TSTP Solution File: NUM814^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : NUM814^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n025.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 : Mon Jun 24 13:18:01 EDT 2024
% Result : Theorem 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : NUM814^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.13/0.12 % Command : run_vampire %s %d THM
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Jun 23 00:21:24 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.21/0.35 This is a TH0_THM_EQU_NAR problem
% 0.21/0.35 Running higher-order theorem proving
% 0.21/0.35 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.21/0.38 % (22950)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.38 % (22952)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)
% 0.21/0.38 % (22951)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)
% 0.21/0.38 % (22953)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (22954)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)
% 0.21/0.38 % (22956)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)
% 0.21/0.38 % (22957)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38 % (22953)Instruction limit reached!
% 0.21/0.38 % (22953)------------------------------
% 0.21/0.38 % (22953)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (22953)Termination reason: Unknown
% 0.21/0.38 % (22953)Termination phase: Property scanning
% 0.21/0.38
% 0.21/0.38 % (22953)Memory used [KB]: 895
% 0.21/0.38 % (22953)Time elapsed: 0.003 s
% 0.21/0.38 % (22953)Instructions burned: 2 (million)
% 0.21/0.38 % (22953)------------------------------
% 0.21/0.38 % (22953)------------------------------
% 0.21/0.38 % (22954)Instruction limit reached!
% 0.21/0.38 % (22954)------------------------------
% 0.21/0.38 % (22954)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (22954)Termination reason: Unknown
% 0.21/0.38 % (22954)Termination phase: Property scanning
% 0.21/0.38
% 0.21/0.38 % (22954)Memory used [KB]: 1023
% 0.21/0.38 % (22954)Time elapsed: 0.004 s
% 0.21/0.38 % (22954)Instructions burned: 2 (million)
% 0.21/0.38 % (22954)------------------------------
% 0.21/0.38 % (22954)------------------------------
% 0.21/0.38 % (22956)Refutation not found, incomplete strategy
% 0.21/0.38 % (22956)------------------------------
% 0.21/0.38 % (22956)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (22956)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38
% 0.21/0.38
% 0.21/0.38 % (22956)Memory used [KB]: 5500
% 0.21/0.38 % (22956)Time elapsed: 0.005 s
% 0.21/0.38 % (22956)Instructions burned: 3 (million)
% 0.21/0.38 % (22956)------------------------------
% 0.21/0.38 % (22956)------------------------------
% 0.21/0.38 % (22951)Instruction limit reached!
% 0.21/0.38 % (22951)------------------------------
% 0.21/0.38 % (22951)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (22951)Termination reason: Unknown
% 0.21/0.38 % (22951)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (22951)Memory used [KB]: 5500
% 0.21/0.38 % (22951)Time elapsed: 0.005 s
% 0.21/0.38 % (22951)Instructions burned: 5 (million)
% 0.21/0.38 % (22951)------------------------------
% 0.21/0.38 % (22951)------------------------------
% 0.21/0.38 % (22952)Refutation not found, incomplete strategy
% 0.21/0.38 % (22952)------------------------------
% 0.21/0.38 % (22952)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (22952)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38
% 0.21/0.38
% 0.21/0.38 % (22952)Memory used [KB]: 5500
% 0.21/0.38 % (22952)Time elapsed: 0.007 s
% 0.21/0.38 % (22952)Instructions burned: 6 (million)
% 0.21/0.38 % (22952)------------------------------
% 0.21/0.38 % (22952)------------------------------
% 0.21/0.39 % (22957)Instruction limit reached!
% 0.21/0.39 % (22957)------------------------------
% 0.21/0.39 % (22957)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.39 % (22957)Termination reason: Unknown
% 0.21/0.39 % (22957)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (22957)Memory used [KB]: 5628
% 0.21/0.39 % (22957)Time elapsed: 0.016 s
% 0.21/0.39 % (22957)Instructions burned: 19 (million)
% 0.21/0.39 % (22957)------------------------------
% 0.21/0.39 % (22957)------------------------------
% 0.21/0.39 % (22958)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)
% 0.21/0.39 % (22959)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)
% 0.21/0.39 % (22960)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)
% 0.21/0.39 % (22961)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)
% 0.21/0.40 % (22958)Instruction limit reached!
