0.06/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s 0.12/0.34 % Computer : n028.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 300 0.12/0.34 % WCLimit : 300 0.12/0.34 % DateTime : Fri Jul 5 04:28:09 EDT 2024 0.12/0.34 % CPUTime : 0.12/0.36 This is a THF_ problem 0.12/0.36 Running vampire_ho --cores 8 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p 0.12/0.38 % (30329)lrs+1002_1:1_au=on:s2a=on:s2agt=32:sgt=8:ss=axioms:i=385:si=on:rtra=on_0 on theBenchmark for (2999ds/385Mi) 0.12/0.39 % (30330)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi) 0.12/0.39 % (30328)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on theBenchmark for (2999ds/34Mi) 0.12/0.39 % (30326)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2999ds/96Mi) 0.12/0.39 % (30331)ott+1010_1:1_cnfonf=lazy_gen:fe=off:kws=inv_arity:plsq=on:plsqc=1:plsqr=32,1:prag=on:sp=const_frequency:i=74:si=on:rtra=on_0 on theBenchmark for (2999ds/74Mi) 0.12/0.39 % (30332)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi) 0.12/0.39 % (30333)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=915:si=on:rtra=on_0 on theBenchmark for (2999ds/915Mi) 0.20/0.39 % (30332)Instruction limit reached! 0.20/0.39 % (30332)------------------------------ 0.20/0.39 % (30332)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.39 % (30332)Termination reason: Unknown 0.20/0.39 % (30332)Termination phase: shuffling 0.20/0.39 0.20/0.39 % (30332)Memory used [KB]: 1279 0.20/0.39 % (30332)Time elapsed: 0.004 s 0.20/0.39 % (30332)Instructions burned: 4 (million) 0.20/0.39 % (30332)------------------------------ 0.20/0.39 % (30332)------------------------------ 0.20/0.39 % (30327)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on theBenchmark for (2999ds/36Mi) 0.20/0.40 % (30330)Instruction limit reached! 0.20/0.40 % (30330)------------------------------ 0.20/0.40 % (30330)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.40 % (30330)Termination reason: Unknown 0.20/0.40 % (30330)Termination phase: shuffling 0.20/0.40 0.20/0.40 % (30330)Memory used [KB]: 1535 0.20/0.40 % (30330)Time elapsed: 0.011 s 0.20/0.40 % (30330)Instructions burned: 17 (million) 0.20/0.40 % (30330)------------------------------ 0.20/0.40 % (30330)------------------------------ 0.20/0.40 % (30329)Refutation not found, incomplete strategy 0.20/0.40 % (30329)------------------------------ 0.20/0.40 % (30329)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.40 % (30329)Termination reason: Refutation not found, incomplete strategy 0.20/0.40 0.20/0.40 0.20/0.40 % (30329)Memory used [KB]: 6268 0.20/0.40 % (30329)Time elapsed: 0.017 s 0.20/0.40 % (30329)Instructions burned: 58 (million) 0.20/0.40 % (30329)------------------------------ 0.20/0.40 % (30329)------------------------------ 0.20/0.41 % (30328)Instruction limit reached! 0.20/0.41 % (30328)------------------------------ 0.20/0.41 % (30328)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.41 % (30328)Termination reason: Unknown 0.20/0.41 % (30328)Termination phase: Property scanning 0.20/0.41 0.20/0.41 % (30328)Memory used [KB]: 1791 0.20/0.41 % (30328)Time elapsed: 0.019 s 0.20/0.41 % (30328)Instructions burned: 35 (million) 0.20/0.41 % (30328)------------------------------ 0.20/0.41 % (30328)------------------------------ 0.20/0.41 % (30336)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on theBenchmark for (2999ds/1021Mi) 0.20/0.41 % (30334)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi) 0.20/0.41 % (30327)Instruction limit reached! 0.20/0.41 % (30327)------------------------------ 0.20/0.41 % (30327)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.41 % (30327)Termination reason: Unknown 0.20/0.41 % (30327)Termination phase: Property scanning 0.20/0.41 0.20/0.41 % (30327)Memory used [KB]: 1791 0.20/0.41 % (30327)Time elapsed: 0.020 s 0.20/0.41 % (30327)Instructions burned: 38 (million) 0.20/0.41 % (30327)------------------------------ 0.20/0.41 % (30327)------------------------------ 0.20/0.41 % (30335)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi) 0.20/0.42 % (30335)Instruction limit reached! 0.20/0.42 % (30335)------------------------------ 0.20/0.42 % (30335)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.42 % (30335)Termination reason: Unknown 0.20/0.42 % (30335)Termination phase: shuffling 0.20/0.42 0.20/0.42 % (30335)Memory used [KB]: 1407 0.20/0.42 % (30335)Time elapsed: 0.006 s 0.20/0.42 % (30335)Instructions burned: 8 (million) 0.20/0.42 % (30335)------------------------------ 0.20/0.42 % (30335)------------------------------ 0.20/0.42 % (30334)Instruction limit reached! 