2883147)------------------------------ 18.46/3.23 % (2883147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.23 % (2883147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.23 % (2883147)CaDiCaL version: 2.1.3 18.46/3.23 % (2883147)Termination reason: Instruction limit 18.46/3.23 % (2883147)Termination phase: Saturation 18.46/3.23 % (2883147)Time elapsed: 0.315 s 18.46/3.23 % (2883147)Peak memory usage: 15 MB 18.46/3.23 % (2883147)Instructions burned: 422 (million) 18.46/3.23 % (2883141)Instruction limit reached! 18.46/3.23 % (2883141)------------------------------ 18.46/3.23 % (2883141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.23 % (2883141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.23 % (2883141)CaDiCaL version: 2.1.3 18.46/3.23 % (2883141)Termination reason: Instruction limit 18.46/3.23 % (2883141)Termination phase: Saturation 18.46/3.23 % (2883141)Time elapsed: 0.386 s 18.46/3.23 % (2883141)Peak memory usage: 13 MB 18.46/3.23 % (2883141)Instructions burned: 576 (million) 18.46/3.23 % (2883159)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=1227149025:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1781 on theBenchmark for (1781ds/122Mi) 18.46/3.23 % (2883157)Instruction limit reached! 18.46/3.23 % (2883157)------------------------------ 18.46/3.23 % (2883157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.23 % (2883157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.23 % (2883157)CaDiCaL version: 2.1.3 18.46/3.23 % (2883157)Termination reason: Instruction limit 18.46/3.23 % (2883157)Termination phase: Saturation 18.46/3.23 % (2883157)Time elapsed: 0.081 s 18.46/3.23 % (2883157)Peak memory usage: 12 MB 18.46/3.23 % (2883157)Instructions burned: 112 (million) 18.46/3.23 % (2883160)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=3756156369:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_1780 on theBenchmark for (1780ds/136Mi) 18.46/3.23 % (2883162)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2243850955:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1780 on theBenchmark for (1780ds/232Mi) 18.46/3.23 % (2883159)Instruction limit reached! 18.46/3.23 % (2883159)------------------------------ 18.46/3.23 % (2883159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.23 % (2883159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.23 % (2883159)CaDiCaL version: 2.1.3 18.46/3.23 % (2883159)Termination reason: Instruction limit 18.46/3.23 % (2883159)Termination phase: Saturation 18.46/3.23 % (2883159)Time elapsed: 0.090 s 18.46/3.23 % (2883159)Peak memory usage: 13 MB 18.46/3.23 % (2883159)Instructions burned: 122 (million) 18.46/3.23 % (2883155)Instruction limit reached! 18.46/3.23 % (2883155)------------------------------ 18.46/3.23 % (2883155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.23 % (2883155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.23 % (2883155)CaDiCaL version: 2.1.3 18.46/3.23 % (2883155)Termination reason: Instruction limit 18.46/3.23 % (2883155)Termination phase: Saturation 18.46/3.23 % (2883155)Time elapsed: 0.271 s 18.46/3.23 % (2883155)Peak memory usage: 14 MB 18.46/3.23 % (2883155)Instructions burned: 339 (million) 18.46/3.23 % (2883160)Instruction limit reached! 18.46/3.23 % (2883160)------------------------------ 18.46/3.23 % (2883160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.23 % (2883160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.23 % (2883160)CaDiCaL version: 2.1.3 18.46/3.23 % (2883160)Termination reason: Instruction limit 18.46/3.23 % (2883160)Termination phase: Saturation 18.46/3.23 % (2883160)Time elapsed: 0.095 s 18.46/3.23 % (2883160)Peak memory usage: 12 MB 18.46/3.23 % (2883160)Instructions burned: 136 (million) 18.46/3.23 % (2883165)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=3900254932:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_1779 on theBenchmark for (1779ds/1254Mi) 18.46/3.23 % (2883166)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs 18.46/3.23 % (2883166)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=2286339076:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_1779 on theBenchmark for (1779ds/281Mi) 18.46/3.23 % (2883167)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=639107078:i=619:add=on:rtra=on_1779 on theBenchmark for (1779ds/619Mi) 18.46/3.23 % (2883162)Instruction limit reached! 18.46/3.23 % (2883162)------------------------------ 18.46/3.23 % (2883162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.23 % (2883162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.23 % (2883162)CaDiCaL version: 2.1.3 18.46/3.23 % (2883162)Termination reason: Instruction limit 18.46/3.23 % (2883162)Termination phase: Saturation 18.46/3.23 % (2883162)Time elapsed: 0.212 s 18.46/3.23 % (2883162)Peak memory usage: 14 MB 18.46/3.23 % (2883162)Instructions burned: 233 (million) 18.46/3.23 % (2883171)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=3331766632:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_1777 on theBenchmark for (1777ds/865Mi) 18.46/3.23 % (2883166)Instruction limit reached! 18.46/3.23 % (2883166)------------------------------ 18.46/3.23 % (2883166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.23 % (2883166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.23 % (2883166)CaDiCaL version: 2.1.3 18.46/3.23 % (2883166)Termination reason: Instruction limit 18.46/3.23 % (2883166)Termination phase: Saturation 18.46/3.23 % (2883166)Time elapsed: 0.191 s 18.46/3.23 % (2883166)Peak memory usage: 12 MB 18.46/3.23 % (2883166)Instructions burned: 282 (million) 18.46/3.23 % (2883173)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2655014981:i=212:sd=1:rtra=on:ss=axioms:sgt=64_1777 on theBenchmark for (1777ds/212Mi) 18.46/3.23 % (2883173)Instruction limit reached! 18.46/3.23 % (2883173)------------------------------ 18.46/3.23 % (2883173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.23 % (2883173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.23 % (2883173)CaDiCaL version: 2.1.3 18.46/3.23 % (2883173)Termination reason: Instruction limit 18.46/3.23 % (2883173)Termination phase: Saturation 18.46/3.23 % (2883173)Time elapsed: 0.159 s 18.46/3.23 % (2883173)Peak memory usage: 13 MB 18.46/3.23 % (2883173)Instructions burned: 212 (million) 18.46/3.23 % (2883165) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2882974-2883165"... 18.46/3.23 % (2883167)Instruction limit reached! 18.46/3.23 % (2883167)------------------------------ 18.46/3.23 % (2883167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.23 % (2883167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.23 % (2883167)CaDiCaL version: 2.1.3 18.46/3.23 % (2883167)Termination reason: Instruction limit 18.46/3.23 % (2883167)Termination phase: Saturation 18.46/3.23 % (2883167)Time elapsed: 0.431 s 18.46/3.23 % (2883167)Peak memory usage: 19 MB 18.46/3.23 % (2883167)Instructions burned: 619 (million) 18.46/3.23 % (2883175)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=3436007755:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_1775 on theBenchmark for (1775ds/130Mi) 18.46/3.23 % (2883176)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=872909646:st=1.5:i=346:rtra=on:ss=axioms_1774 on theBenchmark for (1774ds/346Mi) 18.46/3.23 % (2883175)Instruction limit reached! 18.46/3.23 % (2883175)------------------------------ 18.46/3.23 % (2883175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.23 % (2883175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.23 % (2883175)CaDiCaL version: 2.1.3 18.46/3.23 % (2883175)Termination reason: Instruction limit 18.46/3.23 % (2883175)Termination phase: Saturation 18.46/3.23 % (2883175)Time elapsed: 0.115 s 18.46/3.23 % (2883175)Peak memory usage: 13 MB 18.46/3.23 % (2883175)Instructions burned: 131 (million) 18.46/3.23 % (2883165)...printing done. 18.46/3.23 % (2883165)Refutation found. Thanks to Tanya! 18.46/3.23 % SZS status Theorem for theBenchmark 18.46/3.23 % SZS output start Proof for theBenchmark 18.46/3.23 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType). 18.46/3.23 thf(func_def_0, type, c_Eps_i: (($i > $o) > $i)). 18.46/3.23 thf(func_def_1, type, c_False: $o). 18.46/3.23 thf(func_def_2, type, c_True: $o). 18.46/3.23 thf(func_def_3, type, c_not: ($o > $o)). 18.46/3.23 thf(func_def_4, type, c_and: ($o > $o > $o)). 18.46/3.23 thf(func_def_5, type, c_or: ($o > $o > $o)). 18.46/3.23 thf(func_def_6, type, c_iff: ($o > $o > $o)). 18.46/3.23 thf(func_def_7, type, c_In: ($i > $i > $o)). 18.46/3.23 thf(func_def_8, type, c_Subq: ($i > $i > $o)). 18.46/3.23 thf(func_def_10, type, c_Union: ($i > $i)). 18.46/3.23 thf(func_def_11, type, c_Power: ($i > $i)). 18.46/3.23 thf(func_def_12, type, c_Repl: ($i > ($i > $i) > $i)). 18.46/3.23 thf(func_def_13, type, c_TransSet: ($i > $o)). 18.46/3.23 thf(func_def_14, type, c_atleast2: ($i > $o)). 18.46/3.23 thf(func_def_15, type, c_atleast3: ($i > $o)). 18.46/3.23 thf(func_def_16, type, c_atleast4: ($i > $o)). 18.46/3.23 thf(func_def_17, type, c_atleast5: ($i > $o)). 18.46/3.23 thf(func_def_18, type, c_atleast6: ($i > $o)). 18.46/3.23 thf(func_def_19, type, c_exactly2: ($i > $o)). 18.46/3.23 thf(func_def_20, type, c_exactly3: ($i > $o)). 18.46/3.23 thf(func_def_21, type, c_exactly4: ($i > $o)). 18.46/3.23 thf(func_def_22, type, c_exactly5: ($i > $o)). 18.46/3.23 thf(func_def_23, type, c_exu_i: (($i > $o) > $o)). 18.46/3.23 thf(func_def_24, type, c_reflexive_i: (($i > $i > $o) > $o)). 18.46/3.23 thf(func_def_25, type, c_irreflexive_i: (($i > $i > $o) > $o)). 18.46/3.23 thf(func_def_26, type, c_symmetric_i: (($i > $i > $o) > $o)). 18.46/3.23 thf(func_def_27, type, c_antisymmetric_i: (($i > $i > $o) > $o)). 18.46/3.23 thf(func_def_28, type, c_transitive_i: (($i > $i > $o) > $o)). 18.46/3.23 thf(func_def_29, type, c_eqreln_i: (($i > $i > $o) > $o)). 18.46/3.23 thf(func_def_30, type, c_per_i: (($i > $i > $o) > $o)). 18.46/3.23 thf(func_def_31, type, c_linear_i: (($i > $i > $o) > $o)). 18.46/3.23 thf(func_def_32, type, c_trichotomous_or_i: (($i > $i > $o) > $o)). 18.46/3.23 thf(func_def_33, type, c_partialorder_i: (($i > $i > $o) > $o)). 18.46/3.23 thf(func_def_34, type, c_totalorder_i: (($i > $i > $o) > $o)). 18.46/3.23 thf(func_def_35, type, c_strictpartialorder_i: (($i > $i > $o) > $o)). 18.46/3.23 thf(func_def_36, type, c_stricttotalorder_i: (($i > $i > $o) > $o)). 18.46/3.23 thf(func_def_37, type, c_If_i: ($o > $i > $i > $i)). 18.46/3.23 thf(func_def_38, type, c_exactly1of2: ($o > $o > $o)). 18.46/3.23 thf(func_def_39, type, c_exactly1of3: ($o > $o > $o > $o)). 18.46/3.23 thf(func_def_40, type, c_nIn: ($i > $i > $o)). 18.46/3.23 thf(func_def_41, type, c_nSubq: ($i > $i > $o)). 18.46/3.23 thf(func_def_42, type, c_UPair: ($i > $i > $i)). 18.46/3.23 thf(func_def_43, type, c_Sing: ($i > $i)). 18.46/3.23 thf(func_def_44, type, c_binunion: ($i > $i > $i)). 18.46/3.23 thf(func_def_45, type, c_SetAdjoin: ($i > $i > $i)). 18.46/3.23 thf(func_def_46, type, c_famunion: ($i > ($i > $i) > $i)). 18.46/3.23 thf(func_def_47, type, c_Sep: ($i > ($i > $o) > $i)). 18.46/3.23 thf(func_def_48, type, c_ReplSep: ($i > ($i > $o) > ($i > $i) > $i)). 18.46/3.23 thf(func_def_49, type, c_binintersect: ($i > $i > $i)). 18.46/3.23 thf(func_def_50, type, c_setminus: ($i > $i > $i)). 18.46/3.23 thf(func_def_51, type, c_inj: ($i > $i > ($i > $i) > $o)). 18.46/3.23 thf(func_def_52, type, c_bij: ($i > $i > ($i > $i) > $o)). 18.46/3.23 thf(func_def_53, type, c_atleastp: ($i > $i > $o)). 18.46/3.23 thf(func_def_54, type, c_equip: ($i > $i > $o)). 18.46/3.23 thf(func_def_55, type, c_In_rec_poly_G_i: (($i > ($i > $i) > $i) > $i > $i > $o)). 18.46/3.23 thf(func_def_56, type, c_In_rec_poly_i: (($i > ($i > $i) > $i) > $i > $i)). 18.46/3.23 thf(func_def_57, type, c_ordsucc: ($i > $i)). 18.46/3.23 thf(func_def_58, type, c_nat_p: ($i > $o)). 18.46/3.23 thf(func_def_59, type, c_nat_primrec: ($i > ($i > $i > $i) > $i > $i)). 