% 0.21/0.40 % (22958)------------------------------
% 0.21/0.40 % (22958)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.40 % (22958)Termination reason: Unknown
% 0.21/0.40 % (22958)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (22958)Memory used [KB]: 5500
% 0.21/0.40 % (22958)Time elapsed: 0.005 s
% 0.21/0.40 % (22958)Instructions burned: 3 (million)
% 0.21/0.40 % (22958)------------------------------
% 0.21/0.40 % (22958)------------------------------
% 0.21/0.40 % (22962)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)
% 0.21/0.40 % (22961)Instruction limit reached!
% 0.21/0.40 % (22961)------------------------------
% 0.21/0.40 % (22961)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.40 % (22961)Termination reason: Unknown
% 0.21/0.40 % (22961)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (22961)Memory used [KB]: 5500
% 0.21/0.40 % (22961)Time elapsed: 0.004 s
% 0.21/0.40 % (22961)Instructions burned: 3 (million)
% 0.21/0.40 % (22961)------------------------------
% 0.21/0.40 % (22961)------------------------------
% 0.21/0.40 % (22963)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.41 % (22960)Instruction limit reached!
% 0.21/0.41 % (22960)------------------------------
% 0.21/0.41 % (22960)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (22960)Termination reason: Unknown
% 0.21/0.41 % (22960)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (22960)Memory used [KB]: 5628
% 0.21/0.41 % (22960)Time elapsed: 0.013 s
% 0.21/0.41 % (22960)Instructions burned: 15 (million)
% 0.21/0.41 % (22960)------------------------------
% 0.21/0.41 % (22960)------------------------------
% 0.21/0.41 % (22963)Instruction limit reached!
% 0.21/0.41 % (22963)------------------------------
% 0.21/0.41 % (22963)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (22963)Termination reason: Unknown
% 0.21/0.41 % (22963)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (22963)Memory used [KB]: 1023
% 0.21/0.41 % (22963)Time elapsed: 0.007 s
% 0.21/0.41 % (22963)Instructions burned: 7 (million)
% 0.21/0.41 % (22963)------------------------------
% 0.21/0.41 % (22963)------------------------------
% 0.21/0.41 % (22964)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.41 % (22965)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.41 % (22965)Instruction limit reached!
% 0.21/0.41 % (22965)------------------------------
% 0.21/0.41 % (22965)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (22965)Termination reason: Unknown
% 0.21/0.41 % (22965)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (22965)Memory used [KB]: 1023
% 0.21/0.41 % (22965)Time elapsed: 0.004 s
% 0.21/0.41 % (22965)Instructions burned: 3 (million)
% 0.21/0.41 % (22965)------------------------------
% 0.21/0.41 % (22965)------------------------------
% 0.21/0.41 % (22959)Instruction limit reached!
% 0.21/0.41 % (22959)------------------------------
% 0.21/0.41 % (22959)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (22959)Termination reason: Unknown
% 0.21/0.41 % (22959)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (22959)Memory used [KB]: 5884
% 0.21/0.41 % (22959)Time elapsed: 0.024 s
% 0.21/0.41 % (22959)Instructions burned: 37 (million)
% 0.21/0.41 % (22959)------------------------------
% 0.21/0.41 % (22959)------------------------------
% 0.21/0.42 % (22966)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)
% 0.21/0.42 % (22966)Instruction limit reached!
% 0.21/0.42 % (22966)------------------------------
% 0.21/0.42 % (22966)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.42 % (22966)Termination reason: Unknown
% 0.21/0.42 % (22966)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (22966)Memory used [KB]: 1023
% 0.21/0.42 % (22966)Time elapsed: 0.004 s
% 0.21/0.42 % (22966)Instructions burned: 3 (million)
% 0.21/0.42 % (22966)------------------------------
% 0.21/0.42 % (22966)------------------------------
% 0.21/0.42 % (22964)Instruction limit reached!
% 0.21/0.42 % (22964)------------------------------
% 0.21/0.42 % (22964)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.42 % (22964)Termination reason: Unknown
% 0.21/0.42 % (22964)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (22964)Memory used [KB]: 5756
% 0.21/0.42 % (22964)Time elapsed: 0.015 s
% 0.21/0.42 % (22964)Instructions burned: 16 (million)
% 0.21/0.42 % (22964)------------------------------
% 0.21/0.42 % (22964)------------------------------
% 0.21/0.43 % (22967)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.43 % (22950)First to succeed.