0.20/0.42 % (30334)------------------------------ 0.20/0.42 % (30334)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.42 % (30334)Termination reason: Unknown 0.20/0.42 % (30334)Termination phase: shuffling 0.20/0.42 0.20/0.42 % (30334)Memory used [KB]: 1663 0.20/0.42 % (30334)Time elapsed: 0.013 s 0.20/0.42 % (30334)Instructions burned: 22 (million) 0.20/0.42 % (30334)------------------------------ 0.20/0.42 % (30334)------------------------------ 0.20/0.42 % (30337)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on theBenchmark for (2999ds/71Mi) 0.20/0.42 % (30331)Instruction limit reached! 0.20/0.42 % (30331)------------------------------ 0.20/0.42 % (30331)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.42 % (30331)Termination reason: Unknown 0.20/0.42 % (30331)Termination phase: Function definition elimination 0.20/0.42 0.20/0.42 % (30331)Memory used [KB]: 1918 0.20/0.42 % (30331)Time elapsed: 0.035 s 0.20/0.42 % (30331)Instructions burned: 74 (million) 0.20/0.42 % (30331)------------------------------ 0.20/0.42 % (30331)------------------------------ 0.20/0.43 % (30338)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=9:si=on:rtra=on_0 on theBenchmark for (2999ds/9Mi) 0.20/0.43 % (30338)Instruction limit reached! 0.20/0.43 % (30338)------------------------------ 0.20/0.43 % (30338)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.43 % (30338)Termination reason: Unknown 0.20/0.43 % (30338)Termination phase: shuffling 0.20/0.43 0.20/0.43 % (30338)Memory used [KB]: 1407 0.20/0.43 % (30338)Time elapsed: 0.007 s 0.20/0.43 % (30338)Instructions burned: 10 (million) 0.20/0.43 % (30338)------------------------------ 0.20/0.43 % (30338)------------------------------ 0.20/0.43 % (30339)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=1044:si=on:rtra=on_0 on theBenchmark for (2999ds/1044Mi) 0.20/0.43 % (30340)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=128:si=on:rtra=on_0 on theBenchmark for (2999ds/128Mi) 0.20/0.44 % (30326)Instruction limit reached! 0.20/0.44 % (30326)------------------------------ 0.20/0.44 % (30326)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.44 % (30326)Termination reason: Unknown 0.20/0.44 % (30326)Termination phase: Saturation 0.20/0.44 0.20/0.44 % (30326)Memory used [KB]: 6652 0.20/0.44 % (30326)Time elapsed: 0.047 s 0.20/0.44 % (30326)Instructions burned: 97 (million) 0.20/0.44 % (30326)------------------------------ 0.20/0.44 % (30326)------------------------------ 0.20/0.44 % (30341)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on theBenchmark for (2999ds/61Mi) 0.20/0.45 % (30342)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on theBenchmark for (2999ds/14Mi) 0.20/0.45 % (30343)lrs+2_5:1_cnfonf=lazy_not_be_gen:hud=10:inj=on:ntd=on:tnu=1:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi) 0.20/0.45 % (30343)Instruction limit reached! 0.20/0.45 % (30343)------------------------------ 0.20/0.45 % (30343)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.45 % (30343)Termination reason: Unknown 0.20/0.45 % (30343)Termination phase: shuffling 0.20/0.45 0.20/0.45 % (30343)Memory used [KB]: 1279 0.20/0.45 % (30343)Time elapsed: 0.004 s 0.20/0.45 % (30343)Instructions burned: 3 (million) 0.20/0.45 % (30343)------------------------------ 0.20/0.45 % (30343)------------------------------ 0.20/0.46 % (30342)Instruction limit reached! 0.20/0.46 % (30342)------------------------------ 0.20/0.46 % (30342)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.46 % (30342)Termination reason: Unknown 0.20/0.46 % (30342)Termination phase: shuffling 0.20/0.46 0.20/0.46 % (30342)Memory used [KB]: 1663 0.20/0.46 % (30342)Time elapsed: 0.011 s 0.20/0.46 % (30342)Instructions burned: 14 (million) 0.20/0.46 % (30342)------------------------------ 0.20/0.46 % (30342)------------------------------ 0.20/0.46 % (30337)Instruction limit reached! 0.20/0.46 % (30337)------------------------------ 0.20/0.46 % (30337)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.46 % (30337)Termination reason: Unknown 0.20/0.46 % (30337)Termination phase: Function definition elimination 0.20/0.46 0.20/0.46 % (30337)Memory used [KB]: 1791 0.20/0.46 % (30337)Time elapsed: 0.035 s 0.20/0.46 % (30337)Instructions burned: 72 (million) 0.20/0.46 % (30337)------------------------------ 0.20/0.46 % (30337)------------------------------ 0.20/0.46 % (30339)Refutation not found, incomplete strategy 0.20/0.46 % (30339)------------------------------ 0.20/0.46 % (30339)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.46 % (30339)Termination reason: Refutation not found, incomplete strategy 0.20/0.46 0.20/0.46 0.20/0.46 % (30339)Memory used [KB]: 6268 0.20/0.46 % (30339)Time elapsed: 0.030 s 0.20/0.46 % (30339)Instructions burned: 56 (million) 0.20/0.46 % (30339)------------------------------ 0.20/0.46 % (30339)------------------------------ 0.20/0.47 % (30344)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi) 0.20/0.47 % (30345)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on theBenchmark for (2999ds/11Mi) 0.20/0.47 % (30346)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on theBenchmark for (2999ds/140Mi) 0.20/0.47 % (30341)Instruction limit reached! 