18.46/3.23 thf(func_def_60, type, c_add_nat: ($i > $i > $i)). 18.46/3.23 thf(func_def_61, type, c_mul_nat: ($i > $i > $i)). 18.46/3.23 thf(func_def_62, type, c_ordinal: ($i > $o)). 18.46/3.23 thf(func_def_63, type, c_V_: ($i > $i)). 18.46/3.23 thf(func_def_64, type, c_Inj1: ($i > $i)). 18.46/3.23 thf(func_def_65, type, c_Inj0: ($i > $i)). 18.46/3.23 thf(func_def_66, type, c_Unj: ($i > $i)). 18.46/3.23 thf(func_def_67, type, c_combine_funcs: ($i > $i > ($i > $i) > ($i > $i) > $i > $i)). 18.46/3.23 thf(func_def_68, type, c_setsum: ($i > $i > $i)). 18.46/3.23 thf(func_def_69, type, c_proj0: ($i > $i)). 18.46/3.23 thf(func_def_70, type, c_proj1: ($i > $i)). 18.46/3.23 thf(func_def_71, type, c_binrep: ($i > $i > $i)). 18.46/3.23 thf(func_def_72, type, c_lam: ($i > ($i > $i) > $i)). 18.46/3.23 thf(func_def_73, type, c_setprod: ($i > $i > $i)). 18.46/3.23 thf(func_def_74, type, c_ap: ($i > $i > $i)). 18.46/3.23 thf(func_def_75, type, c_setsum_p: ($i > $o)). 18.46/3.23 thf(func_def_76, type, c_tuple_p: ($i > $i > $o)). 18.46/3.23 thf(func_def_77, type, c_Pi: ($i > ($i > $i) > $i)). 18.46/3.23 thf(func_def_78, type, c_setexp: ($i > $i > $i)). 18.46/3.23 thf(func_def_79, type, c_Sep2: ($i > ($i > $i) > ($i > $i > $o) > $i)). 18.46/3.23 thf(func_def_80, type, c_set_of_pairs: ($i > $o)). 18.46/3.23 thf(func_def_81, type, c_lam2: ($i > ($i > $i) > ($i > $i > $i) > $i)). 18.46/3.23 thf(func_def_82, type, c_PNoEq_: ($i > ($i > $o) > ($i > $o) > $o)). 18.46/3.23 thf(func_def_83, type, c_PNoLt_: ($i > ($i > $o) > ($i > $o) > $o)). 18.46/3.23 thf(func_def_84, type, c_PNoLt: ($i > ($i > $o) > $i > ($i > $o) > $o)). 18.46/3.23 thf(func_def_85, type, c_PNoLe: ($i > ($i > $o) > $i > ($i > $o) > $o)). 18.46/3.23 thf(func_def_86, type, c_PNo_downc: (($i > ($i > $o) > $o) > $i > ($i > $o) > $o)). 18.46/3.23 thf(func_def_87, type, c_PNo_upc: (($i > ($i > $o) > $o) > $i > ($i > $o) > $o)). 18.46/3.23 thf(func_def_88, type, c_SNoElts_: ($i > $i)). 18.46/3.23 thf(func_def_89, type, c_SNo_: ($i > $i > $o)). 18.46/3.23 thf(func_def_90, type, c_PSNo: ($i > ($i > $o) > $i)). 18.46/3.23 thf(func_def_91, type, c_SNo: ($i > $o)). 18.46/3.23 thf(func_def_92, type, c_SNoLev: ($i > $i)). 18.46/3.23 thf(func_def_93, type, c_SNoEq_: ($i > $i > $i > $o)). 18.46/3.23 thf(func_def_94, type, c_SNoLt: ($i > $i > $o)). 18.46/3.23 thf(func_def_95, type, c_SNoLe: ($i > $i > $o)). 18.46/3.23 thf(func_def_96, type, c_binop_on: ($i > ($i > $i > $i) > $o)). 18.46/3.23 thf(func_def_97, type, c_Loop: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o)). 18.46/3.23 thf(func_def_98, type, c_Loop_with_defs: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o)). 18.46/3.23 thf(func_def_99, type, c_Loop_with_defs_cex1: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o)). 18.46/3.23 thf(func_def_100, type, c_Loop_with_defs_cex2: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o)). 18.46/3.23 thf(func_def_101, type, c_combinator: ($i > $o)). 18.46/3.23 thf(func_def_102, type, c_combinator_equiv: ($i > $i > $o)). 18.46/3.23 thf(func_def_103, type, c_equip_mod: ($i > $i > $i > $o)). 18.46/3.23 thf(func_def_105, type, db3: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_106, type, db0: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_107, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))). 18.46/3.23 thf(func_def_108, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))). 18.46/3.23 thf(func_def_109, type, db4: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_110, type, db1: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_111, type, db2: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_112, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))). 18.46/3.23 thf(func_def_113, type, vIMP: ($o > $o > $o)). 18.46/3.23 thf(func_def_114, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))). 18.46/3.23 thf(func_def_117, type, db5: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_118, type, db6: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_119, type, db13: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_120, type, db12: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_121, type, db11: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_122, type, db10: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_123, type, db9: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_124, type, db8: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_125, type, db7: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_126, type, db14: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_127, type, db15: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_128, type, db16: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_129, type, db17: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_130, type, db18: !>[X0: $tType]:(X0)). 18.46/3.23 thf(func_def_131, type, vNOT: ($o > $o)). 18.46/3.23 thf(func_def_144, type, sF12: $o). 18.46/3.23 thf(func_def_145, type, sF13: $o). 18.46/3.23 thf(func_def_146, type, sF14: $o). 18.46/3.23 thf(func_def_147, type, sK15: $o). 18.46/3.23 thf(f6,axiom,( 18.46/3.23 ((^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_ordinal @ X1) @ (c_SNo_ @ X1 @ X0)))) = c_SNo)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax96)). 18.46/3.23 thf(f9,axiom,( 18.46/3.23 (c_Sep = (^[X0 : $i, X1 : ($i > $o)] : ((c_If_i @ ? [X2 : $i] : (c_and @ (c_In @ X2 @ X0) @ (X1 @ X2)) @ (c_Repl @ X0 @ (^[X2 : $i] : (((^[X3 : $i] : ((c_If_i @ (X1 @ X3) @ X3 @ (c_Eps_i @ (^[X4 : $i] : ((c_and @ (c_In @ X4 @ X0) @ (X1 @ X4)))))))) @ X2)))) @ c_Empty))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52)). 18.46/3.23 thf(f12,axiom,( 18.46/3.23 ((^[X0 : $i] : (! [X1 : $i] : ((c_In @ X1 @ X0) => (c_Subq @ X1 @ X0)))) = c_TransSet)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18)). 18.46/3.23 thf(f13,axiom,( 18.46/3.23 ((^[X0 : $i, X1 : ($i > $i)] : ((c_famunion @ X0 @ (^[X2 : $i] : ((c_Repl @ (X1 @ X2) @ (^[X3 : $i] : ((c_setsum @ X2 @ X3))))))))) = c_lam)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax77)). 18.46/3.23 thf(f14,axiom,( 18.46/3.23 (c_not = (^[X0 : $o] : (X0 => c_False)))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13)). 18.46/3.23 thf(f19,axiom,( 18.46/3.23 ((^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_In @ X1 @ X0) @ (c_not @ (c_Subq @ X0 @ (c_Power @ X1)))))) = c_atleast2)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19)). 18.46/3.23 thf(f22,axiom,( 18.46/3.23 (c_binrep = (^[X0 : $i, X1 : $i] : ((c_setsum @ X0 @ (c_Power @ X1)))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76)). 18.46/3.23 thf(f23,axiom,( 18.46/3.23 (c_Inj0 = (^[X0 : $i] : ((c_Repl @ X0 @ (^[X1 : $i] : ((c_Inj1 @ X1)))))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax70)). 18.46/3.23 thf(f26,axiom,( 18.46/3.23 ((^[X0 : $i] : ((c_and @ (c_TransSet @ X0) @ ! [X1 : $i] : ((c_In @ X1 @ X0) => (c_TransSet @ X1))))) = c_ordinal)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax67)). 18.46/3.23 thf(f28,axiom,( 18.46/3.23 ((^[X0 : ($i > ($i > $i) > $i), X1 : $i] : ((c_Eps_i @ (^[X2 : $i] : ((c_In_rec_poly_G_i @ X0 @ X1 @ X2)))))) = c_In_rec_poly_i)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61)). 18.46/3.23 thf(f29,axiom,( 18.46/3.23 (c_SetAdjoin = (^[X0 : $i, X1 : $i] : ((c_binunion @ X0 @ (c_Sing @ X1)))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50)). 18.46/3.23 thf(f30,axiom,( 18.46/3.23 (c_setprod = (^[X0 : $i, X1 : $i] : ((c_lam @ X0 @ (^[X2 : $i] : (X1))))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78)). 18.46/3.23 thf(f31,axiom,( 18.46/3.23 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5)). 18.46/3.23 thf(f32,axiom,( 18.46/3.23 ((^[X0 : $i, X1 : ($i > $i)] : ((c_Union @ (c_Repl @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))) = c_famunion)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51)). 18.46/3.23 thf(f39,axiom,( 18.46/3.23 (c_In_rec_poly_G_i = (^[X0 : ($i > ($i > $i) > $i), X1 : $i, X2 : $i] : (! [X3 : ($i > $i > $o)] : (! [X4 : $i,X5 : ($i > $i)] : (! [X6 : $i] : ((c_In @ X6 @ X4) => (X3 @ X6 @ (X5 @ X6))) => (X3 @ X4 @ (X0 @ X4 @ X5))) => (X3 @ X1 @ X2)))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60)). 18.46/3.23 thf(f40,axiom,( 18.46/3.23 (c_SNoElts_ = (^[X0 : $i] : ((c_binunion @ X0 @ (c_Repl @ X0 @ (^[X1 : $i] : (((^[X2 : $i] : ((c_SetAdjoin @ X2 @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X1))))))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93)). 18.46/3.23 thf(f48,axiom,( 18.46/3.23 ((^[X0 : $i, X1 : $i] : ((c_Union @ (c_UPair @ X0 @ X1)))) = c_binunion)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49)). 18.46/3.23 thf(f49,axiom,( 18.46/3.23 (c_Sing = (^[X0 : $i] : ((c_UPair @ X0 @ X0))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48)). 18.46/3.23 thf(f61,axiom,( 18.46/3.23 ((^[X0 : $i, X1 : $i] : ((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[X2 : $i] : ((c_If_i @ (c_In @ c_Empty @ X2) @ X0 @ X1)))))) = c_UPair)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47)). 18.46/3.23 thf(f67,axiom,( 18.46/3.23 (c_binintersect = (^[X0 : $i, X1 : $i] : ((c_Sep @ X0 @ (^[X2 : $i] : ((c_In @ X2 @ X1)))))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54)). 18.46/3.23 thf(f70,axiom,( 18.46/3.23 (c_If_i = (^[X0 : $o, X1 : $i, X2 : $i] : ((c_Eps_i @ (^[X3 : $i] : ((c_or @ (c_and @ X0 @ (X3 = X1)) @ (c_and @ (c_not @ X0) @ (X3 = X2)))))))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42)). 18.46/3.23 thf(f75,axiom,( 18.46/3.23 ((^[X0 : $o, X1 : $o] : ((c_or @ (c_and @ X0 @ (c_not @ X1)) @ (c_and @ (c_not @ X0) @ X1)))) = c_exactly1of2)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43)). 18.46/3.23 thf(f77,axiom,( 18.46/3.23 ((^[X0 : $i, X1 : $i] : ((c_and @ (c_Subq @ X1 @ (c_SNoElts_ @ X0)) @ ! [X2 : $i] : ((c_In @ X2 @ X0) => (c_exactly1of2 @ (c_In @ ((^[X3 : $i] : ((c_SetAdjoin @ X3 @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X2) @ X1) @ (c_In @ X2 @ X1)))))) = c_SNo_)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax94)). 18.46/3.23 thf(f83,axiom,( 18.46/3.23 ((^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))) = c_Subq)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17)). 18.46/3.23 thf(f87,axiom,( 18.46/3.23 ((^[X0 : $i] : ((c_binunion @ X0 @ (c_Sing @ X0)))) = c_ordsucc)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62)). 18.46/3.23 thf(f91,conjecture,( 18.46/3.23 (c_not @ ! [X0 : ($i > $o),X1 : ($i > $i)] : (c_and @ ((X0 @ (X1 @ (c_binintersect @ (X1 @ (c_Power @ c_Empty)) @ (X1 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (X1 @ c_Empty)) => ! [X2 : $i] : ((c_In @ X2 @ c_Empty) => ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ (c_exactly2 @ (c_ordsucc @ (X1 @ X3))))))) => ? [X2 : $i] : (c_and @ ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ (X2 = ((X1 @ X2))) => ? [X4 : $i] : (c_and @ (c_Subq @ X4 @ X2) @ (c_not @ (X0 @ (c_setprod @ X3 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty)))))))) @ (c_not @ (c_SNo @ X2))) @ (c_not @ (X0 @ (X1 @ (X1 @ (X1 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty))))))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)). 18.46/3.23 thf(f92,negated_conjecture,( 18.46/3.23 ~(c_not @ ! [X0 : ($i > $o),X1 : ($i > $i)] : (c_and @ ((X0 @ (X1 @ (c_binintersect @ (X1 @ (c_Power @ c_Empty)) @ (X1 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (X1 @ c_Empty)) => ! [X2 : $i] : ((c_In @ X2 @ c_Empty) => ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ (c_exactly2 @ (c_ordsucc @ (X1 @ X3))))))) => ? [X2 : $i] : (c_and @ ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ (X2 = ((X1 @ X2))) => ? [X4 : $i] : (c_and @ (c_Subq @ X4 @ X2) @ (c_not @ (X0 @ (c_setprod @ X3 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty)))))))) @ (c_not @ (c_SNo @ X2))) @ (c_not @ (X0 @ (X1 @ (X1 @ (X1 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty))))))))), 18.46/3.23 inference(negated_conjecture,[status(cth)],[f91])). 