TSTP Solution File: NUN025^3 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUN025^3 : TPTP v8.2.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% 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
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:16:58 EDT 2024
% Result : Theorem 0.15s 0.41s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUN025^3 : TPTP v8.2.0. Released v6.4.0.
% 0.11/0.14 % 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
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 15:05:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.37 % (20321)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.37 % (20321)Instruction limit reached!
% 0.15/0.37 % (20321)------------------------------
% 0.15/0.37 % (20321)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (20321)Termination reason: Unknown
% 0.15/0.37 % (20321)Termination phase: Saturation
% 0.15/0.37
% 0.15/0.37 % (20321)Memory used [KB]: 5500
% 0.15/0.37 % (20321)Time elapsed: 0.002 s
% 0.15/0.37 % (20321)Instructions burned: 2 (million)
% 0.15/0.37 % (20321)------------------------------
% 0.15/0.37 % (20321)------------------------------
% 0.15/0.38 % (20319)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.38 % (20320)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.38 % (20322)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.38 % (20318)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38 % (20324)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.38 % (20323)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 (2999ds/275Mi)
% 0.15/0.38 % (20325)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.38 % (20322)Instruction limit reached!
% 0.15/0.38 % (20322)------------------------------
% 0.15/0.38 % (20322)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (20322)Termination reason: Unknown
% 0.15/0.38 % (20322)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (20322)Memory used [KB]: 895
% 0.15/0.38 % (20322)Time elapsed: 0.003 s
% 0.15/0.38 % (20322)Instructions burned: 2 (million)
% 0.15/0.38 % (20322)------------------------------
% 0.15/0.38 % (20322)------------------------------
% 0.15/0.38 % (20325)Instruction limit reached!
% 0.15/0.38 % (20325)------------------------------
% 0.15/0.38 % (20325)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (20325)Termination reason: Unknown
% 0.15/0.38 % (20325)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (20325)Memory used [KB]: 5500
% 0.15/0.38 % (20325)Time elapsed: 0.004 s
% 0.15/0.38 % (20325)Instructions burned: 3 (million)
% 0.15/0.38 % (20325)------------------------------
% 0.15/0.38 % (20325)------------------------------
% 0.15/0.38 % (20326)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.15/0.38 % (20319)Instruction limit reached!
% 0.15/0.38 % (20319)------------------------------
% 0.15/0.38 % (20319)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (20319)Termination reason: Unknown
% 0.15/0.38 % (20319)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (20319)Memory used [KB]: 5500
% 0.15/0.38 % (20319)Time elapsed: 0.006 s
% 0.15/0.38 % (20319)Instructions burned: 5 (million)
% 0.15/0.38 % (20319)------------------------------
% 0.15/0.38 % (20319)------------------------------
% 0.15/0.39 % (20323)Refutation not found, incomplete strategy
% 0.15/0.39 % (20323)------------------------------
% 0.15/0.39 % (20323)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (20323)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.39
% 0.15/0.39
% 0.15/0.39 % (20323)Memory used [KB]: 5500
% 0.15/0.39 % (20323)Time elapsed: 0.009 s
% 0.15/0.39 % (20323)Instructions burned: 9 (million)
% 0.15/0.39 % (20323)------------------------------
% 0.15/0.39 % (20323)------------------------------
% 0.15/0.39 % (20320)Refutation not found, incomplete strategy
% 0.15/0.39 % (20320)------------------------------
% 0.15/0.39 % (20320)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (20320)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.39
% 0.15/0.39
% 0.15/0.39 % (20320)Memory used [KB]: 5500
% 0.15/0.39 % (20320)Time elapsed: 0.010 s
% 0.15/0.39 % (20320)Instructions burned: 10 (million)
% 0.15/0.39 % (20320)------------------------------
% 0.15/0.39 % (20320)------------------------------
% 0.15/0.39 % (20324)Instruction limit reached!