% 0.21/0.43 % (22950)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Theorem for theBenchmark
% 0.21/0.43 % SZS output start Proof for theBenchmark
% 0.21/0.43 thf(func_def_1, type, cS: $i > $i).
% 0.21/0.43 thf(func_def_2, type, cEVEN1: $i > $o).
% 0.21/0.43 thf(func_def_4, type, cODD1: $i > $o).
% 0.21/0.43 thf(func_def_18, type, sK1: ($i > $o) > $i).
% 0.21/0.43 thf(func_def_19, type, sK2: ($i > $o) > $i).
% 0.21/0.43 thf(func_def_20, type, ph3: !>[X0: $tType]:(X0)).
% 0.21/0.43 thf(func_def_21, type, sK4: $i > $i).
% 0.21/0.43 thf(f877,plain,(
% 0.21/0.43 $false),
% 0.21/0.43 inference(equality_resolution,[],[f876])).
% 0.21/0.43 thf(f876,plain,(
% 0.21/0.43 ( ! [X0 : $i] : ((c0 != X0)) )),
% 0.21/0.43 inference(subsumption_resolution,[],[f875,f44])).
% 0.21/0.43 thf(f44,plain,(
% 0.21/0.43 ( ! [X1 : $i] : ((c0 != (cS @ X1))) )),
% 0.21/0.43 inference(equality_proxy_clausification,[],[f43])).
% 0.21/0.43 thf(f43,plain,(
% 0.21/0.43 ( ! [X1 : $i] : (($false = (c0 = (cS @ X1)))) )),
% 0.21/0.43 inference(not_proxy_clausification,[],[f42])).
% 0.21/0.43 thf(f42,plain,(
% 0.21/0.43 ( ! [X1 : $i] : (((~ (c0 = (cS @ X1))) = $true)) )),
% 0.21/0.43 inference(beta_eta_normalization,[],[f41])).
% 0.21/0.43 thf(f41,plain,(
% 0.21/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (~ (c0 = (cS @ Y0)))) @ X1))) )),
% 0.21/0.43 inference(pi_clausification,[],[f32])).
% 0.21/0.43 thf(f32,plain,(
% 0.21/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: (~ (c0 = (cS @ Y0))))))),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f31])).
% 0.21/0.43 thf(f31,plain,(
% 0.21/0.43 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (~ (c0 = (cS @ Y0)))))))),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f29])).
% 0.21/0.43 thf(f29,plain,(
% 0.21/0.43 ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (~ (c0 = (cS @ Y0)))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ Y0))))))),
% 0.21/0.43 inference(beta_eta_normalization,[],[f28])).
% 0.21/0.43 thf(f28,plain,(
% 0.21/0.43 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (~ (c0 = (cS @ Y0)))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))) = $true)),
% 0.21/0.43 inference(definition_unfolding,[],[f22,f26])).
% 0.21/0.43 thf(f26,plain,(
% 0.21/0.43 (cPEANO1 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (~ (c0 = (cS @ Y0)))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 0.21/0.43 inference(definition_unfolding,[],[f21,f20])).
% 0.21/0.43 thf(f20,plain,(
% 0.21/0.43 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 0.21/0.43 inference(cnf_transformation,[],[f13])).
% 0.21/0.43 thf(f13,plain,(
% 0.21/0.43 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 0.21/0.43 inference(fool_elimination,[],[f12])).
% 0.21/0.43 thf(f12,plain,(
% 0.21/0.43 (! [X0 : $i > $o] : ((! [X1] : ((X0 @ X1) => (X0 @ (cS @ X1))) & (X0 @ c0)) => ! [X2] : (X0 @ X2)) = cIND)),
% 0.21/0.43 inference(rectify,[],[f2])).
% 0.21/0.43 thf(f2,axiom,(
% 0.21/0.43 (! [X1 : $i > $o] : ((! [X2] : ((X1 @ X2) => (X1 @ (cS @ X2))) & (X1 @ c0)) => ! [X2] : (X1 @ X2)) = cIND)),
% 0.21/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cIND_def)).