18.46/3.23 thf(f93,axiom,( 18.46/3.23 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14)). 18.46/3.23 thf(f98,axiom,( 18.46/3.23 ((^[X0 : $i, X1 : $i] : ((c_binunion @ (c_Repl @ X0 @ (^[X2 : $i] : ((c_Inj0 @ X2)))) @ (c_Repl @ X1 @ (^[X2 : $i] : ((c_Inj1 @ X2))))))) = c_setsum)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73)). 18.46/3.23 thf(f101,axiom,( 18.46/3.23 (c_Inj1 = ((c_In_rec_poly_i @ (^[X0 : $i, X1 : ($i > $i)] : ((c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69)). 18.46/3.23 thf(f103,axiom,( 18.46/3.23 ((^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_Subq @ X1 @ X0) @ (c_and @ (c_not @ (c_Subq @ X0 @ X1)) @ (c_atleast2 @ X1))))) = c_atleast3)), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20)). 18.46/3.23 thf(f106,axiom,( 18.46/3.23 (c_exactly2 = (^[X0 : $i] : ((c_and @ (c_atleast2 @ X0) @ (c_not @ (c_atleast3 @ X0))))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24)). 18.46/3.23 thf(f107,axiom,( 18.46/3.23 (c_or = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => X2) => ((X1 => X2) => X2)))))), 18.46/3.23 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15)). 18.46/3.23 thf(f115,plain,( 18.46/3.23 (c_SetAdjoin = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ Y0 @ (c_Sing @ Y1))))))), 18.46/3.23 inference(fool_elimination,[],[f29])). 18.46/3.23 thf(f120,plain,( 18.46/3.23 (c_Sing = (^[Y0 : $i]: (c_UPair @ Y0 @ Y0)))), 18.46/3.23 inference(fool_elimination,[],[f49])). 18.46/3.23 thf(f121,plain,( 18.46/3.23 ((^[X0 : $i] : (! [X1 : $i] : ((c_In @ X1 @ X0) => (c_Subq @ X1 @ X0)))) = c_TransSet)), 18.46/3.23 inference(rectify,[],[f12])). 18.46/3.23 thf(f122,plain,( 18.46/3.23 (c_TransSet = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_Subq @ Y1 @ Y0))))))), 18.46/3.23 inference(fool_elimination,[],[f121])). 18.46/3.23 thf(f134,plain,( 18.46/3.23 (c_not = (^[X0 : $o] : (X0 => c_False)))), 18.46/3.23 inference(rectify,[],[f14])). 18.46/3.23 thf(f135,plain,( 18.46/3.23 (c_not = (^[Y0 : $o]: (Y0 => c_False)))), 18.46/3.23 inference(fool_elimination,[],[f134])). 18.46/3.23 thf(f138,plain,( 18.46/3.23 (c_or = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => X2) => ((X1 => X2) => X2)))))), 18.46/3.23 inference(rectify,[],[f107])). 18.46/3.23 thf(f139,plain,( 18.46/3.23 (c_or = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => Y2) => ((Y1 => Y2) => Y2))))))))), 18.46/3.23 inference(fool_elimination,[],[f138])). 18.46/3.23 thf(f150,plain,( 18.46/3.23 ((^[X0 : $i, X1 : ($i > $i)] : ((c_famunion @ X0 @ (^[X2 : $i] : ((c_Repl @ (X1 @ X2) @ (^[X3 : $i] : ((c_setsum @ X2 @ X3))))))))) = c_lam)), 18.46/3.23 inference(rectify,[],[f13])). 18.46/3.23 thf(f151,plain,( 18.46/3.23 (c_lam = (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_famunion @ Y0 @ (^[Y2 : $i]: (c_Repl @ (Y1 @ Y2) @ (^[Y3 : $i]: (c_setsum @ Y2 @ Y3)))))))))), 18.46/3.23 inference(fool_elimination,[],[f150])). 18.46/3.23 thf(f160,plain,( 18.46/3.23 ((^[X0 : $i, X1 : $i] : ((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[X2 : $i] : ((c_If_i @ (c_In @ c_Empty @ X2) @ X0 @ X1)))))) = c_UPair)), 18.46/3.23 inference(rectify,[],[f61])). 18.46/3.23 thf(f161,plain,( 18.46/3.23 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: (c_If_i @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))), 18.46/3.23 inference(fool_elimination,[],[f160])). 18.46/3.23 thf(f167,plain,( 18.46/3.23 ((^[X0 : $i, X1 : ($i > $i)] : ((c_Union @ (c_Repl @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))) = c_famunion)), 18.46/3.23 inference(rectify,[],[f32])). 18.46/3.23 thf(f168,plain,( 18.46/3.23 (c_famunion = (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_Union @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))), 18.46/3.23 inference(fool_elimination,[],[f167])). 18.46/3.23 thf(f179,plain,( 18.46/3.23 (c_exactly1of2 = (^[Y0 : $o]: ((^[Y1 : $o]: (c_or @ (c_and @ Y0 @ (c_not @ Y1)) @ (c_and @ (c_not @ Y0) @ Y1))))))), 18.46/3.23 inference(fool_elimination,[],[f75])). 18.46/3.23 thf(f185,plain,( 18.46/3.23 (c_binrep = (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ Y0 @ (c_Power @ Y1))))))), 18.46/3.23 inference(fool_elimination,[],[f22])). 18.46/3.23 thf(f186,plain,( 18.46/3.23 (c_Inj0 = (^[X0 : $i] : ((c_Repl @ X0 @ (^[X1 : $i] : ((c_Inj1 @ X1)))))))), 18.46/3.23 inference(rectify,[],[f23])). 18.46/3.23 thf(f187,plain,( 18.46/3.23 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: (c_Inj1 @ Y1)))))), 18.46/3.23 inference(fool_elimination,[],[f186])). 18.46/3.23 thf(f188,plain,( 18.46/3.23 (c_SNoElts_ = (^[X0 : $i] : ((c_binunion @ X0 @ (c_Repl @ X0 @ (^[X1 : $i] : (((^[X2 : $i] : ((c_SetAdjoin @ X2 @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X1))))))))), 18.46/3.23 inference(rectify,[],[f40])). 18.46/3.23 thf(f189,plain,( 18.46/3.23 (c_SNoElts_ = (^[Y0 : $i]: (c_binunion @ Y0 @ (c_Repl @ Y0 @ (^[Y1 : $i]: ((^[Y2 : $i]: (c_SetAdjoin @ Y2 @ (c_Sing @ (c_ordsucc @ c_Empty)))) @ Y1))))))), 18.46/3.23 inference(fool_elimination,[],[f188])). 18.46/3.23 thf(f190,plain,( 18.46/3.23 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))), 18.46/3.23 inference(rectify,[],[f93])). 18.46/3.23 thf(f191,plain,( 18.46/3.23 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))), 18.46/3.23 inference(fool_elimination,[],[f190])). 18.46/3.23 thf(f198,plain,( 18.46/3.23 ((^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_In @ X1 @ X0) @ (c_not @ (c_Subq @ X0 @ (c_Power @ X1)))))) = c_atleast2)), 18.46/3.23 inference(rectify,[],[f19])). 18.46/3.23 thf(f199,plain,( 18.46/3.23 (c_atleast2 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_In @ Y1 @ Y0) @ (c_not @ (c_Subq @ Y0 @ (c_Power @ Y1))))))))), 18.46/3.23 inference(fool_elimination,[],[f198])). 18.46/3.23 thf(f200,plain,( 18.46/3.23 ((^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_ordinal @ X1) @ (c_SNo_ @ X1 @ X0)))) = c_SNo)), 18.46/3.23 inference(rectify,[],[f6])). 18.46/3.23 thf(f201,plain,( 18.46/3.23 (c_SNo = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_ordinal @ Y1) @ (c_SNo_ @ Y1 @ Y0))))))), 18.46/3.23 inference(fool_elimination,[],[f200])). 18.46/3.23 thf(f207,plain,( 18.46/3.23 ~(c_not @ ! [X0 : ($i > $o),X1 : ($i > $i)] : (c_and @ ((X0 @ (X1 @ (c_binintersect @ (X1 @ (c_Power @ c_Empty)) @ (X1 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (X1 @ c_Empty)) => ! [X2 : $i] : ((c_In @ X2 @ c_Empty) => ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ (c_exactly2 @ (c_ordsucc @ (X1 @ X3))))))) => ? [X4 : $i] : (c_and @ ? [X5 : $i] : (c_and @ (c_Subq @ X5 @ X4) @ (((X1 @ X4)) = X4) => ? [X6 : $i] : (c_and @ (c_Subq @ X6 @ X4) @ (c_not @ (X0 @ (c_setprod @ X5 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty)))))))) @ (c_not @ (c_SNo @ X4))) @ (c_not @ (X0 @ (X1 @ (X1 @ (X1 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty))))))))), 18.46/3.23 inference(rectify,[],[f92])). 18.46/3.23 thf(f208,plain,( 18.46/3.23 ($true = ((~ (c_not @ (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (c_and @ (((Y1 @ (Y0 @ (c_binintersect @ (Y0 @ (c_Power @ c_Empty)) @ (Y0 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (Y0 @ c_Empty)) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ c_Empty) => (?? @ $i @ (^[Y3 : $i]: (c_and @ (c_Subq @ Y3 @ Y2) @ (c_exactly2 @ (c_ordsucc @ (Y0 @ Y3))))))))))) => (?? @ $i @ (^[Y2 : $i]: (c_and @ (?? @ $i @ (^[Y3 : $i]: (c_and @ (c_Subq @ Y3 @ Y2) @ (((Y0 @ Y2) = Y2) => (?? @ $i @ (^[Y4 : $i]: (c_and @ (c_Subq @ Y4 @ Y2) @ (c_not @ (Y1 @ (c_setprod @ Y3 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty))))))))))))) @ (c_not @ (c_SNo @ Y2)))))) @ (c_not @ (Y1 @ (Y0 @ (Y0 @ (Y0 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty)))))))))))))))), 18.46/3.23 inference(fool_elimination,[],[f207])). 18.46/3.23 thf(f211,plain,( 18.46/3.23 (c_Sep = (^[X0 : $i, X1 : ($i > $o)] : ((c_If_i @ ? [X2 : $i] : (c_and @ (c_In @ X2 @ X0) @ (X1 @ X2)) @ (c_Repl @ X0 @ (^[X3 : $i] : (((^[X4 : $i] : ((c_If_i @ (X1 @ X4) @ X4 @ (c_Eps_i @ (^[X5 : $i] : ((c_and @ (c_In @ X5 @ X0) @ (X1 @ X5)))))))) @ X3)))) @ c_Empty))))), 18.46/3.23 inference(rectify,[],[f9])). 18.46/3.23 thf(f212,plain,( 18.46/3.23 (c_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (c_If_i @ (?? @ $i @ (^[Y2 : $i]: (c_and @ (c_In @ Y2 @ Y0) @ (Y1 @ Y2)))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (c_If_i @ (Y1 @ Y3) @ Y3 @ (c_Eps_i @ (^[Y4 : $i]: (c_and @ (c_In @ Y4 @ Y0) @ (Y1 @ Y4)))))) @ Y2))) @ c_Empty)))))), 18.46/3.23 inference(fool_elimination,[],[f211])). 18.46/3.23 thf(f217,plain,( 18.46/3.23 ((^[X0 : $i, X1 : $i] : ((c_and @ (c_Subq @ X1 @ (c_SNoElts_ @ X0)) @ ! [X2 : $i] : ((c_In @ X2 @ X0) => (c_exactly1of2 @ (c_In @ ((^[X3 : $i] : ((c_SetAdjoin @ X3 @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X2) @ X1) @ (c_In @ X2 @ X1)))))) = c_SNo_)), 18.46/3.23 inference(rectify,[],[f77])). 18.46/3.23 thf(f218,plain,( 18.46/3.23 (c_SNo_ = (^[Y0 : $i]: ((^[Y1 : $i]: (c_and @ (c_Subq @ Y1 @ (c_SNoElts_ @ Y0)) @ (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_exactly1of2 @ (c_In @ ((^[Y3 : $i]: (c_SetAdjoin @ Y3 @ (c_Sing @ (c_ordsucc @ c_Empty)))) @ Y2) @ Y1) @ (c_In @ Y2 @ Y1))))))))))), 18.46/3.23 inference(fool_elimination,[],[f217])). 18.46/3.23 thf(f225,plain,( 18.46/3.23 ((^[X0 : ($i > ($i > $i) > $i), X1 : $i] : ((c_Eps_i @ (^[X2 : $i] : ((c_In_rec_poly_G_i @ X0 @ X1 @ X2)))))) = c_In_rec_poly_i)), 18.46/3.23 inference(rectify,[],[f28])). 18.46/3.23 thf(f226,plain,( 18.46/3.23 (c_In_rec_poly_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2)))))))), 18.46/3.23 inference(fool_elimination,[],[f225])). 18.46/3.23 thf(f239,plain,( 18.46/3.23 (c_In_rec_poly_G_i = (^[X0 : ($i > ($i > $i) > $i), X1 : $i, X2 : $i] : (! [X3 : ($i > $i > $o)] : (! [X4 : $i,X5 : ($i > $i)] : (! [X6 : $i] : ((c_In @ X6 @ X4) => (X3 @ X6 @ (X5 @ X6))) => (X3 @ X4 @ (X0 @ X4 @ X5))) => (X3 @ X1 @ X2)))))), 18.46/3.23 inference(rectify,[],[f39])). 18.46/3.23 thf(f240,plain,( 18.46/3.23 (c_In_rec_poly_G_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y4 : $i > $i]: (!! @ $i @ (^[Y5 : $i]: ((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (Y3 @ Y6 @ (Y4 @ Y6))))) => (Y3 @ Y5 @ (Y0 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2))))))))))), 18.46/3.23 inference(fool_elimination,[],[f239])). 18.46/3.23 thf(f241,plain,( 18.46/3.23 (c_binintersect = (^[X0 : $i, X1 : $i] : ((c_Sep @ X0 @ (^[X2 : $i] : ((c_In @ X2 @ X1)))))))), 18.46/3.23 inference(rectify,[],[f67])). 18.46/3.23 thf(f242,plain,( 18.46/3.23 (c_binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Sep @ Y0 @ (^[Y2 : $i]: (c_In @ Y2 @ Y1)))))))), 18.46/3.23 inference(fool_elimination,[],[f241])). 18.46/3.23 thf(f247,plain,( 18.46/3.23 (c_ordsucc = (^[Y0 : $i]: (c_binunion @ Y0 @ (c_Sing @ Y0))))), 18.46/3.23 inference(fool_elimination,[],[f87])). 18.46/3.23 thf(f253,plain,( 18.46/3.23 ((^[X0 : $i, X1 : $i] : ((c_binunion @ (c_Repl @ X0 @ (^[X2 : $i] : ((c_Inj0 @ X2)))) @ (c_Repl @ X1 @ (^[X3 : $i] : ((c_Inj1 @ X3))))))) = c_setsum)), 18.46/3.23 inference(rectify,[],[f98])). 18.46/3.23 thf(f254,plain,( 18.46/3.23 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y2 : $i]: (c_Inj0 @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: (c_Inj1 @ Y2))))))))), 18.46/3.23 inference(fool_elimination,[],[f253])). 18.46/3.23 thf(f255,plain,( 18.46/3.23 ((^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_Subq @ X1 @ X0) @ (c_and @ (c_not @ (c_Subq @ X0 @ X1)) @ (c_atleast2 @ X1))))) = c_atleast3)), 18.46/3.23 inference(rectify,[],[f103])). 18.46/3.23 thf(f256,plain,( 18.46/3.23 (c_atleast3 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_Subq @ Y1 @ Y0) @ (c_and @ (c_not @ (c_Subq @ Y0 @ Y1)) @ (c_atleast2 @ Y1)))))))), 18.46/3.23 inference(fool_elimination,[],[f255])). 18.46/3.23 thf(f261,plain,( 18.46/3.23 (c_If_i = (^[X0 : $o, X1 : $i, X2 : $i] : ((c_Eps_i @ (^[X3 : $i] : ((c_or @ (c_and @ X0 @ (X3 = X1)) @ (c_and @ (c_not @ X0) @ (X3 = X2)))))))))), 18.46/3.23 inference(rectify,[],[f70])). 