% 0.15/0.39 % (20324)------------------------------
% 0.15/0.39 % (20324)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (20324)Termination reason: Unknown
% 0.15/0.39 % (20324)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (20324)Memory used [KB]: 5628
% 0.15/0.39 % (20324)Time elapsed: 0.015 s
% 0.15/0.39 % (20324)Instructions burned: 19 (million)
% 0.15/0.39 % (20324)------------------------------
% 0.15/0.39 % (20324)------------------------------
% 0.15/0.39 % (20326)Instruction limit reached!
% 0.15/0.39 % (20326)------------------------------
% 0.15/0.39 % (20326)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (20326)Termination reason: Unknown
% 0.15/0.39 % (20326)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (20326)Memory used [KB]: 5756
% 0.15/0.39 % (20326)Time elapsed: 0.014 s
% 0.15/0.39 % (20326)Instructions burned: 38 (million)
% 0.15/0.39 % (20326)------------------------------
% 0.15/0.39 % (20326)------------------------------
% 0.15/0.39 % (20327)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.15/0.40 % (20328)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.40 % (20329)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)
% 0.15/0.40 % (20328)Instruction limit reached!
% 0.15/0.40 % (20328)------------------------------
% 0.15/0.40 % (20328)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (20328)Termination reason: Unknown
% 0.15/0.40 % (20328)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (20328)Memory used [KB]: 5500
% 0.15/0.40 % (20328)Time elapsed: 0.004 s
% 0.15/0.40 % (20328)Instructions burned: 3 (million)
% 0.15/0.40 % (20328)------------------------------
% 0.15/0.40 % (20328)------------------------------
% 0.15/0.40 % (20330)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.40 % (20331)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.15/0.40 % (20333)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.40 % (20333)Instruction limit reached!
% 0.15/0.40 % (20333)------------------------------
% 0.15/0.40 % (20333)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (20333)Termination reason: Unknown
% 0.15/0.40 % (20333)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (20333)Memory used [KB]: 5500
% 0.15/0.40 % (20333)Time elapsed: 0.003 s
% 0.15/0.40 % (20333)Instructions burned: 4 (million)
% 0.15/0.40 % (20333)------------------------------
% 0.15/0.40 % (20333)------------------------------
% 0.15/0.40 % (20327)First to succeed.
% 0.15/0.41 % (20327)Refutation found. Thanks to Tanya!
% 0.15/0.41 % SZS status Theorem for theBenchmark
% 0.15/0.41 % SZS output start Proof for theBenchmark
% 0.15/0.41 thf(func_def_1, type, s: $i > $i).
% 0.15/0.41 thf(func_def_2, type, ite: $o > $i > $i > $i).
% 0.15/0.41 thf(func_def_3, type, h: $i > $i).
% 0.15/0.41 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 0.15/0.41 thf(f105,plain,(
% 0.15/0.41 $false),
% 0.15/0.41 inference(avatar_sat_refutation,[],[f80,f95,f104])).
% 0.15/0.41 thf(f104,plain,(
% 0.15/0.41 spl0_2),
% 0.15/0.41 inference(avatar_contradiction_clause,[],[f103])).
% 0.15/0.41 thf(f103,plain,(
% 0.15/0.41 $false | spl0_2),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f100])).
% 0.15/0.41 thf(f100,plain,(
% 0.15/0.41 ((s @ zero) != (s @ zero)) | (zero != zero) | spl0_2),
% 0.15/0.41 inference(superposition,[],[f79,f48])).
% 0.15/0.41 thf(f48,plain,(
% 0.15/0.41 ( ! [X0 : $i] : ((zero = (h @ X0)) | ((s @ zero) != X0)) )),
% 0.15/0.41 inference(forward_demodulation,[],[f47,f16])).
% 0.15/0.41 thf(f16,plain,(
% 0.15/0.41 ( ! [X2 : $i,X3 : $i] : (((ite @ $true @ X2 @ X3) = X2)) )),
% 0.15/0.41 inference(equality_resolution,[],[f14])).
% 0.15/0.41 thf(f14,plain,(
% 0.15/0.41 ( ! [X2 : $i,X3 : $i,X1 : $o] : (($true != X1) | ((ite @ X1 @ X2 @ X3) = X2)) )),
% 0.15/0.41 inference(cnf_transformation,[],[f9])).