0.20/0.47 % (30341)------------------------------ 0.20/0.47 % (30341)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.47 % (30341)Termination reason: Unknown 0.20/0.47 % (30341)Termination phase: Property scanning 0.20/0.47 0.20/0.47 % (30341)Memory used [KB]: 2942 0.20/0.47 % (30341)Time elapsed: 0.036 s 0.20/0.47 % (30341)Instructions burned: 62 (million) 0.20/0.47 % (30341)------------------------------ 0.20/0.47 % (30341)------------------------------ 0.20/0.48 % (30345)Instruction limit reached! 0.20/0.48 % (30345)------------------------------ 0.20/0.48 % (30345)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.48 % (30345)Termination reason: Unknown 0.20/0.48 % (30347)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=26:si=on:rtra=on_0 on theBenchmark for (2999ds/26Mi) 0.20/0.48 % (30345)Termination phase: shuffling 0.20/0.48 0.20/0.48 % (30345)Memory used [KB]: 1407 0.20/0.48 % (30345)Time elapsed: 0.008 s 0.20/0.48 % (30345)Instructions burned: 12 (million) 0.20/0.48 % (30345)------------------------------ 0.20/0.48 % (30345)------------------------------ 0.20/0.48 % (30333)Refutation not found, incomplete strategy 0.20/0.48 % (30333)------------------------------ 0.20/0.48 % (30333)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.48 % (30333)Termination reason: Refutation not found, incomplete strategy 0.20/0.48 0.20/0.48 0.20/0.48 % (30333)Memory used [KB]: 8315 0.20/0.48 % (30333)Time elapsed: 0.088 s 0.20/0.48 % (30333)Instructions burned: 164 (million) 0.20/0.48 % (30333)------------------------------ 0.20/0.48 % (30333)------------------------------ 0.20/0.49 % (30347)Instruction limit reached! 0.20/0.49 % (30347)------------------------------ 0.20/0.49 % (30347)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.49 % (30347)Termination reason: Unknown 0.20/0.49 % (30347)Termination phase: shuffling 0.20/0.49 0.20/0.49 % (30347)Memory used [KB]: 1791 0.20/0.49 % (30347)Time elapsed: 0.013 s 0.20/0.49 % (30347)Instructions burned: 26 (million) 0.20/0.49 % (30347)------------------------------ 0.20/0.49 % (30347)------------------------------ 0.20/0.49 % (30350)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi) 0.20/0.49 % (30348)lrs+1002_1:4_au=on:av=off:bsr=on:cbe=off:nm=2:i=56:si=on:rtra=on_0 on theBenchmark for (2998ds/56Mi) 0.20/0.49 % (30350)Instruction limit reached! 0.20/0.49 % (30350)------------------------------ 0.20/0.49 % (30350)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.49 % (30350)Termination reason: Unknown 0.20/0.49 % (30350)Termination phase: shuffling 0.20/0.49 0.20/0.49 % (30350)Memory used [KB]: 1279 0.20/0.49 % (30350)Time elapsed: 0.002 s 0.20/0.49 % (30350)Instructions burned: 3 (million) 0.20/0.49 % (30350)------------------------------ 0.20/0.49 % (30350)------------------------------ 0.20/0.49 % (30349)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2998ds/275Mi) 0.20/0.49 % (30340)First to succeed. 0.20/0.49 % (30346)Refutation not found, incomplete strategy 0.20/0.49 % (30346)------------------------------ 0.20/0.49 % (30346)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.49 % (30346)Termination reason: Refutation not found, incomplete strategy 0.20/0.49 0.20/0.49 0.20/0.49 % (30346)Memory used [KB]: 6268 0.20/0.49 % (30346)Time elapsed: 0.025 s 0.20/0.49 % (30346)Instructions burned: 51 (million) 0.20/0.49 % (30346)------------------------------ 0.20/0.49 % (30346)------------------------------ 0.20/0.50 % (30351)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2998ds/19Mi) 0.20/0.50 % (30340)Refutation found. Thanks to Tanya! 0.20/0.50 % SZS status Theorem for theBenchmark 0.20/0.50 % SZS output start Proof for theBenchmark 0.20/0.50 thf(type_def_5, type, term: $tType). 0.20/0.50 thf(type_def_7, type, subst: $tType). 0.20/0.50 thf(func_def_0, type, term: $tType). 0.20/0.50 thf(func_def_1, type, subst: $tType). 0.20/0.50 thf(func_def_2, type, one: term). 0.20/0.50 thf(func_def_3, type, ap: term > term > term). 0.20/0.50 thf(func_def_4, type, lam: term > term). 0.20/0.50 thf(func_def_5, type, sub: term > subst > term). 0.20/0.50 thf(func_def_6, type, id: subst). 0.20/0.50 thf(func_def_7, type, sh: subst). 0.20/0.50 thf(func_def_8, type, push: term > subst > subst). 0.20/0.50 thf(func_def_9, type, comp: subst > subst > subst). 0.20/0.50 thf(func_def_10, type, var: term > $o). 0.20/0.50 thf(func_def_18, type, hoasap: subst > term > subst > term > term). 0.20/0.50 thf(func_def_73, type, hoaslam: subst > (subst > term > term) > term). 0.20/0.50 thf(func_def_86, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o). 