18.46/3.23 thf(f262,plain,( 18.46/3.23 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: (c_or @ (c_and @ Y0 @ (Y1 = Y3)) @ (c_and @ (c_not @ Y0) @ (Y2 = Y3)))))))))))), 18.46/3.23 inference(fool_elimination,[],[f261])). 18.46/3.23 thf(f273,plain,( 18.46/3.23 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))), 18.46/3.23 inference(rectify,[],[f31])). 18.46/3.23 thf(f274,plain,( 18.46/3.23 ($true = ((c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))))), 18.46/3.23 inference(fool_elimination,[],[f273])). 18.46/3.23 thf(f281,plain,( 18.46/3.23 ((^[X0 : $i] : ((c_and @ (c_TransSet @ X0) @ ! [X1 : $i] : ((c_In @ X1 @ X0) => (c_TransSet @ X1))))) = c_ordinal)), 18.46/3.23 inference(rectify,[],[f26])). 18.46/3.23 thf(f282,plain,( 18.46/3.23 (c_ordinal = (^[Y0 : $i]: (c_and @ (c_TransSet @ Y0) @ (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_TransSet @ Y1)))))))), 18.46/3.23 inference(fool_elimination,[],[f281])). 18.46/3.23 thf(f283,plain,( 18.46/3.23 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ (c_UPair @ Y0 @ Y1))))))), 18.46/3.23 inference(fool_elimination,[],[f48])). 18.46/3.23 thf(f292,plain,( 18.46/3.23 (c_Inj1 = ((c_In_rec_poly_i @ (^[X0 : $i, X1 : ($i > $i)] : ((c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))))), 18.46/3.23 inference(rectify,[],[f101])). 18.46/3.23 thf(f293,plain,( 18.46/3.23 (c_Inj1 = ((c_In_rec_poly_i @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 18.46/3.23 inference(fool_elimination,[],[f292])). 18.46/3.23 thf(f295,plain,( 18.46/3.23 ((^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))) = c_Subq)), 18.46/3.23 inference(rectify,[],[f83])). 18.46/3.23 thf(f296,plain,( 18.46/3.23 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))), 18.46/3.23 inference(fool_elimination,[],[f295])). 18.46/3.23 thf(f297,plain,( 18.46/3.23 (c_setprod = (^[X0 : $i, X1 : $i] : ((c_lam @ X0 @ (^[X2 : $i] : (X1))))))), 18.46/3.23 inference(rectify,[],[f30])). 18.46/3.23 thf(f298,plain,( 18.46/3.23 (c_setprod = (^[Y0 : $i]: ((^[Y1 : $i]: (c_lam @ Y0 @ (^[Y2 : $i]: (Y1)))))))), 18.46/3.23 inference(fool_elimination,[],[f297])). 18.46/3.23 thf(f301,plain,( 18.46/3.23 (c_exactly2 = (^[Y0 : $i]: (c_and @ (c_atleast2 @ Y0) @ (c_not @ (c_atleast3 @ Y0)))))), 18.46/3.23 inference(fool_elimination,[],[f106])). 18.46/3.23 thf(f308,plain,( 18.46/3.23 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))), 18.46/3.23 inference(cnf_transformation,[],[f296])). 18.46/3.23 thf(f312,plain,( 18.46/3.23 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ (c_UPair @ Y0 @ Y1))))))), 18.46/3.23 inference(cnf_transformation,[],[f283])). 18.46/3.23 thf(f316,plain,( 18.46/3.23 (c_Inj1 = ((c_In_rec_poly_i @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 18.46/3.23 inference(cnf_transformation,[],[f293])). 18.46/3.23 thf(f319,plain,( 18.46/3.23 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y2 : $i]: (c_Inj0 @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: (c_Inj1 @ Y2))))))))), 18.46/3.23 inference(cnf_transformation,[],[f254])). 18.46/3.23 thf(f322,plain,( 18.46/3.23 (c_setprod = (^[Y0 : $i]: ((^[Y1 : $i]: (c_lam @ Y0 @ (^[Y2 : $i]: (Y1)))))))), 18.46/3.23 inference(cnf_transformation,[],[f298])). 18.46/3.23 thf(f324,plain,( 18.46/3.23 ($true = ((c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))))), 18.46/3.23 inference(cnf_transformation,[],[f274])). 18.46/3.23 thf(f326,plain,( 18.46/3.23 (c_SNo = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_ordinal @ Y1) @ (c_SNo_ @ Y1 @ Y0))))))), 18.46/3.23 inference(cnf_transformation,[],[f201])). 18.46/3.23 thf(f327,plain,( 18.46/3.23 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))), 18.46/3.23 inference(cnf_transformation,[],[f191])). 18.46/3.23 thf(f329,plain,( 18.46/3.23 (c_famunion = (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_Union @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))), 18.46/3.23 inference(cnf_transformation,[],[f168])). 18.46/3.23 thf(f331,plain,( 18.46/3.23 (c_ordinal = (^[Y0 : $i]: (c_and @ (c_TransSet @ Y0) @ (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_TransSet @ Y1)))))))), 18.46/3.23 inference(cnf_transformation,[],[f282])). 18.46/3.23 thf(f334,plain,( 18.46/3.23 (c_SetAdjoin = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ Y0 @ (c_Sing @ Y1))))))), 18.46/3.23 inference(cnf_transformation,[],[f115])). 18.46/3.23 thf(f339,plain,( 18.46/3.23 (c_exactly2 = (^[Y0 : $i]: (c_and @ (c_atleast2 @ Y0) @ (c_not @ (c_atleast3 @ Y0)))))), 18.46/3.23 inference(cnf_transformation,[],[f301])). 18.46/3.23 thf(f343,plain,( 18.46/3.23 (c_binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Sep @ Y0 @ (^[Y2 : $i]: (c_In @ Y2 @ Y1)))))))), 18.46/3.23 inference(cnf_transformation,[],[f242])). 18.46/3.23 thf(f345,plain,( 18.46/3.23 ($true = ((~ (c_not @ (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (c_and @ (((Y1 @ (Y0 @ (c_binintersect @ (Y0 @ (c_Power @ c_Empty)) @ (Y0 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (Y0 @ c_Empty)) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ c_Empty) => (?? @ $i @ (^[Y3 : $i]: (c_and @ (c_Subq @ Y3 @ Y2) @ (c_exactly2 @ (c_ordsucc @ (Y0 @ Y3))))))))))) => (?? @ $i @ (^[Y2 : $i]: (c_and @ (?? @ $i @ (^[Y3 : $i]: (c_and @ (c_Subq @ Y3 @ Y2) @ (((Y0 @ Y2) = Y2) => (?? @ $i @ (^[Y4 : $i]: (c_and @ (c_Subq @ Y4 @ Y2) @ (c_not @ (Y1 @ (c_setprod @ Y3 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty))))))))))))) @ (c_not @ (c_SNo @ Y2)))))) @ (c_not @ (Y1 @ (Y0 @ (Y0 @ (Y0 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty)))))))))))))))), 18.46/3.23 inference(cnf_transformation,[],[f208])). 18.46/3.23 thf(f348,plain,( 18.46/3.23 (c_binrep = (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ Y0 @ (c_Power @ Y1))))))), 18.46/3.23 inference(cnf_transformation,[],[f185])). 18.46/3.23 thf(f354,plain,( 18.46/3.23 (c_atleast2 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_In @ Y1 @ Y0) @ (c_not @ (c_Subq @ Y0 @ (c_Power @ Y1))))))))), 18.46/3.23 inference(cnf_transformation,[],[f199])). 18.46/3.23 thf(f355,plain,( 18.46/3.23 (c_In_rec_poly_G_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y4 : $i > $i]: (!! @ $i @ (^[Y5 : $i]: ((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (Y3 @ Y6 @ (Y4 @ Y6))))) => (Y3 @ Y5 @ (Y0 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2))))))))))), 18.46/3.23 inference(cnf_transformation,[],[f240])). 18.46/3.23 thf(f357,plain,( 18.46/3.23 (c_exactly1of2 = (^[Y0 : $o]: ((^[Y1 : $o]: (c_or @ (c_and @ Y0 @ (c_not @ Y1)) @ (c_and @ (c_not @ Y0) @ Y1))))))), 18.46/3.23 inference(cnf_transformation,[],[f179])). 18.46/3.23 thf(f362,plain,( 18.46/3.23 (c_not = (^[Y0 : $o]: (Y0 => c_False)))), 18.46/3.23 inference(cnf_transformation,[],[f135])). 18.46/3.23 thf(f366,plain,( 18.46/3.23 (c_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (c_If_i @ (?? @ $i @ (^[Y2 : $i]: (c_and @ (c_In @ Y2 @ Y0) @ (Y1 @ Y2)))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (c_If_i @ (Y1 @ Y3) @ Y3 @ (c_Eps_i @ (^[Y4 : $i]: (c_and @ (c_In @ Y4 @ Y0) @ (Y1 @ Y4)))))) @ Y2))) @ c_Empty)))))), 18.46/3.23 inference(cnf_transformation,[],[f212])). 18.46/3.23 thf(f369,plain,( 18.46/3.23 (c_atleast3 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_Subq @ Y1 @ Y0) @ (c_and @ (c_not @ (c_Subq @ Y0 @ Y1)) @ (c_atleast2 @ Y1)))))))), 18.46/3.23 inference(cnf_transformation,[],[f256])). 18.46/3.23 thf(f371,plain,( 18.46/3.23 (c_lam = (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_famunion @ Y0 @ (^[Y2 : $i]: (c_Repl @ (Y1 @ Y2) @ (^[Y3 : $i]: (c_setsum @ Y2 @ Y3)))))))))), 18.46/3.23 inference(cnf_transformation,[],[f151])). 18.46/3.23 thf(f377,plain,( 18.46/3.23 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: (c_Inj1 @ Y1)))))), 18.46/3.23 inference(cnf_transformation,[],[f187])). 18.46/3.23 thf(f379,plain,( 18.46/3.23 (c_SNo_ = (^[Y0 : $i]: ((^[Y1 : $i]: (c_and @ (c_Subq @ Y1 @ (c_SNoElts_ @ Y0)) @ (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_exactly1of2 @ (c_In @ ((^[Y3 : $i]: (c_SetAdjoin @ Y3 @ (c_Sing @ (c_ordsucc @ c_Empty)))) @ Y2) @ Y1) @ (c_In @ Y2 @ Y1))))))))))), 18.46/3.23 inference(cnf_transformation,[],[f218])). 18.46/3.23 thf(f381,plain,( 18.46/3.23 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: (c_If_i @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))), 18.46/3.23 inference(cnf_transformation,[],[f161])). 18.46/3.23 thf(f391,plain,( 18.46/3.23 (c_Sing = (^[Y0 : $i]: (c_UPair @ Y0 @ Y0)))), 18.46/3.23 inference(cnf_transformation,[],[f120])). 18.46/3.23 thf(f394,plain,( 18.46/3.23 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: (c_or @ (c_and @ Y0 @ (Y1 = Y3)) @ (c_and @ (c_not @ Y0) @ (Y2 = Y3)))))))))))), 18.46/3.23 inference(cnf_transformation,[],[f262])). 18.46/3.23 thf(f400,plain,( 18.46/3.23 (c_TransSet = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_Subq @ Y1 @ Y0))))))), 18.46/3.23 inference(cnf_transformation,[],[f122])). 18.46/3.23 thf(f407,plain,( 18.46/3.23 (c_SNoElts_ = (^[Y0 : $i]: (c_binunion @ Y0 @ (c_Repl @ Y0 @ (^[Y1 : $i]: ((^[Y2 : $i]: (c_SetAdjoin @ Y2 @ (c_Sing @ (c_ordsucc @ c_Empty)))) @ Y1))))))), 18.46/3.23 inference(cnf_transformation,[],[f189])). 18.46/3.23 thf(f409,plain,( 18.46/3.23 (c_or = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => Y2) => ((Y1 => Y2) => Y2))))))))), 18.46/3.23 inference(cnf_transformation,[],[f139])). 18.46/3.23 thf(f411,plain,( 18.46/3.23 (c_ordsucc = (^[Y0 : $i]: (c_binunion @ Y0 @ (c_Sing @ Y0))))), 18.46/3.23 inference(cnf_transformation,[],[f247])). 18.46/3.23 thf(f413,plain,( 18.46/3.23 (c_In_rec_poly_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2)))))))), 18.46/3.23 inference(cnf_transformation,[],[f226])). 18.46/3.23 thf(f418,definition,( 18.46/3.23 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )), 18.46/3.23 introduced(theory,[fool_exhaustiveness_axiom])). 18.46/3.23 thf(f420,plain,( 18.46/3.23 (c_TransSet = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y1 @ Y0))))))), 18.46/3.23 inference(definition_unfolding,[],[f400,f308])). 18.46/3.23 thf(f421,plain,( 18.46/3.23 (c_atleast2 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (c_In @ Y1 @ Y0) @ ((^[Y2 : $o]: (Y2 => c_False)) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y0 @ (c_Power @ Y1))))))))), 18.46/3.23 inference(definition_unfolding,[],[f354,f327,f362,f308])). 18.46/3.23 thf(f422,plain,( 18.46/3.23 (c_atleast3 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y1 @ Y0) @ ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ ((^[Y2 : $o]: (Y2 => c_False)) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y0 @ Y1)) @ ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ (c_In @ Y3 @ Y2) @ ((^[Y4 : $o]: (Y4 => c_False)) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y2 @ (c_Power @ Y3))))))) @ Y1)))))))), 18.46/3.23 inference(definition_unfolding,[],[f369,f327,f308,f327,f362,f308,f421])). 18.46/3.23 thf(f426,plain,( 18.46/3.23 (c_exactly2 = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $o]: (!! @ $o @ (^[Y3 : $o]: ((Y1 => (Y2 => Y3)) => Y3)))))) @ ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ (c_In @ Y2 @ Y1) @ ((^[Y3 : $o]: (Y3 => c_False)) @ ((^[Y3 : $i]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y4))))))) @ Y1 @ (c_Power @ Y2))))))) @ Y0) @ ((^[Y1 : $o]: (Y1 => c_False)) @ ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ ((^[Y3 : $i]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y4))))))) @ Y2 @ Y1) @ ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ ((^[Y3 : $o]: (Y3 => c_False)) @ ((^[Y3 : $i]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y4))))))) @ Y1 @ Y2)) @ ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ (c_In @ Y4 @ Y3) @ ((^[Y5 : $o]: (Y5 => c_False)) @ ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y6))))))) @ Y3 @ (c_Power @ Y4))))))) @ Y2)))))) @ Y0)))))), 18.46/3.23 inference(definition_unfolding,[],[f339,f327,f421,f362,f422])). 