% 0.15/0.41 thf(f9,plain,(
% 0.15/0.41 ! [X0] : (zero != (s @ X0)) & ! [X1 : $o,X2,X3] : (($true != X1) | ((ite @ X1 @ X2 @ X3) = X2)) & ! [X4,X5,X6 : $o] : (((ite @ X6 @ X4 @ X5) = X5) | ($true = X6)) & ! [X7] : ((s @ X7) != X7) & ! [X8 : $i > $i] : (((s @ zero) != (X8 @ (s @ (s @ zero)))) | ((s @ zero) != (X8 @ zero)) | (zero != (X8 @ (s @ zero)))) & ! [X9] : ((ite @ (zero = X9) @ (s @ zero) @ (ite @ ((s @ zero) = X9) @ zero @ (s @ zero))) = (h @ X9))),
% 0.15/0.41 inference(rectify,[],[f8])).
% 0.15/0.41 thf(f8,plain,(
% 0.15/0.41 ! [X3] : ((s @ X3) != zero) & ! [X0 : $o,X1,X2] : (($true != X0) | ((ite @ X0 @ X1 @ X2) = X1)) & ! [X5,X6,X7 : $o] : (((ite @ X7 @ X5 @ X6) = X6) | ($true = X7)) & ! [X8] : ((s @ X8) != X8) & ! [X9 : $i > $i] : (((s @ zero) != (X9 @ (s @ (s @ zero)))) | ((s @ zero) != (X9 @ zero)) | (zero != (X9 @ (s @ zero)))) & ! [X4] : ((ite @ (zero = X4) @ (s @ zero) @ (ite @ ((s @ zero) = X4) @ zero @ (s @ zero))) = (h @ X4))),
% 0.15/0.41 inference(flattening,[],[f7])).
% 0.15/0.41 thf(f7,plain,(
% 0.15/0.41 ! [X9 : $i > $i] : (((s @ zero) != (X9 @ (s @ (s @ zero)))) | ((s @ zero) != (X9 @ zero)) | (zero != (X9 @ (s @ zero)))) & (! [X8] : ((s @ X8) != X8) & ! [X3] : ((s @ X3) != zero) & ! [X4] : ((ite @ (zero = X4) @ (s @ zero) @ (ite @ ((s @ zero) = X4) @ zero @ (s @ zero))) = (h @ X4)) & ! [X5,X6,X7 : $o] : (((ite @ X7 @ X5 @ X6) = X6) | ($true = X7)) & ! [X0 : $o,X1,X2] : (($true != X0) | ((ite @ X0 @ X1 @ X2) = X1)))),
% 0.15/0.41 inference(ennf_transformation,[],[f6])).
% 0.15/0.41 thf(f6,plain,(
% 0.15/0.41 ~((! [X8] : ((s @ X8) != X8) & ! [X3] : ((s @ X3) != zero) & ! [X4] : ((ite @ (zero = X4) @ (s @ zero) @ (ite @ ((s @ zero) = X4) @ zero @ (s @ zero))) = (h @ X4)) & ! [X5,X6,X7 : $o] : (($true != X7) => ((ite @ X7 @ X5 @ X6) = X6)) & ! [X0 : $o,X1,X2] : (($true = X0) => ((ite @ X0 @ X1 @ X2) = X1))) => ? [X9 : $i > $i] : (((s @ zero) = (X9 @ zero)) & (zero = (X9 @ (s @ zero))) & ((s @ zero) = (X9 @ (s @ (s @ zero))))))),
% 0.15/0.41 inference(flattening,[],[f5])).
% 0.15/0.41 thf(f5,plain,(
% 0.15/0.41 ~((! [X0 : $o,X1,X2] : (($true = X0) => ((ite @ X0 @ X1 @ X2) = X1)) & ! [X3] : ((s @ X3) != zero) & ! [X4] : ((ite @ (zero = X4) @ (s @ zero) @ (ite @ ((s @ zero) = X4) @ zero @ (s @ zero))) = (h @ X4)) & ! [X5,X6,X7 : $o] : (~($true = X7) => ((ite @ X7 @ X5 @ X6) = X6)) & ! [X8] : ((s @ X8) != X8)) => ? [X9 : $i > $i] : (((s @ zero) = (X9 @ zero)) & (zero = (X9 @ (s @ zero))) & ((s @ zero) = (X9 @ (s @ (s @ zero))))))),
% 0.15/0.41 inference(fool_elimination,[],[f4])).