0.20/0.50 thf(func_def_107, type, hoasvar: subst > term > subst > $o). 0.20/0.50 thf(func_def_121, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o). 0.20/0.50 thf(func_def_142, type, sK1: subst > term > term). 0.20/0.50 thf(func_def_143, type, sK2: subst > term > term). 0.20/0.50 thf(func_def_144, type, sK3: term). 0.20/0.50 thf(func_def_145, type, sK4: subst). 0.20/0.50 thf(f620,plain,( 0.20/0.50 $false), 0.20/0.50 inference(trivial_inequality_removal,[],[f619])). 0.20/0.50 thf(f619,plain,( 0.20/0.50 ((sK1 @ sK4 @ sK3) != (sK1 @ sK4 @ sK3))), 0.20/0.50 inference(superposition,[],[f577,f614])). 0.20/0.50 thf(f614,plain,( 0.20/0.50 ( ! [X0 : term,X1 : subst] : (((sK2 @ X1 @ X0) = (sK1 @ X1 @ X0))) )), 0.20/0.50 inference(forward_demodulation,[],[f613,f587])). 0.20/0.50 thf(f587,plain,( 0.20/0.50 ( ! [X0 : term,X1 : subst] : (((sK1 @ X1 @ X0) = (sub @ (sK1 @ sh @ one) @ (push @ X0 @ X1)))) )), 0.20/0.50 inference(superposition,[],[f579,f538])). 0.20/0.50 thf(f538,plain,( 0.20/0.50 ( ! [X2 : term,X1 : subst] : (((comp @ sh @ (push @ X2 @ X1)) = X1)) )), 0.20/0.50 inference(equality_proxy_clausification,[],[f537])). 0.20/0.50 thf(f537,plain,( 0.20/0.50 ( ! [X2 : term,X1 : subst] : ((((comp @ sh @ (push @ X2 @ X1)) = X1) = $true)) )), 0.20/0.50 inference(beta_eta_normalization,[],[f536])). 0.20/0.50 thf(f536,plain,( 0.20/0.50 ( ! [X2 : term,X1 : subst] : (($true = ((^[Y0 : term]: ((comp @ sh @ (push @ Y0 @ X1)) = X1)) @ X2))) )), 0.20/0.50 inference(pi_clausification,[],[f535])). 0.20/0.50 thf(f535,plain,( 0.20/0.50 ( ! [X1 : subst] : (($true = (!! @ term @ (^[Y0 : term]: ((comp @ sh @ (push @ Y0 @ X1)) = X1))))) )), 0.20/0.50 inference(beta_eta_normalization,[],[f534])). 0.20/0.50 thf(f534,plain,( 0.20/0.50 ( ! [X1 : subst] : (($true = ((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((comp @ sh @ (push @ Y1 @ Y0)) = Y0)))) @ X1))) )), 0.20/0.50 inference(pi_clausification,[],[f533])). 0.20/0.50 thf(f533,plain,( 0.20/0.50 ($true = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((comp @ sh @ (push @ Y1 @ Y0)) = Y0))))))), 0.20/0.50 inference(binary_proxy_clausification,[],[f525])). 0.20/0.50 thf(f525,plain,( 0.20/0.50 (((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((comp @ sh @ (push @ Y1 @ Y0)) = Y0))))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))) => (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2))))))))) => (((lam @ (Y0 @ sh @ one)) = (lam @ (Y1 @ sh @ one))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ Y3 @ Y2) = (Y1 @ Y3 @ Y2))))))))))))))) = $false)), 0.20/0.50 inference(binary_proxy_clausification,[],[f524])). 0.20/0.50 thf(f524,plain,( 0.20/0.50 ($true != ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sub @ one @ (push @ Y1 @ Y0)) = Y1))))) => ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((comp @ sh @ (push @ Y1 @ Y0)) = Y0))))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))) => (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2))))))))) => (((lam @ (Y0 @ sh @ one)) = (lam @ (Y1 @ sh @ one))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ Y3 @ Y2) = (Y1 @ Y3 @ Y2)))))))))))))))))), 0.20/0.50 inference(beta_eta_normalization,[],[f523])). 0.20/0.50 thf(f523,plain,( 0.20/0.50 ($true != ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sub @ one @ (push @ Y1 @ Y0)) = Y1))))) => ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((comp @ sh @ (push @ Y1 @ Y0)) = Y0))))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))) => (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2))))))))) => ((((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3))))) = ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3)))))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ Y3 @ Y2) = (Y1 @ Y3 @ Y2)))))))))))))))))), 0.20/0.50 inference(definition_unfolding,[],[f412,f498])). 0.20/0.50 thf(f498,plain,( 0.20/0.50 (hoaslaminj_lthm = ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sub @ one @ (push @ Y1 @ Y0)) = Y1))))) => ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((comp @ sh @ (push @ Y1 @ Y0)) = Y0))))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))) => (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2))))))))) => ((((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3))))) = ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3)))))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ Y3 @ Y2) = (Y1 @ Y3 @ Y2)))))))))))))))))), 0.20/0.50 inference(definition_unfolding,[],[f398,f432,f381,f402,f453])). 0.20/0.50 thf(f453,plain,( 0.20/0.50 (hoaslaminj = (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2))))))))) => ((((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3))))) = ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3)))))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ Y3 @ Y2) = (Y1 @ Y3 @ Y2))))))))))))))), 0.20/0.50 inference(definition_unfolding,[],[f411,f352,f352])). 