18.46/3.23 thf(f440,plain,( 18.46/3.23 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => Y6) => ((Y5 => Y6) => Y6))))))) @ ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ Y0 @ (Y1 = Y3)) @ ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ ((^[Y4 : $o]: (Y4 => c_False)) @ Y0) @ (Y2 = Y3)))))))))))), 18.46/3.23 inference(definition_unfolding,[],[f394,f409,f327,f327,f362])). 18.46/3.23 thf(f441,plain,( 18.46/3.23 (c_exactly1of2 = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => Y4) => ((Y3 => Y4) => Y4))))))) @ ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ Y0 @ ((^[Y2 : $o]: (Y2 => c_False)) @ Y1)) @ ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ ((^[Y2 : $o]: (Y2 => c_False)) @ Y0) @ Y1))))))), 18.46/3.23 inference(definition_unfolding,[],[f357,f409,f327,f362,f327,f362])). 18.46/3.23 thf(f445,plain,( 18.46/3.23 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => Y9) => ((Y8 => Y9) => Y9))))))) @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ Y3 @ (Y4 = Y6)) @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ ((^[Y7 : $o]: (Y7 => c_False)) @ Y3) @ (Y5 = Y6)))))))))) @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))), 18.46/3.23 inference(definition_unfolding,[],[f381,f440])). 18.46/3.23 thf(f446,plain,( 18.46/3.23 (c_Sing = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (c_In @ c_Empty @ Y3) @ Y1 @ Y2)))))) @ Y0 @ Y0)))), 18.46/3.23 inference(definition_unfolding,[],[f391,f445])). 18.46/3.23 thf(f447,plain,( 18.46/3.23 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => Y11) => ((Y10 => Y11) => Y11))))))) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ Y5 @ (Y6 = Y8)) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ ((^[Y9 : $o]: (Y9 => c_False)) @ Y5) @ (Y7 = Y8)))))))))) @ (c_In @ c_Empty @ Y4) @ Y2 @ Y3)))))) @ Y0 @ Y1))))))), 18.46/3.23 inference(definition_unfolding,[],[f312,f445])). 18.46/3.23 thf(f448,plain,( 18.46/3.23 (c_SetAdjoin = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Union @ ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => Y13) => ((Y12 => Y13) => Y13))))))) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ Y7 @ (Y8 = Y10)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ ((^[Y11 : $o]: (Y11 => c_False)) @ Y7) @ (Y9 = Y10)))))))))) @ (c_In @ c_Empty @ Y6) @ Y4 @ Y5)))))) @ Y2 @ Y3))))) @ Y0 @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y6 @ (Y7 = Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y6) @ (Y8 = Y9)))))))))) @ (c_In @ c_Empty @ Y5) @ Y3 @ Y4)))))) @ Y2 @ Y2)) @ Y1))))))), 18.46/3.23 inference(definition_unfolding,[],[f334,f447,f446])). 18.46/3.23 thf(f449,plain,( 18.46/3.23 (c_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => Y8) => ((Y7 => Y8) => Y8))))))) @ ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => (Y7 => Y8)) => Y8)))))) @ Y2 @ (Y3 = Y5)) @ ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => (Y7 => Y8)) => Y8)))))) @ ((^[Y6 : $o]: (Y6 => c_False)) @ Y2) @ (Y4 = Y5)))))))))) @ (?? @ $i @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ (c_In @ Y2 @ Y0) @ (Y1 @ Y2)))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (Y1 @ Y3) @ Y3 @ (c_Eps_i @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ (c_In @ Y4 @ Y0) @ (Y1 @ Y4)))))) @ Y2))) @ c_Empty)))))), 18.46/3.23 inference(definition_unfolding,[],[f366,f440,f327,f440,f327])). 18.46/3.23 thf(f451,plain,( 18.46/3.23 (c_binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ (c_In @ Y4 @ Y2) @ (Y3 @ Y4)))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y6 @ (Y7 = Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y6) @ (Y8 = Y9)))))))))) @ (Y3 @ Y5) @ Y5 @ (c_Eps_i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ (c_In @ Y6 @ Y2) @ (Y3 @ Y6)))))) @ Y4))) @ c_Empty)))) @ Y0 @ (^[Y2 : $i]: (c_In @ Y2 @ Y1)))))))), 18.46/3.23 inference(definition_unfolding,[],[f343,f449])). 18.46/3.23 thf(f457,plain,( 18.46/3.23 (c_In_rec_poly_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: ((^[Y3 : $i > ($i > $i) > $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y7 : $i > $i]: (!! @ $i @ (^[Y8 : $i]: ((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (Y6 @ Y9 @ (Y7 @ Y9))))) => (Y6 @ Y8 @ (Y3 @ Y8 @ Y7))))))) => (Y6 @ Y4 @ Y5))))))))) @ Y0 @ Y1 @ Y2)))))))), 18.46/3.23 inference(definition_unfolding,[],[f413,f355])). 18.46/3.23 thf(f458,plain,( 18.46/3.23 (c_ordsucc = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Union @ ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y6 @ (Y7 = Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y6) @ (Y8 = Y9)))))))))) @ (c_In @ c_Empty @ Y5) @ Y3 @ Y4)))))) @ Y1 @ Y2))))) @ Y0 @ ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => Y11) => ((Y10 => Y11) => Y11))))))) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ Y5 @ (Y6 = Y8)) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ ((^[Y9 : $o]: (Y9 => c_False)) @ Y5) @ (Y7 = Y8)))))))))) @ (c_In @ c_Empty @ Y4) @ Y2 @ Y3)))))) @ Y1 @ Y1)) @ Y0))))), 18.46/3.23 inference(definition_unfolding,[],[f411,f447,f446])). 18.46/3.23 thf(f463,plain,( 18.46/3.23 (c_ordinal = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $o]: (!! @ $o @ (^[Y3 : $o]: ((Y1 => (Y2 => Y3)) => Y3)))))) @ ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y1) => ((^[Y3 : $i]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y4))))))) @ Y2 @ Y1))))) @ Y0) @ (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y2) => ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y3 @ Y2))))) @ Y1)))))))), 18.46/3.23 inference(definition_unfolding,[],[f331,f327,f420,f420])). 18.46/3.23 thf(f465,plain,( 18.46/3.23 (c_Inj1 = (((^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: ((^[Y3 : $i > ($i > $i) > $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y7 : $i > $i]: (!! @ $i @ (^[Y8 : $i]: ((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (Y6 @ Y9 @ (Y7 @ Y9))))) => (Y6 @ Y8 @ (Y3 @ Y8 @ Y7))))))) => (Y6 @ Y4 @ Y5))))))))) @ Y0 @ Y1 @ Y2)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Union @ ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: (!! 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@ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ ((^[Y11 : $o]: (Y11 => c_False)) @ Y7) @ (Y9 = Y10)))))))))) @ (c_In @ c_Empty @ Y6) @ Y4 @ Y5)))))) @ Y2 @ Y3))))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! 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@ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y5 @ Y5)) @ c_Empty) @ (c_Repl @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y2))))))))), 18.46/3.23 inference(definition_unfolding,[],[f319,f447,f466,f465])). 18.46/3.23 thf(f472,plain,( 18.46/3.23 (c_binrep = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => c_False)) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y9 @ Y9)) @ c_Empty) @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ Y4))) @ (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => Y17) => ((Y16 => Y17) => Y17))))))) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ Y11 @ (Y12 = Y14)) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ ((^[Y15 : $o]: (Y15 => c_False)) @ Y11) @ (Y13 = Y14)))))))))) @ (c_In @ c_Empty @ Y10) @ Y8 @ Y9)))))) @ Y7 @ Y7)) @ c_Empty) @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4))))))) @ Y0 @ (c_Power @ Y1))))))), 18.46/3.23 inference(definition_unfolding,[],[f348,f469])). 18.46/3.23 thf(f473,plain,( 18.46/3.23 (c_lam = (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: (c_Union @ (c_Repl @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y0 @ (^[Y2 : $i]: (c_Repl @ (Y1 @ Y2) @ (^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Union @ ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => Y17) => ((Y16 => Y17) => Y17))))))) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ Y11 @ (Y12 = Y14)) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ ((^[Y15 : $o]: (Y15 => c_False)) @ Y11) @ (Y13 = Y14)))))))))) @ (c_In @ c_Empty @ Y10) @ Y8 @ Y9)))))) @ Y6 @ Y7))))) @ (c_Repl @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ Y7 @ (^[Y8 : $i]: ((^[Y9 : $i > ($i > $i) > $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: ((^[Y12 : $i > ($i > $i) > $i]: ((^[Y13 : $i]: ((^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (Y12 @ Y17 @ Y16))))))) => (Y15 @ Y13 @ Y14))))))))) @ Y9 @ Y10 @ Y11)))))) @ (^[Y9 : $i]: ((^[Y10 : $i > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Union @ ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $i]: ((^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => Y22) => ((Y21 => Y22) => Y22))))))) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ Y16 @ (Y17 = Y19)) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ ((^[Y20 : $o]: (Y20 => c_False)) @ Y16) @ (Y18 = Y19)))))))))) @ (c_In @ c_Empty @ Y15) @ Y13 @ Y14)))))) @ Y11 @ Y12))))) @ ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $i]: ((^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => Y21) => ((Y20 => Y21) => Y21))))))) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ Y15 @ (Y16 = Y18)) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ ((^[Y19 : $o]: (Y19 => c_False)) @ Y15) @ (Y17 = Y18)))))))))) @ (c_In @ c_Empty @ Y14) @ Y12 @ Y13)))))) @ Y11 @ Y11)) @ c_Empty) @ (c_Repl @ Y9 @ (^[Y11 : $i]: (Y10 @ Y11))))))) @ Y8)))) @ Y6))) @ (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => c_False)) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y9 @ Y9)) @ c_Empty) @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6))))))) @ Y2 @ Y3)))))))))), 18.46/3.23 inference(definition_unfolding,[],[f371,f329,f469])). 18.46/3.23 thf(f474,plain,( 18.46/3.23 (c_setprod = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (c_Union @ (c_Repl @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y2 @ (^[Y4 : $i]: (c_Repl @ (Y3 @ Y4) @ (^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Union @ ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! 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@ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => c_False)) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y9 @ Y9)) @ c_Empty) @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6))))))) @ Y2 @ (c_Power @ Y3))))) @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty)))))))))))))))), 18.46/3.23 inference(definition_unfolding,[],[f345,f362,f327,f451,f472,f420,f327,f308,f426,f458,f327,f327,f308,f327,f308,f362,f474,f472,f472,f362,f492,f362,f472,f472,f472])). 18.46/3.23 thf(f512,definition,( 18.46/3.23 (sF0 = ((c_Power @ c_Empty)))), 18.46/3.23 introduced(definition,[new_symbols(definition,[sF0])],[function_definition])). 18.46/3.23 thf(f513,plain,( 18.46/3.23 (((c_Power @ c_Empty)) = sF0)), 18.46/3.23 inference(reorient_equations,[],[f512])). 18.46/3.23 thf(f514,definition,( 18.46/3.23 (sF1 = ((c_Power @ sF0)))), 18.46/3.23 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])). 18.46/3.23 thf(f515,plain,( 18.46/3.23 (((c_Power @ sF0)) = sF1)), 18.46/3.23 inference(reorient_equations,[],[f514])). 18.46/3.23 thf(f516,definition,( 18.46/3.23 (sF2 = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Repl @ sF1 @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (c_In @ c_Empty @ Y3) @ Y1 @ Y2)))))) @ Y0 @ Y0)) @ c_Empty)))), 18.46/3.23 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])). 18.46/3.23 thf(f517,definition,( 18.46/3.23 (sF3 = ((c_Power @ sF1)))), 18.46/3.23 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])). 18.46/3.23 thf(f518,definition,( 18.46/3.23 (sF4 = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ sF1 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ sF1 @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ sF2 @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ Y4))) @ (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ sF1 @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ sF2 @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4))))))) @ Y0 @ (c_Power @ Y1))))) @ sF3 @ c_Empty)))), 18.46/3.23 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])). 