% 0.15/0.41 thf(f4,plain,(
% 0.15/0.41 ~((! [X0 : $o,X1,X2] : (X0 => ((ite @ X0 @ X1 @ X2) = X1)) & ! [X3] : ((s @ X3) != zero) & ! [X4] : ((ite @ (zero = X4) @ (s @ zero) @ (ite @ ((s @ zero) = X4) @ zero @ (s @ zero))) = (h @ X4)) & ! [X5,X6,X7 : $o] : (~X7 => ((ite @ X7 @ X5 @ X6) = X6)) & ! [X8] : ((s @ X8) != X8)) => ? [X9 : $i > $i] : ((zero = (X9 @ (s @ zero))) & ((s @ zero) = (X9 @ zero)) & ((s @ zero) = (X9 @ (s @ (s @ zero))))))),
% 0.15/0.41 inference(rectify,[],[f2])).
% 0.15/0.41 thf(f2,negated_conjecture,(
% 0.15/0.41 ~((! [X0 : $o,X1,X2] : (X0 => ((ite @ X0 @ X1 @ X2) = X1)) & ! [X3] : ((s @ X3) != zero) & ! [X3] : ((ite @ (zero = X3) @ (s @ zero) @ (ite @ ((s @ zero) = X3) @ zero @ (s @ zero))) = (h @ X3)) & ! [X1,X2,X0 : $o] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3] : ((s @ X3) != X3)) => ? [X4 : $i > $i] : ((zero = (X4 @ (s @ zero))) & ((s @ zero) = (X4 @ zero)) & ((s @ zero) = (X4 @ (s @ (s @ zero))))))),
% 0.15/0.41 inference(negated_conjecture,[],[f1])).
% 0.15/0.41 thf(f1,conjecture,(
% 0.15/0.41 (! [X0 : $o,X1,X2] : (X0 => ((ite @ X0 @ X1 @ X2) = X1)) & ! [X3] : ((s @ X3) != zero) & ! [X3] : ((ite @ (zero = X3) @ (s @ zero) @ (ite @ ((s @ zero) = X3) @ zero @ (s @ zero))) = (h @ X3)) & ! [X1,X2,X0 : $o] : (~X0 => ((ite @ X0 @ X1 @ X2) = X2)) & ! [X3] : ((s @ X3) != X3)) => ? [X4 : $i > $i] : ((zero = (X4 @ (s @ zero))) & ((s @ zero) = (X4 @ zero)) & ((s @ zero) = (X4 @ (s @ (s @ zero)))))),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',n10)).
% 0.15/0.41 thf(f47,plain,(
% 0.15/0.41 ( ! [X0 : $i] : (((s @ zero) != X0) | ((h @ X0) = (ite @ $true @ zero @ (s @ zero)))) )),
% 0.15/0.41 inference(subsumption_resolution,[],[f44,f37])).
% 0.15/0.41 thf(f37,plain,(
% 0.15/0.41 ( ! [X0 : $i] : (((s @ zero) != X0) | (zero != X0)) )),
% 0.15/0.41 inference(superposition,[],[f22,f16])).
% 0.15/0.41 thf(f22,plain,(
% 0.15/0.41 ( ! [X0 : $i] : ((zero != (ite @ $true @ X0 @ (s @ zero))) | ((s @ zero) != X0)) )),
% 0.15/0.41 inference(duplicate_literal_removal,[],[f21])).
% 0.15/0.41 thf(f21,plain,(
% 0.15/0.41 ( ! [X0 : $i] : ((zero != (ite @ $true @ X0 @ (s @ zero))) | ((s @ zero) != X0) | ((s @ zero) != X0)) )),
% 0.15/0.41 inference(forward_demodulation,[],[f19,f16])).