0.20/0.50 thf(f352,plain,( 0.20/0.50 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (lam @ (Y1 @ sh @ one))))))), 0.20/0.50 inference(cnf_transformation,[],[f297])). 0.20/0.50 thf(f297,plain,( 0.20/0.50 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (lam @ (Y1 @ sh @ one))))))), 0.20/0.50 inference(fool_elimination,[],[f296])). 0.20/0.50 thf(f296,plain,( 0.20/0.50 (hoaslam = (^[X0 : subst, X1 : subst > term > term] : (lam @ (X1 @ sh @ one))))), 0.20/0.50 inference(rectify,[],[f56])). 0.20/0.50 thf(f56,axiom,( 0.20/0.50 (hoaslam = (^[X2 : subst, X10 : subst > term > term] : (lam @ (X10 @ sh @ one))))), 0.20/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslam)). 0.20/0.50 thf(f411,plain,( 0.20/0.50 (hoaslaminj = (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2))))))))) => (((hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3))))) = (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3)))))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ Y3 @ Y2) = (Y1 @ Y3 @ Y2))))))))))))))), 0.20/0.50 inference(cnf_transformation,[],[f265])). 0.20/0.50 thf(f265,plain,( 0.20/0.50 (hoaslaminj = (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2))))))))) => (((hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3))))) = (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3)))))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ Y3 @ Y2) = (Y1 @ Y3 @ Y2))))))))))))))), 0.20/0.50 inference(fool_elimination,[],[f264])). 0.20/0.50 thf(f264,plain,( 0.20/0.50 (! [X0 : subst > term > term] : (! [X1 : subst,X2 : term,X3 : subst] : ((sub @ (X0 @ X3 @ X2) @ X1) = (X0 @ (comp @ X3 @ X1) @ (sub @ X2 @ X1))) => ! [X4 : subst > term > term] : (! [X5 : term,X6 : subst,X7 : subst] : ((sub @ (X4 @ X6 @ X5) @ X7) = (X4 @ (comp @ X6 @ X7) @ (sub @ X5 @ X7))) => (((hoaslam @ id @ (^[X8 : subst, X9 : term] : (X0 @ X8 @ X9))) = (hoaslam @ id @ (^[X10 : subst, X11 : term] : (X4 @ X10 @ X11)))) => ! [X12 : subst,X13 : term] : ((X0 @ X12 @ X13) = (X4 @ X12 @ X13))))) = hoaslaminj)), 0.20/0.50 inference(rectify,[],[f64])). 0.20/0.50 thf(f64,axiom,( 0.20/0.50 (! [X10 : subst > term > term] : (! [X3 : subst,X0 : term,X2 : subst] : ((sub @ (X10 @ X2 @ X0) @ X3) = (X10 @ (comp @ X2 @ X3) @ (sub @ X0 @ X3))) => ! [X11 : subst > term > term] : (! [X0 : term,X2 : subst,X3 : subst] : ((sub @ (X11 @ X2 @ X0) @ X3) = (X11 @ (comp @ X2 @ X3) @ (sub @ X0 @ X3))) => (((hoaslam @ id @ (^[X2 : subst, X0 : term] : (X10 @ X2 @ X0))) = (hoaslam @ id @ (^[X2 : subst, X0 : term] : (X11 @ X2 @ X0)))) => ! [X2 : subst,X0 : term] : ((X10 @ X2 @ X0) = (X11 @ X2 @ X0))))) = hoaslaminj)), 0.20/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj)). 0.20/0.50 thf(f402,plain,( 0.20/0.50 (laminj = (!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))))), 0.20/0.50 inference(cnf_transformation,[],[f231])). 0.20/0.50 thf(f231,plain,( 0.20/0.50 (laminj = (!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))))), 0.20/0.50 inference(fool_elimination,[],[f230])). 0.20/0.50 thf(f230,plain,( 0.20/0.50 (! [X0 : term,X1 : term] : (((lam @ X0) = (lam @ X1)) => (X0 = X1)) = laminj)), 0.20/0.50 inference(rectify,[],[f18])). 0.20/0.50 thf(f18,axiom,( 0.20/0.50 (! [X1 : term,X0 : term] : (((lam @ X0) = (lam @ X1)) => (X0 = X1)) = laminj)), 0.20/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p',laminj)). 0.20/0.50 thf(f381,plain,( 0.20/0.50 (axshiftcons = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((comp @ sh @ (push @ Y1 @ Y0)) = Y0))))))), 0.20/0.50 inference(cnf_transformation,[],[f154])). 0.20/0.50 thf(f154,plain,( 0.20/0.50 (axshiftcons = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((comp @ sh @ (push @ Y1 @ Y0)) = Y0))))))), 0.20/0.50 inference(fool_elimination,[],[f153])). 0.20/0.50 thf(f153,plain,( 0.20/0.50 (! [X0 : term,X1 : subst] : ((comp @ sh @ (push @ X0 @ X1)) = X1) = axshiftcons)), 0.20/0.50 inference(rectify,[],[f7])). 0.20/0.50 thf(f7,axiom,( 0.20/0.50 (! [X0 : term,X2 : subst] : ((comp @ sh @ (push @ X0 @ X2)) = X2) = axshiftcons)), 0.20/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axshiftcons)). 0.20/0.50 thf(f432,plain,( 0.20/0.50 (axvarcons = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sub @ one @ (push @ Y1 @ Y0)) = Y1))))))), 0.20/0.50 inference(cnf_transformation,[],[f326])). 0.20/0.50 thf(f326,plain,( 0.20/0.50 (axvarcons = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sub @ one @ (push @ Y1 @ Y0)) = Y1))))))), 0.20/0.50 inference(fool_elimination,[],[f325])). 0.20/0.50 thf(f325,plain,( 0.20/0.50 (! [X0 : term,X1 : subst] : ((sub @ one @ (push @ X0 @ X1)) = X0) = axvarcons)), 0.20/0.50 inference(rectify,[],[f2])). 