18.46/3.23 thf(f519,definition,( 18.46/3.23 (sF5 = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ sF1 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ sF1 @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ sF2 @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ Y4))) @ (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ sF1 @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ sF2 @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4))))))) @ Y0 @ (c_Power @ Y1))))) @ sF1 @ c_Empty)))), 18.46/3.23 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])). 18.46/3.23 thf(f520,definition,( 18.46/3.23 (sF6 = ((c_Power @ sF5)))), 18.46/3.23 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])). 18.46/3.23 thf(f521,plain,( 18.46/3.23 (((c_Power @ sF5)) = sF6)), 18.46/3.23 inference(reorient_equations,[],[f520])). 18.46/3.23 thf(f522,definition,( 18.46/3.23 (sF7 = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ sF1 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ sF1 @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! 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@ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ sF1 @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => c_False)) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ sF2 @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ Y4))) @ (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ sF1 @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! 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@ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (c_In @ c_Empty @ Y3) @ Y1 @ Y2)))))) @ Y0 @ Y0)) @ sF8)) = sF9)), 18.46/3.23 inference(reorient_equations,[],[f525])). 18.46/3.23 thf(f527,definition,( 18.46/3.23 (sF10 = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ sF1 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! 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@ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $i > ($i > $i) > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (Y10 @ Y15 @ Y14))))))) => (Y13 @ Y11 @ Y12))))))))) @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ sF1 @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! 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@ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y7) => ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: ((c_In @ Y11 @ Y9) => (c_In @ Y11 @ Y10))))))) @ Y8 @ Y7))))) @ Y6)))))) @ Y4) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y8))))))) @ Y6 @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Union @ ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ sF1 @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => c_False)) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y8 @ Y9))))) @ Y7 @ (c_Repl @ Y7 @ (^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Union @ ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Repl @ sF1 @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $i]: ((^[Y19 : $i]: (c_Eps_i @ (^[Y20 : $i]: ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => Y23) => ((Y22 => Y23) => Y23))))))) @ ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => (Y22 => Y23)) => Y23)))))) @ Y17 @ (Y18 = Y20)) @ ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => (Y22 => Y23)) => Y23)))))) @ ((^[Y21 : $o]: (Y21 => c_False)) @ Y17) @ (Y19 = Y20)))))))))) @ (c_In @ c_Empty @ Y16) @ Y14 @ Y15)))))) @ Y12 @ Y13))))) @ Y10 @ ((^[Y12 : $i]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Repl @ sF1 @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $i]: ((^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => Y22) => ((Y21 => Y22) => Y22))))))) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ Y16 @ (Y17 = Y19)) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ ((^[Y20 : $o]: (Y20 => c_False)) @ Y16) @ (Y18 = Y19)))))))))) @ (c_In @ c_Empty @ Y15) @ Y13 @ Y14)))))) @ Y12 @ Y12)) @ Y11))))) @ Y9 @ sF9)) @ Y8))))) @ Y5)) @ (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y8 @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y8) @ Y9))))) @ (c_In @ ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Union @ ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Repl @ sF1 @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $i]: ((^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => Y22) => ((Y21 => Y22) => Y22))))))) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ Y16 @ (Y17 = Y19)) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ ((^[Y20 : $o]: (Y20 => c_False)) @ Y16) @ (Y18 = Y19)))))))))) @ (c_In @ c_Empty @ Y15) @ Y13 @ Y14)))))) @ Y11 @ Y12))))) @ Y9 @ ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Repl @ sF1 @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $i]: ((^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => Y21) => ((Y20 => Y21) => Y21))))))) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ Y15 @ (Y16 = Y18)) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ ((^[Y19 : $o]: (Y19 => c_False)) @ Y15) @ (Y17 = Y18)))))))))) @ (c_In @ c_Empty @ Y14) @ Y12 @ Y13)))))) @ Y11 @ Y11)) @ Y10))))) @ Y8 @ sF9)) @ Y7) @ Y6) @ (c_In @ Y7 @ Y6))))))))) @ Y4 @ Y3))))) @ Y2)))))) @ ((^[Y2 : $o]: (Y2 => c_False)) @ (Y1 @ (Y0 @ (Y0 @ (Y0 @ sF11))))))))))) = sF12)), 18.46/3.23 inference(reorient_equations,[],[f530])). 18.46/3.23 thf(f532,definition,( 18.46/3.23 (sF13 = (((^[Y0 : $o]: (Y0 => c_False)) @ sF12)))), 18.46/3.23 introduced(definition,[new_symbols(definition,[sF13])],[function_definition])). 18.46/3.23 thf(f533,definition,( 18.46/3.23 (sF14 = ((~ sF13)))), 18.46/3.23 introduced(definition,[new_symbols(definition,[sF14])],[function_definition])). 18.46/3.23 thf(f534,plain,( 18.46/3.23 (sF14 = $true)), 18.46/3.23 inference(definition_folding,[],[f505,f533,f532,f531,f529,f527,f513,f521,f519,f515,f513,f516,f515,f513,f515,f513,f516,f515,f513,f515,f513,f515,f513,f516,f515,f513,f515,f513,f516,f515,f513,f515,f513,f515,f513,f516,f515,f513,f515,f513,f516,f515,f513,f515,f513,f515,f513,f526,f524,f515,f513,f515,f513,f515,f513,f515,f513,f515,f513,f526,f524,f515,f513,f515,f513,f515,f513,f515,f513,f515,f513,f515,f513,f523,f515,f513,f521,f519,f515,f513,f516,f515,f513,f515,f513,f516,f515,f513,f515,f513,f515,f513,f516,f515,f513,f515,f513,f516,f515,f513,f515,f513,f515,f513,f516,f515,f513,f515,f513,f516,f515,f513,f515,f513,f515,f513,f515,f513,f515,f513,f518,f517,f515,f513,f516,f515,f513,f515,f513,f516,f515,f513,f515,f513,f515,f513,f513])). 18.46/3.23 thf(f545,plain,( 18.46/3.23 (sF13 = ((sF12 => c_False)))), 18.46/3.23 inference(beta-eta_normalization,[],[f532])). 18.46/3.23 thf(f548,plain,( 18.46/3.23 (((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $o @ (^[Y2 : $o]: (((((Y1 @ (Y0 @ (c_Eps_i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $o @ (^[Y5 : $o]: (((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (Y0 @ sF0)) => ((c_In @ Y6 @ (Y0 @ sF4)) => Y7)) => Y7))))) => (((c_Repl @ (Y0 @ sF0) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ Y6 @ (Y0 @ sF4)) => ((Y6 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ Y6 @ (Y0 @ sF4)) => c_False) => (((c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ (Y0 @ sF0)) => ((c_In @ Y10 @ (Y0 @ sF4)) => Y11)) => Y11))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))) = Y3) => Y5)) => Y5))) => Y4) => (((!! @ $o @ (^[Y5 : $o]: ((((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (Y0 @ sF0)) => ((c_In @ Y6 @ (Y0 @ sF4)) => Y7)) => Y7))))) => c_False) => ((c_Empty = Y3) => Y5)) => Y5))) => Y4) => Y4)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ (Y0 @ c_Empty)) => (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y3) => (c_In @ Y4 @ (Y0 @ c_Empty)))))))) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ c_Empty) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y3)))) => ((!! @ $o @ (^[Y6 : $o]: (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((Y0 @ Y4) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ sF1 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((Y0 @ Y4) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => c_False) => (((Y0 @ Y4) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((Y0 @ Y4) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))))) => (c_In @ Y9 @ (c_Power @ Y7))))) => c_False) => Y8)) => Y8))))) => (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((Y0 @ Y4) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12))))))))))))) => ((!! @ $o @ (^[Y9 : $o]: ((((!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((Y0 @ Y4) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => (((Y0 @ Y4) = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => (((Y0 @ Y4) = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))))) => (c_In @ Y10 @ Y7)))) => c_False) => ((?? @ $i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ Y7) => (((!! @ $i @ (^[Y12 : $i]: ((c_In @ Y12 @ Y7) => (c_In @ Y12 @ (c_Power @ Y10))))) => c_False) => Y11)) => Y11))))) => Y9)) => Y9))) => Y8)) => Y8))))) => c_False) => Y6)) => Y6))) => Y5)) => Y5)))))))))) => (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y3)))) => ((((Y0 @ Y3) = Y3) => (?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y3)))) => (((Y1 @ (c_Union @ (c_Repl @ Y5 @ (^[Y9 : $i]: (c_Repl @ sF7 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((c_Repl @ Y9 @ (^[Y15 : $i]: (c_Repl @ Y15 @ (^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: (!! @ ($i > $i > $o) @ (^[Y18 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y19 : $i > $i]: (!! @ $i @ (^[Y20 : $i]: ((!! @ $i @ (^[Y21 : $i]: ((c_In @ Y21 @ Y20) => (Y18 @ Y21 @ (Y19 @ Y21))))) => (Y18 @ Y20 @ (c_Union @ (c_Repl @ sF1 @ (^[Y21 : $i]: (c_Eps_i @ (^[Y22 : $i]: (!! @ $o @ (^[Y23 : $o]: (((!! @ $o @ (^[Y24 : $o]: (((c_In @ c_Empty @ Y21) => ((sF2 = Y22) => Y24)) => Y24))) => Y23) => (((!! @ $o @ (^[Y24 : $o]: ((((c_In @ c_Empty @ Y21) => c_False) => (((c_Repl @ Y20 @ Y19) = Y22) => Y24)) => Y24))) => Y23) => Y23))))))))))))))) => (Y18 @ Y16 @ Y17)))))))))) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ Y10 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ ($i > $i > $o) @ (^[Y17 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y18 : $i > $i]: (!! @ $i @ (^[Y19 : $i]: ((!! @ $i @ (^[Y20 : $i]: ((c_In @ Y20 @ Y19) => (Y17 @ Y20 @ (Y18 @ Y20))))) => (Y17 @ Y19 @ (c_Union @ (c_Repl @ sF1 @ (^[Y20 : $i]: (c_Eps_i @ (^[Y21 : $i]: (!! @ $o @ (^[Y22 : $o]: (((!! @ $o @ (^[Y23 : $o]: (((c_In @ c_Empty @ Y20) => ((sF2 = Y21) => Y23)) => Y23))) => Y22) => (((!! @ $o @ (^[Y23 : $o]: ((((c_In @ c_Empty @ Y20) => c_False) => (((c_Repl @ Y19 @ Y18) = Y21) => Y23)) => Y23))) => Y22) => Y22))))))))))))))) => (Y17 @ Y15 @ Y16)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))))))) => c_False) => Y8)) => Y8)))))) => Y6)) => Y6))))) => (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (c_In @ Y9 @ Y5))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ Y9) => (c_In @ Y10 @ Y8)))))))))) => Y7)) => Y7))) => ((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y3) => (c_In @ Y8 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((Y5 = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ Y5 @ (^[Y13 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => ((Y13 = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF9 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => c_False) => ((sF9 = Y19) => Y21)) => Y21))) => Y20) => Y20)))))))) = Y15) => Y17)) => Y17))) => Y16) => Y16))))))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11))))))))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y8 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))) @ Y3) => (((c_In @ Y8 @ Y3) => c_False) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y8 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))) @ Y3) => c_False) => ((c_In @ Y8 @ Y3) => Y10)) => Y10))) => Y9) => Y9))))))) => Y7)) => Y7))) => Y6)) => Y6))))) => c_False) => Y4)) => Y4)))))) => (((Y1 @ (Y0 @ (Y0 @ (Y0 @ sF11)))) => c_False) => Y2)) => Y2)))))))) = sF12)), 18.46/3.23 inference(beta-eta_normalization,[],[f531])). 