% 0.21/0.43 thf(f21,plain,(
% 0.21/0.43 (cPEANO1 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (~ (c0 = (cS @ Y0)))))) & cIND))),
% 0.21/0.43 inference(cnf_transformation,[],[f17])).
% 0.21/0.43 thf(f17,plain,(
% 0.21/0.43 (cPEANO1 = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (~ (c0 = (cS @ Y0)))))) & cIND))),
% 0.21/0.43 inference(fool_elimination,[],[f16])).
% 0.21/0.43 thf(f16,plain,(
% 0.21/0.43 (cPEANO1 = cIND & ! [X0] : (c0 != (cS @ X0)) & ! [X1,X2] : (((cS @ X2) = (cS @ X1)) => (X1 = X2)))),
% 0.21/0.43 inference(rectify,[],[f4])).
% 0.21/0.43 thf(f4,axiom,(
% 0.21/0.43 (cPEANO1 = cIND & ! [X3] : (c0 != (cS @ X3)) & ! [X5,X4] : (((cS @ X4) = (cS @ X5)) => (X4 = X5)))),
% 0.21/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPEANO1_def)).
% 0.21/0.43 thf(f22,plain,(
% 0.21/0.43 (cPEANO1 = $true)),
% 0.21/0.43 inference(cnf_transformation,[],[f18])).
% 0.21/0.43 thf(f18,plain,(
% 0.21/0.43 ! [X0] : ((cODD1 @ X0) != $true) & (cPEANO1 = $true)),
% 0.21/0.43 inference(ennf_transformation,[],[f9])).
% 0.21/0.43 thf(f9,plain,(
% 0.21/0.43 ~((cPEANO1 = $true) => ? [X0] : ((cODD1 @ X0) = $true))),
% 0.21/0.43 inference(fool_elimination,[],[f8])).
% 0.21/0.43 thf(f8,plain,(
% 0.21/0.43 ~(cPEANO1 => ? [X0] : (cODD1 @ X0))),
% 0.21/0.43 inference(rectify,[],[f6])).
% 0.21/0.43 thf(f6,negated_conjecture,(
% 0.21/0.43 ~(cPEANO1 => ? [X0] : (cODD1 @ X0))),
% 0.21/0.43 inference(negated_conjecture,[],[f5])).
% 0.21/0.43 thf(f5,conjecture,(
% 0.21/0.43 cPEANO1 => ? [X0] : (cODD1 @ X0)),
% 0.21/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM404)).
% 0.21/0.43 thf(f875,plain,(
% 0.21/0.43 ( ! [X0 : $i] : ((c0 = (cS @ X0)) | (c0 != X0)) )),
% 0.21/0.43 inference(equality_resolution,[],[f859])).
% 0.21/0.43 thf(f859,plain,(
% 0.21/0.43 ( ! [X0 : $i,X1 : $i] : (((cS @ X1) != X0) | (c0 != X1) | (c0 = X0)) )),
% 0.21/0.43 inference(superposition,[],[f44,f579])).
% 0.21/0.43 thf(f579,plain,(
% 0.21/0.43 ( ! [X0 : $i,X1 : $i] : (((cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X1) | ((cS @ X1) != X0) | (c0 = X0)) )),
% 0.21/0.43 inference(superposition,[],[f40,f229])).
% 0.21/0.43 thf(f229,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (((cS @ (cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0)))))) = X0) | (c0 = X0)) )),
% 0.21/0.43 inference(equality_proxy_clausification,[],[f228])).
% 0.21/0.43 thf(f228,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (($true = (X0 = c0)) | ((cS @ (cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0)))))) = X0)) )),
% 0.21/0.43 inference(not_proxy_clausification,[],[f227])).
% 0.21/0.43 thf(f227,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (($false = (~ (X0 = c0))) | ((cS @ (cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0)))))) = X0)) )),
% 0.21/0.43 inference(beta_eta_normalization,[],[f201])).
% 0.21/0.43 thf(f201,plain,(
% 0.21/0.43 ( ! [X0 : $i] : ((((^[Y0 : $i]: (~ (X0 = Y0))) @ c0) = $false) | ((cS @ (cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0)))))) = X0)) )),
% 0.21/0.43 inference(leibniz_equality_elimination,[],[f63])).