% 0.15/0.41 thf(f19,plain,(
% 0.15/0.41 ( ! [X0 : $i] : (((s @ zero) != X0) | (zero != (ite @ $true @ X0 @ (s @ zero))) | ((s @ zero) != (ite @ $true @ X0 @ zero))) )),
% 0.15/0.41 inference(superposition,[],[f11,f16])).
% 0.15/0.41 thf(f11,plain,(
% 0.15/0.41 ( ! [X8 : $i > $i] : (((s @ zero) != (X8 @ (s @ (s @ zero)))) | ((s @ zero) != (X8 @ zero)) | (zero != (X8 @ (s @ zero)))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f9])).
% 0.15/0.41 thf(f44,plain,(
% 0.15/0.41 ( ! [X0 : $i] : ((zero = X0) | ((s @ zero) != X0) | ((h @ X0) = (ite @ $true @ zero @ (s @ zero)))) )),
% 0.15/0.41 inference(equality_proxy_clausification,[],[f39])).
% 0.15/0.41 thf(f39,plain,(
% 0.15/0.41 ( ! [X0 : $i] : (($false = ((s @ zero) = X0)) | (zero = X0) | ((h @ X0) = (ite @ $true @ zero @ (s @ zero)))) )),
% 0.15/0.41 inference(fool_paramodulation,[],[f32])).
% 0.15/0.41 thf(f32,plain,(
% 0.15/0.41 ( ! [X0 : $i] : (((h @ X0) = (ite @ ((s @ zero) = X0) @ zero @ (s @ zero))) | (zero = X0)) )),
% 0.15/0.41 inference(equality_proxy_clausification,[],[f26])).
% 0.15/0.41 thf(f26,plain,(
% 0.15/0.41 ( ! [X0 : $i] : (((h @ X0) = (ite @ ((s @ zero) = X0) @ zero @ (s @ zero))) | ((zero = X0) = $true)) )),
% 0.15/0.41 inference(superposition,[],[f10,f13])).
% 0.15/0.41 thf(f13,plain,(
% 0.15/0.41 ( ! [X6 : $o,X4 : $i,X5 : $i] : (((ite @ X6 @ X4 @ X5) = X5) | ($true = X6)) )),
% 0.15/0.41 inference(cnf_transformation,[],[f9])).
% 0.15/0.41 thf(f10,plain,(
% 0.15/0.41 ( ! [X9 : $i] : (((ite @ (zero = X9) @ (s @ zero) @ (ite @ ((s @ zero) = X9) @ zero @ (s @ zero))) = (h @ X9))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f9])).
% 0.15/0.41 thf(f79,plain,(
% 0.15/0.41 (zero != (h @ (s @ zero))) | spl0_2),
% 0.15/0.41 inference(avatar_component_clause,[],[f77])).
% 0.15/0.41 thf(f77,plain,(
% 0.15/0.41 spl0_2 <=> (zero = (h @ (s @ zero)))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.15/0.41 thf(f95,plain,(
% 0.15/0.41 spl0_1),
% 0.15/0.41 inference(avatar_contradiction_clause,[],[f94])).
% 0.15/0.41 thf(f94,plain,(
% 0.15/0.41 $false | spl0_1),
% 0.15/0.41 inference(subsumption_resolution,[],[f93,f15])).
% 0.15/0.41 thf(f15,plain,(
% 0.15/0.41 ( ! [X0 : $i] : ((zero != (s @ X0))) )),
% 0.15/0.41 inference(cnf_transformation,[],[f9])).
% 0.15/0.41 thf(f93,plain,(
% 0.15/0.41 (zero = (s @ zero)) | spl0_1),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f87])).
% 0.15/0.41 thf(f87,plain,(
% 0.15/0.41 ((s @ zero) != (s @ zero)) | (zero = (s @ zero)) | spl0_1),
% 0.15/0.41 inference(superposition,[],[f75,f46])).
% 0.15/0.41 thf(f46,plain,(
% 0.15/0.41 ( ! [X0 : $i] : (((s @ zero) = (h @ X0)) | ((s @ zero) = X0)) )),
% 0.15/0.41 inference(subsumption_resolution,[],[f45,f34])).