0.20/0.50 thf(f2,axiom,( 0.20/0.50 (! [X0 : term,X2 : subst] : ((sub @ one @ (push @ X0 @ X2)) = X0) = axvarcons)), 0.20/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarcons)). 0.20/0.50 thf(f398,plain,( 0.20/0.50 (hoaslaminj_lthm = (axvarcons => (axshiftcons => (laminj => hoaslaminj))))), 0.20/0.50 inference(cnf_transformation,[],[f156])). 0.20/0.50 thf(f156,plain,( 0.20/0.50 (hoaslaminj_lthm = (axvarcons => (axshiftcons => (laminj => hoaslaminj))))), 0.20/0.50 inference(fool_elimination,[],[f155])). 0.20/0.50 thf(f155,plain,( 0.20/0.50 (axvarcons => (axshiftcons => (laminj => hoaslaminj)) = hoaslaminj_lthm)), 0.20/0.50 inference(rectify,[],[f66])). 0.20/0.50 thf(f66,axiom,( 0.20/0.50 (axvarcons => (axshiftcons => (laminj => hoaslaminj)) = hoaslaminj_lthm)), 0.20/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj_lthm)). 0.20/0.50 thf(f412,plain,( 0.20/0.50 (hoaslaminj_lthm != $true)), 0.20/0.50 inference(cnf_transformation,[],[f331])). 0.20/0.50 thf(f331,plain,( 0.20/0.50 (hoaslaminj_lthm != $true)), 0.20/0.50 inference(flattening,[],[f291])). 0.20/0.50 thf(f291,plain,( 0.20/0.50 ~(hoaslaminj_lthm = $true)), 0.20/0.50 inference(fool_elimination,[],[f290])). 0.20/0.50 thf(f290,plain,( 0.20/0.50 ~hoaslaminj_lthm), 0.20/0.50 inference(rectify,[],[f115])). 0.20/0.50 thf(f115,negated_conjecture,( 0.20/0.50 ~hoaslaminj_lthm), 0.20/0.50 inference(negated_conjecture,[],[f114])). 0.20/0.50 thf(f114,conjecture,( 0.20/0.50 hoaslaminj_lthm), 0.20/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)). 0.20/0.50 thf(f579,plain,( 0.20/0.50 ( ! [X2 : subst,X0 : term,X1 : subst] : (((sK1 @ (comp @ X2 @ (push @ X0 @ X1)) @ X0) = (sub @ (sK1 @ X2 @ one) @ (push @ X0 @ X1)))) )), 0.20/0.50 inference(superposition,[],[f558,f531])). 0.20/0.50 thf(f531,plain,( 0.20/0.50 ( ! [X2 : term,X1 : subst] : (((sub @ one @ (push @ X2 @ X1)) = X2)) )), 0.20/0.50 inference(equality_proxy_clausification,[],[f530])). 0.20/0.50 thf(f530,plain,( 0.20/0.50 ( ! [X2 : term,X1 : subst] : ((((sub @ one @ (push @ X2 @ X1)) = X2) = $true)) )), 0.20/0.50 inference(beta_eta_normalization,[],[f529])). 0.20/0.50 thf(f529,plain,( 0.20/0.50 ( ! [X2 : term,X1 : subst] : (($true = ((^[Y0 : term]: ((sub @ one @ (push @ Y0 @ X1)) = Y0)) @ X2))) )), 0.20/0.50 inference(pi_clausification,[],[f528])). 0.20/0.50 thf(f528,plain,( 0.20/0.50 ( ! [X1 : subst] : (($true = (!! @ term @ (^[Y0 : term]: ((sub @ one @ (push @ Y0 @ X1)) = Y0))))) )), 0.20/0.50 inference(beta_eta_normalization,[],[f527])). 0.20/0.50 thf(f527,plain,( 0.20/0.50 ( ! [X1 : subst] : ((((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sub @ one @ (push @ Y1 @ Y0)) = Y1)))) @ X1) = $true)) )), 0.20/0.50 inference(pi_clausification,[],[f526])). 0.20/0.50 thf(f526,plain,( 0.20/0.50 ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sub @ one @ (push @ Y1 @ Y0)) = Y1))))) = $true)), 0.20/0.50 inference(binary_proxy_clausification,[],[f524])). 0.20/0.50 thf(f558,plain,( 0.20/0.50 ( ! [X2 : term,X3 : subst,X1 : subst] : (((sK1 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)) = (sub @ (sK1 @ X1 @ X2) @ X3))) )), 0.20/0.50 inference(equality_proxy_clausification,[],[f557])). 0.20/0.50 thf(f557,plain,( 0.20/0.50 ( ! [X2 : term,X3 : subst,X1 : subst] : (($true = ((sub @ (sK1 @ X1 @ X2) @ X3) = (sK1 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3))))) )), 0.20/0.50 inference(beta_eta_normalization,[],[f556])). 0.20/0.50 thf(f556,plain,( 0.20/0.50 ( ! [X2 : term,X3 : subst,X1 : subst] : ((((^[Y0 : subst]: ((sub @ (sK1 @ X1 @ X2) @ Y0) = (sK1 @ (comp @ X1 @ Y0) @ (sub @ X2 @ Y0)))) @ X3) = $true)) )), 0.20/0.50 inference(pi_clausification,[],[f555])). 0.20/0.50 thf(f555,plain,( 0.20/0.50 ( ! [X2 : term,X1 : subst] : (($true = (!! @ subst @ (^[Y0 : subst]: ((sub @ (sK1 @ X1 @ X2) @ Y0) = (sK1 @ (comp @ X1 @ Y0) @ (sub @ X2 @ Y0))))))) )), 0.20/0.50 inference(beta_eta_normalization,[],[f554])). 0.20/0.50 thf(f554,plain,( 0.20/0.50 ( ! [X2 : term,X1 : subst] : (($true = ((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (sK1 @ X1 @ Y0) @ Y1) = (sK1 @ (comp @ X1 @ Y1) @ (sub @ Y0 @ Y1)))))) @ X2))) )), 0.20/0.50 inference(pi_clausification,[],[f553])). 0.20/0.50 thf(f553,plain,( 0.20/0.50 ( ! [X1 : subst] : (($true = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (sK1 @ X1 @ Y0) @ Y1) = (sK1 @ (comp @ X1 @ Y1) @ (sub @ Y0 @ Y1))))))))) )), 0.20/0.50 inference(beta_eta_normalization,[],[f552])). 0.20/0.50 thf(f552,plain,( 0.20/0.50 ( ! [X1 : subst] : ((((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2)))))))) @ X1) = $true)) )), 0.20/0.50 inference(pi_clausification,[],[f551])). 0.20/0.50 thf(f551,plain,( 0.20/0.50 ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2))))))))) = $true)), 0.20/0.50 inference(binary_proxy_clausification,[],[f549])). 