% 0.21/0.43 thf(f63,plain,(
% 0.21/0.43 ( ! [X0 : $i,X1 : $i > $o] : (((X1 @ (cS @ (cS @ (sK2 @ X1)))) = $false) | ((X1 @ c0) = $false) | ((X1 @ X0) = $true)) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f62])).
% 0.21/0.43 thf(f62,plain,(
% 0.21/0.43 ( ! [X0 : $i,X1 : $i > $o] : ((((X1 @ (sK2 @ X1)) => (X1 @ (cS @ (cS @ (sK2 @ X1))))) = $false) | ((X1 @ X0) = $true) | ((X1 @ c0) = $false)) )),
% 0.21/0.43 inference(beta_eta_normalization,[],[f61])).
% 0.21/0.43 thf(f61,plain,(
% 0.21/0.43 ( ! [X0 : $i,X1 : $i > $o] : (((X1 @ c0) = $false) | ((X1 @ X0) = $true) | (((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ (cS @ Y0))))) @ (sK2 @ X1)) = $false)) )),
% 0.21/0.43 inference(sigma_clausification,[],[f60])).
% 0.21/0.43 thf(f60,plain,(
% 0.21/0.43 ( ! [X0 : $i,X1 : $i > $o] : (((X1 @ c0) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ (cS @ Y0))))))) | ((X1 @ X0) = $true)) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f59])).
% 0.21/0.43 thf(f59,plain,(
% 0.21/0.43 ( ! [X0 : $i,X1 : $i > $o] : ((((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ (cS @ Y0)))))) & (X1 @ c0)) = $false) | ((X1 @ X0) = $true)) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f58])).
% 0.21/0.43 thf(f58,plain,(
% 0.21/0.43 ( ! [X0 : $i,X1 : $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ (cS @ Y0)))))) & (X1 @ c0)) => (X1 @ X0)))) )),
% 0.21/0.43 inference(beta_eta_normalization,[],[f57])).
% 0.21/0.43 thf(f57,plain,(
% 0.21/0.43 ( ! [X0 : $i,X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ (cS @ Y1)))))) & (Y0 @ c0)) => (Y0 @ X0))) @ X1))) )),
% 0.21/0.43 inference(pi_clausification,[],[f56])).
% 0.21/0.43 thf(f56,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ (cS @ Y1)))))) & (Y0 @ c0)) => (Y0 @ X0)))))) )),
% 0.21/0.43 inference(not_proxy_clausification,[],[f55])).
% 0.21/0.43 thf(f55,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (((~ (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ (cS @ Y1)))))) & (Y0 @ c0)) => (Y0 @ X0))))) != $true)) )),
% 0.21/0.43 inference(beta_eta_normalization,[],[f27])).
% 0.21/0.43 thf(f27,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (($true != ((^[Y0 : $i]: (~ ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (cS @ (cS @ Y3)))))) & (Y2 @ c0)) => (Y2 @ Y1))))) @ Y0))) @ X0))) )),
% 0.21/0.43 inference(definition_unfolding,[],[f23,f25])).
% 0.21/0.43 thf(f25,plain,(
% 0.21/0.43 (cODD1 = (^[Y0 : $i]: (~ ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (cS @ (cS @ Y3)))))) & (Y2 @ c0)) => (Y2 @ Y1))))) @ Y0))))),
% 0.21/0.43 inference(definition_unfolding,[],[f24,f19])).
% 0.21/0.43 thf(f19,plain,(
% 0.21/0.43 (cEVEN1 = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (cS @ (cS @ Y2)))))) & (Y1 @ c0)) => (Y1 @ Y0))))))),
% 0.21/0.43 inference(cnf_transformation,[],[f11])).
% 0.21/0.43 thf(f11,plain,(
% 0.21/0.43 (cEVEN1 = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (cS @ (cS @ Y2)))))) & (Y1 @ c0)) => (Y1 @ Y0))))))),
% 0.21/0.43 inference(fool_elimination,[],[f10])).
% 0.21/0.43 thf(f10,plain,(
% 0.21/0.43 (cEVEN1 = (^[X0 : $i] : (! [X1 : $i > $o] : (((X1 @ c0) & ! [X2] : ((X1 @ X2) => (X1 @ (cS @ (cS @ X2))))) => (X1 @ X0)))))),
% 0.21/0.43 inference(rectify,[],[f1])).