% 0.15/0.41 thf(f34,plain,(
% 0.15/0.41 ( ! [X9 : $i] : (((s @ zero) = (h @ X9)) | (zero != X9)) )),
% 0.15/0.41 inference(forward_demodulation,[],[f29,f16])).
% 0.15/0.41 thf(f29,plain,(
% 0.15/0.41 ( ! [X9 : $i] : ((zero != X9) | ((ite @ $true @ (s @ zero) @ (ite @ ((s @ zero) = X9) @ zero @ (s @ zero))) = (h @ X9))) )),
% 0.15/0.41 inference(equality_proxy_clausification,[],[f23])).
% 0.15/0.41 thf(f23,plain,(
% 0.15/0.41 ( ! [X9 : $i] : (($false = (zero = X9)) | ((ite @ $true @ (s @ zero) @ (ite @ ((s @ zero) = X9) @ zero @ (s @ zero))) = (h @ X9))) )),
% 0.15/0.41 inference(fool_paramodulation,[],[f10])).
% 0.15/0.41 thf(f45,plain,(
% 0.15/0.41 ( ! [X0 : $i] : (((s @ zero) = (h @ X0)) | ((s @ zero) = X0) | (zero = X0)) )),
% 0.15/0.41 inference(equality_proxy_clausification,[],[f40])).
% 0.15/0.41 thf(f40,plain,(
% 0.15/0.41 ( ! [X0 : $i] : ((zero = X0) | ((s @ zero) = (h @ X0)) | (((s @ zero) = X0) = $true)) )),
% 0.15/0.41 inference(superposition,[],[f32,f13])).
% 0.15/0.41 thf(f75,plain,(
% 0.15/0.41 ((s @ zero) != (h @ zero)) | spl0_1),
% 0.15/0.41 inference(avatar_component_clause,[],[f73])).
% 0.15/0.41 thf(f73,plain,(
% 0.15/0.41 spl0_1 <=> ((s @ zero) = (h @ zero))),
% 0.15/0.41 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.15/0.41 thf(f80,plain,(
% 0.15/0.41 ~spl0_1 | ~spl0_2),
% 0.15/0.41 inference(avatar_split_clause,[],[f71,f77,f73])).
% 0.15/0.41 thf(f71,plain,(
% 0.15/0.41 ((s @ zero) != (h @ zero)) | (zero != (h @ (s @ zero)))),
% 0.15/0.41 inference(subsumption_resolution,[],[f70,f12])).
% 0.15/0.41 thf(f12,plain,(
% 0.15/0.41 ( ! [X7 : $i] : (((s @ X7) != X7)) )),
% 0.15/0.41 inference(cnf_transformation,[],[f9])).
% 0.15/0.41 thf(f70,plain,(
% 0.15/0.41 ((s @ zero) != (h @ zero)) | ((s @ zero) = (s @ (s @ zero))) | (zero != (h @ (s @ zero)))),
% 0.15/0.41 inference(trivial_inequality_removal,[],[f69])).
% 0.15/0.41 thf(f69,plain,(
% 0.15/0.41 ((s @ zero) != (h @ zero)) | ((s @ zero) != (s @ zero)) | (zero != (h @ (s @ zero))) | ((s @ zero) = (s @ (s @ zero)))),
% 0.15/0.41 inference(superposition,[],[f11,f46])).
% 0.15/0.41 % SZS output end Proof for theBenchmark
% 0.15/0.41 % (20327)------------------------------
% 0.15/0.41 % (20327)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (20327)Termination reason: Refutation
% 0.15/0.41
% 0.15/0.41 % (20327)Memory used [KB]: 5628
% 0.15/0.41 % (20327)Time elapsed: 0.013 s
% 0.15/0.41 % (20327)Instructions burned: 13 (million)
% 0.15/0.41 % (20327)------------------------------
% 0.15/0.41 % (20327)------------------------------
% 0.15/0.41 % (20317)Success in time 0.03 s
% 0.15/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------