0.20/0.50 thf(f549,plain,( 0.20/0.50 (((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK1 @ Y0 @ Y1) @ Y2) = (sK1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2))))))))) => (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((sub @ (Y0 @ Y2 @ Y3) @ Y1) = (Y0 @ (comp @ Y2 @ Y1) @ (sub @ Y3 @ Y1))))))))) => (((lam @ (sK1 @ sh @ one)) = (lam @ (Y0 @ sh @ one))) => (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sK1 @ Y2 @ Y1) = (Y0 @ Y2 @ Y1))))))))))) = $false)), 0.20/0.50 inference(beta_eta_normalization,[],[f548])). 0.20/0.50 thf(f548,plain,( 0.20/0.50 ($false = ((^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2))))))))) => (((lam @ (Y0 @ sh @ one)) = (lam @ (Y1 @ sh @ one))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ Y3 @ Y2) = (Y1 @ Y3 @ Y2)))))))))))) @ sK1))), 0.20/0.50 inference(sigma_clausification,[],[f539])). 0.20/0.50 thf(f539,plain,( 0.20/0.50 ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2))))))))) => (((lam @ (Y0 @ sh @ one)) = (lam @ (Y1 @ sh @ one))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ Y3 @ Y2) = (Y1 @ Y3 @ Y2))))))))))))) = $false)), 0.20/0.50 inference(binary_proxy_clausification,[],[f532])). 0.20/0.50 thf(f532,plain,( 0.20/0.50 (((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))) => (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y1 @ Y2) @ Y3) = (Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((sub @ (Y1 @ Y3 @ Y4) @ Y2) = (Y1 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2))))))))) => (((lam @ (Y0 @ sh @ one)) = (lam @ (Y1 @ sh @ one))) => (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ Y3 @ Y2) = (Y1 @ Y3 @ Y2)))))))))))))) = $false)), 0.20/0.50 inference(binary_proxy_clausification,[],[f525])). 0.20/0.50 thf(f613,plain,( 0.20/0.50 ( ! [X0 : term,X1 : subst] : (((sK2 @ X1 @ X0) = (sub @ (sK1 @ sh @ one) @ (push @ X0 @ X1)))) )), 0.20/0.50 inference(forward_demodulation,[],[f609,f586])). 0.20/0.50 thf(f586,plain,( 0.20/0.50 ((sK1 @ sh @ one) = (sK2 @ sh @ one))), 0.20/0.50 inference(equality_resolution,[],[f581])). 0.20/0.50 thf(f581,plain,( 0.20/0.50 ( ! [X0 : term] : (((lam @ X0) != (lam @ (sK1 @ sh @ one))) | ((sK2 @ sh @ one) = X0)) )), 0.20/0.50 inference(superposition,[],[f547,f572])). 0.20/0.50 thf(f572,plain,( 0.20/0.50 ((lam @ (sK1 @ sh @ one)) = (lam @ (sK2 @ sh @ one)))), 0.20/0.50 inference(equality_proxy_clausification,[],[f571])). 0.20/0.50 thf(f571,plain,( 0.20/0.50 ($true = ((lam @ (sK1 @ sh @ one)) = (lam @ (sK2 @ sh @ one))))), 0.20/0.50 inference(binary_proxy_clausification,[],[f561])). 0.20/0.50 thf(f561,plain,( 0.20/0.50 ($false = (((lam @ (sK1 @ sh @ one)) = (lam @ (sK2 @ sh @ one))) => (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sK1 @ Y1 @ Y0) = (sK2 @ Y1 @ Y0))))))))), 0.20/0.50 inference(binary_proxy_clausification,[],[f560])). 0.20/0.50 thf(f560,plain,( 0.20/0.50 ($false = ((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((sub @ (sK2 @ Y1 @ Y2) @ Y0) = (sK2 @ (comp @ Y1 @ Y0) @ (sub @ Y2 @ Y0))))))))) => (((lam @ (sK1 @ sh @ one)) = (lam @ (sK2 @ sh @ one))) => (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sK1 @ Y1 @ Y0) = (sK2 @ Y1 @ Y0)))))))))), 0.20/0.50 inference(beta_eta_normalization,[],[f559])). 0.20/0.50 thf(f559,plain,( 0.20/0.50 ($false = ((^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((sub @ (Y0 @ Y2 @ Y3) @ Y1) = (Y0 @ (comp @ Y2 @ Y1) @ (sub @ Y3 @ Y1))))))))) => (((lam @ (sK1 @ sh @ one)) = (lam @ (Y0 @ sh @ one))) => (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sK1 @ Y2 @ Y1) = (Y0 @ Y2 @ Y1))))))))) @ sK2))), 0.20/0.50 inference(sigma_clausification,[],[f550])). 0.20/0.50 thf(f550,plain,( 0.20/0.50 ($false = (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((sub @ (Y0 @ Y2 @ Y3) @ Y1) = (Y0 @ (comp @ Y2 @ Y1) @ (sub @ Y3 @ Y1))))))))) => (((lam @ (sK1 @ sh @ one)) = (lam @ (Y0 @ sh @ one))) => (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sK1 @ Y2 @ Y1) = (Y0 @ Y2 @ Y1)))))))))))), 0.20/0.50 inference(binary_proxy_clausification,[],[f549])). 0.20/0.50 thf(f547,plain,( 0.20/0.50 ( ! [X2 : term,X1 : term] : (((lam @ X1) != (lam @ X2)) | (X1 = X2)) )), 0.20/0.50 inference(equality_proxy_clausification,[],[f546])). 0.20/0.50 thf(f546,plain,( 0.20/0.50 ( ! [X2 : term,X1 : term] : ((X1 = X2) | ($false = ((lam @ X2) = (lam @ X1)))) )), 0.20/0.50 inference(equality_proxy_clausification,[],[f545])). 0.20/0.50 thf(f545,plain,( 0.20/0.50 ( ! [X2 : term,X1 : term] : (((X2 = X1) = $true) | ($false = ((lam @ X2) = (lam @ X1)))) )), 0.20/0.50 inference(binary_proxy_clausification,[],[f544])). 0.20/0.50 thf(f544,plain,( 0.20/0.50 ( ! [X2 : term,X1 : term] : (($true = (((lam @ X2) = (lam @ X1)) => (X2 = X1)))) )), 0.20/0.50 inference(beta_eta_normalization,[],[f543])). 