18.46/3.23 thf(f552,plain,( 18.46/3.23 ($true = (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) => c_False)))), 18.46/3.23 inference(beta-eta_normalization,[],[f504])). 18.46/3.23 thf(f555,plain,( 18.46/3.23 (((~ sF13)) = $true)), 18.46/3.23 inference(backward_demodulation,[],[f533,f534])). 18.46/3.23 thf(f557,plain,( 18.46/3.23 ($true = ((~ $true))) | ($false = sF13)), 18.46/3.23 inference(superposition,[],[f555,f418])). 18.46/3.23 thf(f558,plain,( 18.46/3.23 ($true = $false) | ($false = sF13)), 18.46/3.23 inference(boolean_simplification,[],[f557])). 18.46/3.23 thf(f559,plain,( 18.46/3.23 ($false = sF13)), 18.46/3.23 inference(trivial_inequality_removal,[],[f558])). 18.46/3.23 thf(f561,plain,( 18.46/3.23 ($false = ((sF12 => c_False)))), 18.46/3.23 inference(backward_demodulation,[],[f545,f559])). 18.46/3.24 thf(f564,plain,( 18.46/3.24 ($true = sF12)), 18.46/3.24 inference(imp_proxy_clausification,[],[f561])). 18.46/3.24 thf(f565,plain,( 18.46/3.24 (((sF12 => $true)) = $false) | (c_False = $false)), 18.46/3.24 inference(superposition,[],[f561,f418])). 18.46/3.24 thf(f570,plain,( 18.46/3.24 ($true = $false) | (c_False = $false)), 18.46/3.24 inference(boolean_simplification,[],[f565])). 18.46/3.24 thf(f571,plain,( 18.46/3.24 (c_False = $false)), 18.46/3.24 inference(trivial_inequality_removal,[],[f570])). 18.46/3.24 thf(f573,plain,( 18.46/3.24 ($true = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $o @ (^[Y2 : $o]: (((((Y1 @ (Y0 @ (c_Eps_i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $o @ (^[Y5 : $o]: (((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (Y0 @ sF0)) => ((c_In @ Y6 @ (Y0 @ sF4)) => Y7)) => Y7))))) => (((c_Repl @ (Y0 @ sF0) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ Y6 @ (Y0 @ sF4)) => ((Y6 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ Y6 @ (Y0 @ sF4)) => c_False) => (((c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ (Y0 @ sF0)) => ((c_In @ Y10 @ (Y0 @ sF4)) => Y11)) => Y11))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))) = Y3) => Y5)) => Y5))) => Y4) => (((!! @ $o @ (^[Y5 : $o]: ((((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (Y0 @ sF0)) => ((c_In @ Y6 @ (Y0 @ sF4)) => Y7)) => Y7))))) => c_False) => ((c_Empty = Y3) => Y5)) => Y5))) => Y4) => Y4)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ (Y0 @ c_Empty)) => (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y3) => (c_In @ Y4 @ (Y0 @ c_Empty)))))))) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ c_Empty) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y3)))) => ((!! @ $o @ (^[Y6 : $o]: (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((Y0 @ Y4) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ sF1 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((Y0 @ Y4) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => c_False) => (((Y0 @ Y4) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((Y0 @ Y4) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))))) => (c_In @ Y9 @ (c_Power @ Y7))))) => c_False) => Y8)) => Y8))))) => (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((Y0 @ Y4) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12))))))))))))) => ((!! @ $o @ (^[Y9 : $o]: ((((!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((Y0 @ Y4) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => (((Y0 @ Y4) = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => (((Y0 @ Y4) = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))))) => (c_In @ Y10 @ Y7)))) => c_False) => ((?? @ $i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ Y7) => (((!! @ $i @ (^[Y12 : $i]: ((c_In @ Y12 @ Y7) => (c_In @ Y12 @ (c_Power @ Y10))))) => c_False) => Y11)) => Y11))))) => Y9)) => Y9))) => Y8)) => Y8))))) => c_False) => Y6)) => Y6))) => Y5)) => Y5)))))))))) => (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y3)))) => ((((Y0 @ Y3) = Y3) => (?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y3)))) => (((Y1 @ (c_Union @ (c_Repl @ Y5 @ (^[Y9 : $i]: (c_Repl @ sF7 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((c_Repl @ Y9 @ (^[Y15 : $i]: (c_Repl @ Y15 @ (^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: (!! @ ($i > $i > $o) @ (^[Y18 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y19 : $i > $i]: (!! @ $i @ (^[Y20 : $i]: ((!! @ $i @ (^[Y21 : $i]: ((c_In @ Y21 @ Y20) => (Y18 @ Y21 @ (Y19 @ Y21))))) => (Y18 @ Y20 @ (c_Union @ (c_Repl @ sF1 @ (^[Y21 : $i]: (c_Eps_i @ (^[Y22 : $i]: (!! @ $o @ (^[Y23 : $o]: (((!! @ $o @ (^[Y24 : $o]: (((c_In @ c_Empty @ Y21) => ((sF2 = Y22) => Y24)) => Y24))) => Y23) => (((!! @ $o @ (^[Y24 : $o]: ((((c_In @ c_Empty @ Y21) => c_False) => (((c_Repl @ Y20 @ Y19) = Y22) => Y24)) => Y24))) => Y23) => Y23))))))))))))))) => (Y18 @ Y16 @ Y17)))))))))) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ Y10 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ ($i > $i > $o) @ (^[Y17 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y18 : $i > $i]: (!! @ $i @ (^[Y19 : $i]: ((!! @ $i @ (^[Y20 : $i]: ((c_In @ Y20 @ Y19) => (Y17 @ Y20 @ (Y18 @ Y20))))) => (Y17 @ Y19 @ (c_Union @ (c_Repl @ sF1 @ (^[Y20 : $i]: (c_Eps_i @ (^[Y21 : $i]: (!! @ $o @ (^[Y22 : $o]: (((!! @ $o @ (^[Y23 : $o]: (((c_In @ c_Empty @ Y20) => ((sF2 = Y21) => Y23)) => Y23))) => Y22) => (((!! @ $o @ (^[Y23 : $o]: ((((c_In @ c_Empty @ Y20) => c_False) => (((c_Repl @ Y19 @ Y18) = Y21) => Y23)) => Y23))) => Y22) => Y22))))))))))))))) => (Y17 @ Y15 @ Y16)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))))))) => c_False) => Y8)) => Y8)))))) => Y6)) => Y6))))) => (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (c_In @ Y9 @ Y5))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ Y9) => (c_In @ Y10 @ Y8)))))))))) => Y7)) => Y7))) => ((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y3) => (c_In @ Y8 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((Y5 = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ Y5 @ (^[Y13 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => ((Y13 = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF9 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => c_False) => ((sF9 = Y19) => Y21)) => Y21))) => Y20) => Y20)))))))) = Y15) => Y17)) => Y17))) => Y16) => Y16))))))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11))))))))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y8 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))) @ Y3) => (((c_In @ Y8 @ Y3) => c_False) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y8 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))) @ Y3) => c_False) => ((c_In @ Y8 @ Y3) => Y10)) => Y10))) => Y9) => Y9))))))) => Y7)) => Y7))) => Y6)) => Y6))))) => c_False) => Y4)) => Y4)))))) => (((Y1 @ (Y0 @ (Y0 @ (Y0 @ sF11)))) => c_False) => Y2)) => Y2)))))))))), 18.46/3.24 inference(backward_demodulation,[],[f548,f564])). 18.46/3.24 thf(f577,plain,( 18.46/3.24 ($true = (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) => $false)))), 18.46/3.24 inference(backward_demodulation,[],[f552,f571])). 18.46/3.24 thf(f579,plain,( 18.46/3.24 ($true = ((~ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))))), 18.46/3.24 inference(boolean_simplification,[],[f577])). 18.46/3.24 thf(f586,plain,( 18.46/3.24 (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))) = $false)), 18.46/3.24 inference(not_proxy_clausification,[],[f579])). 18.46/3.24 thf(f598,plain,( 18.46/3.24 ( ! [X1 : ($i > $i)] : (($true = (((^[Y0 : $i > $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $o @ (^[Y2 : $o]: (((((Y1 @ (Y0 @ (c_Eps_i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $o @ (^[Y5 : $o]: (((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (Y0 @ sF0)) => ((c_In @ Y6 @ (Y0 @ sF4)) => Y7)) => Y7))))) => (((c_Repl @ (Y0 @ sF0) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ Y6 @ (Y0 @ sF4)) => ((Y6 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ Y6 @ (Y0 @ sF4)) => c_False) => (((c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ (Y0 @ sF0)) => ((c_In @ Y10 @ (Y0 @ sF4)) => Y11)) => Y11))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))) = Y3) => Y5)) => Y5))) => Y4) => (((!! @ $o @ (^[Y5 : $o]: ((((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (Y0 @ sF0)) => ((c_In @ Y6 @ (Y0 @ sF4)) => Y7)) => Y7))))) => c_False) => ((c_Empty = Y3) => Y5)) => Y5))) => Y4) => Y4)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ (Y0 @ c_Empty)) => (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y3) => (c_In @ Y4 @ (Y0 @ c_Empty)))))))) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ c_Empty) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y3)))) => ((!! @ $o @ (^[Y6 : $o]: (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((Y0 @ Y4) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ sF1 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((Y0 @ Y4) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => c_False) => (((Y0 @ Y4) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((Y0 @ Y4) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))))) => (c_In @ Y9 @ (c_Power @ Y7))))) => c_False) => Y8)) => Y8))))) => (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ (c_Union @ (c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((Y0 @ Y4) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => c_False) => (((c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((Y0 @ Y4) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))) = Y11) => Y13)) => Y13))) => Y12) => Y12))))))))))))) => ((!! @ $o @ (^[Y9 : $o]: ((((!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((Y0 @ Y4) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => (((Y0 @ Y4) = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => (((Y0 @ Y4) = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))))) => (c_In @ Y10 @ Y7)))) => c_False) => ((?? @ $i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ Y7) => (((!! @ $i @ (^[Y12 : $i]: ((c_In @ Y12 @ Y7) => (c_In @ Y12 @ (c_Power @ Y10))))) => c_False) => Y11)) => Y11))))) => Y9)) => Y9))) => Y8)) => Y8))))) => c_False) => Y6)) => Y6))) => Y5)) => Y5)))))))))) => (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y3)))) => ((((Y0 @ Y3) = Y3) => (?