% 0.21/0.43 thf(f1,axiom,(
% 0.21/0.43 (cEVEN1 = (^[X0 : $i] : (! [X1 : $i > $o] : (((X1 @ c0) & ! [X2] : ((X1 @ X2) => (X1 @ (cS @ (cS @ X2))))) => (X1 @ X0)))))),
% 0.21/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEVEN1_def)).
% 0.21/0.43 thf(f24,plain,(
% 0.21/0.43 (cODD1 = (^[Y0 : $i]: (~ (cEVEN1 @ Y0))))),
% 0.21/0.43 inference(cnf_transformation,[],[f15])).
% 0.21/0.43 thf(f15,plain,(
% 0.21/0.43 (cODD1 = (^[Y0 : $i]: (~ (cEVEN1 @ Y0))))),
% 0.21/0.43 inference(fool_elimination,[],[f14])).
% 0.21/0.43 thf(f14,plain,(
% 0.21/0.43 ((^[X0 : $i] : (~(cEVEN1 @ X0))) = cODD1)),
% 0.21/0.43 inference(rectify,[],[f3])).
% 0.21/0.43 thf(f3,axiom,(
% 0.21/0.43 ((^[X0 : $i] : (~(cEVEN1 @ X0))) = cODD1)),
% 0.21/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cODD1_def)).
% 0.21/0.43 thf(f23,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (((cODD1 @ X0) != $true)) )),
% 0.21/0.43 inference(cnf_transformation,[],[f18])).
% 0.21/0.43 thf(f40,plain,(
% 0.21/0.43 ( ! [X2 : $i,X1 : $i] : (((cS @ X2) != (cS @ X1)) | (X1 = X2)) )),
% 0.21/0.43 inference(equality_proxy_clausification,[],[f39])).
% 0.21/0.43 thf(f39,plain,(
% 0.21/0.43 ( ! [X2 : $i,X1 : $i] : (($true = (X2 = X1)) | ((cS @ X2) != (cS @ X1))) )),
% 0.21/0.43 inference(equality_proxy_clausification,[],[f38])).
% 0.21/0.43 thf(f38,plain,(
% 0.21/0.43 ( ! [X2 : $i,X1 : $i] : (($false = ((cS @ X1) = (cS @ X2))) | ($true = (X2 = X1))) )),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f37])).
% 0.21/0.43 thf(f37,plain,(
% 0.21/0.43 ( ! [X2 : $i,X1 : $i] : (($true = (((cS @ X1) = (cS @ X2)) => (X2 = X1)))) )),
% 0.21/0.43 inference(beta_eta_normalization,[],[f36])).
% 0.21/0.43 thf(f36,plain,(
% 0.21/0.43 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (((cS @ X1) = (cS @ Y0)) => (Y0 = X1))) @ X2) = $true)) )),
% 0.21/0.43 inference(pi_clausification,[],[f35])).
% 0.21/0.43 thf(f35,plain,(
% 0.21/0.43 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((cS @ X1) = (cS @ Y0)) => (Y0 = X1)))))) )),
% 0.21/0.43 inference(beta_eta_normalization,[],[f34])).
% 0.21/0.43 thf(f34,plain,(
% 0.21/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0))))) @ X1))) )),
% 0.21/0.43 inference(pi_clausification,[],[f33])).
% 0.21/0.43 thf(f33,plain,(
% 0.21/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cS @ Y0) = (cS @ Y1)) => (Y1 = Y0)))))))),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f31])).
% 0.21/0.43 % SZS output end Proof for theBenchmark
% 0.21/0.43 % (22950)------------------------------
% 0.21/0.43 % (22950)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.43 % (22950)Termination reason: Refutation
% 0.21/0.43
% 0.21/0.43 % (22950)Memory used [KB]: 5756
% 0.21/0.43 % (22950)Time elapsed: 0.054 s
% 0.21/0.43 % (22950)Instructions burned: 77 (million)
% 0.21/0.43 % (22950)------------------------------
% 0.21/0.43 % (22950)------------------------------
% 0.21/0.43 % (22949)Success in time 0.062 s
%------------------------------------------------------------------------------