0.20/0.50 thf(f543,plain,( 0.20/0.50 ( ! [X2 : term,X1 : term] : (($true = ((^[Y0 : term]: (((lam @ Y0) = (lam @ X1)) => (Y0 = X1))) @ X2))) )), 0.20/0.50 inference(pi_clausification,[],[f542])). 0.20/0.50 thf(f542,plain,( 0.20/0.50 ( ! [X1 : term] : (($true = (!! @ term @ (^[Y0 : term]: (((lam @ Y0) = (lam @ X1)) => (Y0 = X1)))))) )), 0.20/0.50 inference(beta_eta_normalization,[],[f541])). 0.20/0.50 thf(f541,plain,( 0.20/0.50 ( ! [X1 : term] : ((((^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0))))) @ X1) = $true)) )), 0.20/0.50 inference(pi_clausification,[],[f540])). 0.20/0.50 thf(f540,plain,( 0.20/0.50 ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: (((lam @ Y1) = (lam @ Y0)) => (Y1 = Y0)))))) = $true)), 0.20/0.50 inference(binary_proxy_clausification,[],[f532])). 0.20/0.50 thf(f609,plain,( 0.20/0.50 ( ! [X0 : term,X1 : subst] : (((sub @ (sK2 @ sh @ one) @ (push @ X0 @ X1)) = (sK2 @ X1 @ X0))) )), 0.20/0.50 inference(superposition,[],[f583,f538])). 0.20/0.50 thf(f583,plain,( 0.20/0.50 ( ! [X2 : subst,X0 : term,X1 : subst] : (((sub @ (sK2 @ X2 @ one) @ (push @ X0 @ X1)) = (sK2 @ (comp @ X2 @ (push @ X0 @ X1)) @ X0))) )), 0.20/0.50 inference(superposition,[],[f569,f531])). 0.20/0.50 thf(f569,plain,( 0.20/0.50 ( ! [X2 : subst,X3 : term,X1 : subst] : (((sub @ (sK2 @ X2 @ X3) @ X1) = (sK2 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1)))) )), 0.20/0.50 inference(equality_proxy_clausification,[],[f568])). 0.20/0.50 thf(f568,plain,( 0.20/0.50 ( ! [X2 : subst,X3 : term,X1 : subst] : (($true = ((sub @ (sK2 @ X2 @ X3) @ X1) = (sK2 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1))))) )), 0.20/0.50 inference(beta_eta_normalization,[],[f567])). 0.20/0.50 thf(f567,plain,( 0.20/0.50 ( ! [X2 : subst,X3 : term,X1 : subst] : (($true = ((^[Y0 : term]: ((sub @ (sK2 @ X2 @ Y0) @ X1) = (sK2 @ (comp @ X2 @ X1) @ (sub @ Y0 @ X1)))) @ X3))) )), 0.20/0.50 inference(pi_clausification,[],[f566])). 0.20/0.50 thf(f566,plain,( 0.20/0.50 ( ! [X2 : subst,X1 : subst] : (($true = (!! @ term @ (^[Y0 : term]: ((sub @ (sK2 @ X2 @ Y0) @ X1) = (sK2 @ (comp @ X2 @ X1) @ (sub @ Y0 @ X1))))))) )), 0.20/0.50 inference(beta_eta_normalization,[],[f565])). 0.20/0.50 thf(f565,plain,( 0.20/0.50 ( ! [X2 : subst,X1 : subst] : ((((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sub @ (sK2 @ Y0 @ Y1) @ X1) = (sK2 @ (comp @ Y0 @ X1) @ (sub @ Y1 @ X1)))))) @ X2) = $true)) )), 0.20/0.50 inference(pi_clausification,[],[f564])). 0.20/0.50 thf(f564,plain,( 0.20/0.50 ( ! [X1 : subst] : (($true = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sub @ (sK2 @ Y0 @ Y1) @ X1) = (sK2 @ (comp @ Y0 @ X1) @ (sub @ Y1 @ X1))))))))) )), 0.20/0.50 inference(beta_eta_normalization,[],[f563])). 0.20/0.50 thf(f563,plain,( 0.20/0.50 ( ! [X1 : subst] : (($true = ((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((sub @ (sK2 @ Y1 @ Y2) @ Y0) = (sK2 @ (comp @ Y1 @ Y0) @ (sub @ Y2 @ Y0)))))))) @ X1))) )), 0.20/0.50 inference(pi_clausification,[],[f562])). 0.20/0.50 thf(f562,plain,( 0.20/0.50 ($true = (!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((sub @ (sK2 @ Y1 @ Y2) @ Y0) = (sK2 @ (comp @ Y1 @ Y0) @ (sub @ Y2 @ Y0))))))))))), 0.20/0.50 inference(binary_proxy_clausification,[],[f560])). 0.20/0.50 thf(f577,plain,( 0.20/0.50 ((sK2 @ sK4 @ sK3) != (sK1 @ sK4 @ sK3))), 0.20/0.50 inference(equality_proxy_clausification,[],[f576])). 0.20/0.50 thf(f576,plain,( 0.20/0.50 ($false = ((sK1 @ sK4 @ sK3) = (sK2 @ sK4 @ sK3)))), 0.20/0.50 inference(beta_eta_normalization,[],[f575])). 0.20/0.50 thf(f575,plain,( 0.20/0.50 ($false = ((^[Y0 : subst]: ((sK1 @ Y0 @ sK3) = (sK2 @ Y0 @ sK3))) @ sK4))), 0.20/0.50 inference(sigma_clausification,[],[f574])). 0.20/0.50 thf(f574,plain,( 0.20/0.50 ($false = (!! @ subst @ (^[Y0 : subst]: ((sK1 @ Y0 @ sK3) = (sK2 @ Y0 @ sK3)))))), 0.20/0.50 inference(beta_eta_normalization,[],[f573])). 0.20/0.50 thf(f573,plain,( 0.20/0.50 ($false = ((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sK1 @ Y1 @ Y0) = (sK2 @ Y1 @ Y0))))) @ sK3))), 0.20/0.50 inference(sigma_clausification,[],[f570])). 0.20/0.50 thf(f570,plain,( 0.20/0.50 ($false = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sK1 @ Y1 @ Y0) = (sK2 @ Y1 @ Y0)))))))), 0.20/0.50 inference(binary_proxy_clausification,[],[f561])). 0.20/0.50 % SZS output end Proof for theBenchmark 0.20/0.50 % (30340)------------------------------ 0.20/0.50 % (30340)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.50 % (30340)Termination reason: Refutation 0.20/0.50 0.20/0.50 % (30340)Memory used [KB]: 6780 0.20/0.50 % (30340)Time elapsed: 0.084 s 0.20/0.50 % (30340)Instructions burned: 117 (million) 0.20/0.50 % (30340)------------------------------ 0.20/0.50 % (30340)------------------------------ 0.20/0.50 % (30325)Success in time 0.129 s 0.20/0.50 % Vampire---4.8 exiting 0.20/0.50 EOF