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y3)))) => (((Y1 @ (c_Union @ (c_Repl @ Y5 @ (^[Y9 : $i]: (c_Repl @ sF7 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((c_Repl @ Y9 @ (^[Y15 : $i]: (c_Repl @ Y15 @ (^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: (!! @ ($i > $i > $o) @ (^[Y18 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y19 : $i > $i]: (!! @ $i @ (^[Y20 : $i]: ((!! @ $i @ (^[Y21 : $i]: ((c_In @ Y21 @ Y20) => (Y18 @ Y21 @ (Y19 @ Y21))))) => (Y18 @ Y20 @ (c_Union @ (c_Repl @ sF1 @ (^[Y21 : $i]: (c_Eps_i @ (^[Y22 : $i]: (!! @ $o @ (^[Y23 : $o]: (((!! @ $o @ (^[Y24 : $o]: (((c_In @ c_Empty @ Y21) => ((sF2 = Y22) => Y24)) => Y24))) => Y23) => (((!! @ $o @ (^[Y24 : $o]: ((((c_In @ c_Empty @ Y21) => c_False) => (((c_Repl @ Y20 @ Y19) = Y22) => Y24)) => Y24))) => Y23) => Y23))))))))))))))) => (Y18 @ Y16 @ Y17)))))))))) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ Y10 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ ($i > $i > $o) @ (^[Y17 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y18 : $i > $i]: (!! @ $i @ (^[Y19 : $i]: ((!! @ $i @ (^[Y20 : $i]: ((c_In @ Y20 @ Y19) => (Y17 @ Y20 @ (Y18 @ Y20))))) => (Y17 @ Y19 @ (c_Union @ (c_Repl @ sF1 @ (^[Y20 : $i]: (c_Eps_i @ (^[Y21 : $i]: (!! @ $o @ (^[Y22 : $o]: (((!! @ $o @ (^[Y23 : $o]: (((c_In @ c_Empty @ Y20) => ((sF2 = Y21) => Y23)) => Y23))) => Y22) => (((!! @ $o @ (^[Y23 : $o]: ((((c_In @ c_Empty @ Y20) => c_False) => (((c_Repl @ Y19 @ Y18) = Y21) => Y23)) => Y23))) => Y22) => Y22))))))))))))))) => (Y17 @ Y15 @ Y16)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))))))) => c_False) => Y8)) => Y8)))))) => Y6)) => Y6))))) => (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (c_In @ Y9 @ Y5))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ Y9) => (c_In @ Y10 @ Y8)))))))))) => Y7)) => Y7))) => ((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y3) => (c_In @ Y8 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((Y5 = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ Y5 @ (^[Y13 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => ((Y13 = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => c_False) => (((c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF9 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => c_False) => ((sF9 = Y19) => Y21)) => Y21))) => Y20) => Y20)))))))) = Y15) => Y17)) => Y17))) => Y16) => Y16))))))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11))))))))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y8 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))) @ Y3) => (((c_In @ Y8 @ Y3) => c_False) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y8 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))) @ Y3) => c_False) => ((c_In @ Y8 @ Y3) => Y10)) => Y10))) => Y9) => Y9))))))) => Y7)) => Y7))) => Y6)) => Y6))))) => c_False) => Y4)) => Y4)))))) => (((Y1 @ (Y0 @ (Y0 @ (Y0 @ sF11)))) => c_False) => Y2)) => Y2)))))) @ X1)))) )), 18.46/3.24 inference(pi_proxy_clausification,[],[f573])). 18.46/3.24 thf(f599,plain,( 18.46/3.24 ( ! 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@ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y2)))) => ((!! @ $o @ (^[Y5 : $o]: (((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y3) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => c_False) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y3) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => c_False) => (((X1 @ Y3) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ (c_Union @ (c_Repl @ sF1 @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((X1 @ Y3) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => c_False) => (((c_Repl @ sF1 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((X1 @ Y3) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => c_False) => (((X1 @ Y3) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))) => (c_In @ Y8 @ (c_Power @ Y6))))) => c_False) => Y7)) => Y7))))) => (((?? 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[X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? 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[X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? 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@ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => $false) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => $false) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => (((c_In @ Y5 @ Y0) => $false) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: ((((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => $false) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3))))) => $false) => Y1)) => Y1)))))) => ((~ (X2 @ (X1 @ (X1 @ (X1 @ sF11))))) => X3)) => X3)))) )), 18.46/3.24 inference(boolean_simplification,[],[f606])). 18.46/3.24 thf(f608,plain,( 18.46/3.24 ( ! [X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => $false) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => $false) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => $false) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => $false) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: ((((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => $false) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => $false) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4)))) => $false) => ((?? 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[X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => $false) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => $false) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => $false) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => $false) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => (((?? 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[X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : ((((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => (((?? 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[X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : (($true = ((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => $false) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4))))) => $false) => Y5)) => Y5))))) => (((?? 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[X2 : ($i > $o),X3 : $o,X1 : ($i > $i)] : ((((((((X2 @ (X1 @ (c_Eps_i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4))))) => (((c_Repl @ (X1 @ sF0) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ Y3 @ (X1 @ sF4)) => ((Y3 = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y3 @ (X1 @ sF4)) => $false) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (X1 @ sF0)) => ((c_In @ Y7 @ (X1 @ sF4)) => Y8)) => Y8))))) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))) = Y0) => Y2)) => Y2))) => Y1) => (((!! @ $o @ (^[Y2 : $o]: (((~ (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X1 @ sF0)) => ((c_In @ Y3 @ (X1 @ sF4)) => Y4)) => Y4)))))) => ((c_Empty = Y0) => Y2)) => Y2))) => Y1) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X1 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X1 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((X1 @ Y1) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ sF1 @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: (((~ (c_In @ c_Empty @ Y10)) => (((X1 @ Y1) = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))) => ((~ (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))) => (c_In @ Y6 @ (c_Power @ Y4)))))) => Y5)) => Y5))))) => ((~ (?? 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@ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => ((~ (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7)))))) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5)))))) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => ((~ (X2 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))))))) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? 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@ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_Union @ (c_Repl @ sF1 @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((X1 @ Y1) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: (((~ (c_In @ c_Empty @ Y7)) => (((c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((X1 @ Y1) = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))) => ((!! @ $o @ (^[Y6 : $o]: (((~ (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((X1 @ Y1) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => (((X1 @ Y1) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))) => (c_In @ Y7 @ Y4))))) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => ((~ (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7)))))) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5)))))) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X1 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => ((~ (X0 @ (c_Union @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_Repl @ sF7 @ (^[Y7 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ Y6 @ (^[Y12 : $i]: (c_Repl @ Y12 @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ ($i > $i > $o) @ (^[Y15 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y16 : $i > $i]: (!! @ $i @ (^[Y17 : $i]: ((!! @ $i @ (^[Y18 : $i]: ((c_In @ Y18 @ Y17) => (Y15 @ Y18 @ (Y16 @ Y18))))) => (Y15 @ Y17 @ (c_Union @ (c_Repl @ sF1 @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((sF2 = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: (((~ (c_In @ c_Empty @ Y18)) => (((c_Repl @ Y17 @ Y16) = Y19) => Y21)) => Y21))) => Y20) => Y20))))))))))))))) => (Y15 @ Y13 @ Y14)))))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ Y7 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ ($i > $i > $o) @ (^[Y14 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y15 : $i > $i]: (!! @ $i @ (^[Y16 : $i]: ((!! @ $i @ (^[Y17 : $i]: ((c_In @ Y17 @ Y16) => (Y14 @ Y17 @ (Y15 @ Y17))))) => (Y14 @ Y16 @ (c_Union @ (c_Repl @ sF1 @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((sF2 = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: (((~ (c_In @ c_Empty @ Y17)) => (((c_Repl @ Y16 @ Y15) = Y18) => Y20)) => Y20))) => Y19) => Y19))))))))))))))) => (Y14 @ Y12 @ Y13)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))))))) => Y5)) => Y5)))))) => Y3)) => Y3))))) => ((~ (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_Union @ (c_Repl @ sF1 @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => ((Y2 = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: (((~ (c_In @ c_Empty @ Y6)) => (((c_Repl @ Y2 @ (^[Y10 : $i]: (c_Union @ (c_Repl @ sF1 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((Y10 = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: (((~ (c_In @ c_Empty @ Y11)) => (((c_Repl @ sF1 @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: (((~ (c_In @ c_Empty @ Y15)) => ((sF9 = Y16) => Y18)) => Y18))) => Y17) => Y17)))))))) = Y12) => Y14)) => Y14))) => Y13) => Y13))))))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8))))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0) => ((~ (c_In @ Y5 @ Y0)) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: (((~ (c_In @ (c_Union @ (c_Repl @ sF1 @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((Y5 = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: (((~ (c_In @ c_Empty @ Y8)) => (((c_Repl @ sF1 @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: (((~ (c_In @ c_Empty @ Y12)) => ((sF9 = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => Y10))))))))) @ Y0)) => ((c_In @ Y5 @ Y0) => Y7)) => Y7))) => Y6) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3)))))) => Y1)) => Y1)))))) => $true) => X2)))) )), 18.46/3.24 inference(boolean_simplification,[],[f636])). 18.46/3.24 thf(f638,plain,( 18.46/3.24 ( ! [X2 : $o,X0 : ($i > $o),X1 : ($i > $i)] : (($true = (($true => X2))) | ($false = ((X0 @ (X1 @ (X1 @ (X1 @ sF11))))))) )), 18.46/3.24 inference(boolean_simplification,[],[f637])). 18.46/3.24 thf(f639,plain,( 18.46/3.24 ( ! [X2 : $o,X0 : ($i > $o),X1 : ($i > $i)] : (($false = ((X0 @ (X1 @ (X1 @ (X1 @ sF11)))))) | ($true = X2)) )), 18.46/3.24 inference(boolean_simplification,[],[f638])). 18.46/3.24 thf(f652,plain,( 18.46/3.24 ( ! [X2 : $o,X1 : ($i > $i)] : (((((^[Y0 : $i]: ($true)) @ (X1 @ (X1 @ (X1 @ sF11))))) = $false) | ($true = X2)) )), 18.46/3.24 inference(primitive_instantiation,[],[f639])). 18.46/3.24 thf(f658,plain,( 18.46/3.24 ( ! [X2 : $o] : (($true = $false) | ($true = X2)) )), 18.46/3.24 inference(beta-eta_normalization,[],[f652])). 18.46/3.24 thf(f659,plain,( 18.46/3.24 ( ! [X2 : $o] : (($true = X2)) )), 18.46/3.24 inference(trivial_inequality_removal,[],[f658])). 18.46/3.24 thf(f671,plain,( 18.46/3.24 ($true = $false)), 18.46/3.24 inference(superposition,[],[f586,f659])). 18.46/3.24 thf(f691,plain,( 18.46/3.24 $false), 18.46/3.24 inference(trivial_inequality_removal,[],[f671])). 18.46/3.24 % SZS output end Proof for theBenchmark 18.46/3.24 % (2883165)------------------------------ 18.46/3.24 % (2883165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.46/3.24 % (2883165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.46/3.24 % (2883165)CaDiCaL version: 2.1.3 18.46/3.24 % (2883165)Termination reason: Refutation 18.46/3.24 % (2883165)Time elapsed: 0.590 s 18.46/3.24 % (2883165)Peak memory usage: 17 MB 18.46/3.24 % (2883165)Instructions burned: 828 (million) 18.46/3.24 % (2882974)Success in time 2.681 s 18.46/3.24 % Vampire exiting 18.46/3.24 EOF