TSTP Solution File: NUM816^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : NUM816^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n027.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 13:18:02 EDT 2024
% Result : Theorem 0.17s 0.37s
% Output : Refutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : NUM816^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.09/0.11 % Command : run_vampire %s %d THM
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Jun 22 20:41:39 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.34 This is a TH0_THM_EQU_NAR problem
% 0.17/0.34 Running higher-order theorem proving
% 0.17/0.34 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
% 0.17/0.36 % (21259)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.17/0.36 % (21255)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)
% 0.17/0.36 % (21254)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)
% 0.17/0.36 % (21258)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)
% 0.17/0.36 % (21253)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.17/0.36 % (21257)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)
% 0.17/0.36 % (21256)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.17/0.36 % (21257)Instruction limit reached!
% 0.17/0.36 % (21257)------------------------------
% 0.17/0.36 % (21257)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.36 % (21257)Termination reason: Unknown
% 0.17/0.36 % (21257)Termination phase: Property scanning
% 0.17/0.36
% 0.17/0.36 % (21257)Memory used [KB]: 895
% 0.17/0.36 % (21257)Time elapsed: 0.003 s
% 0.17/0.36 % (21257)Instructions burned: 2 (million)
% 0.17/0.36 % (21257)------------------------------
% 0.17/0.36 % (21257)------------------------------
% 0.17/0.36 % (21258)Refutation not found, incomplete strategy
% 0.17/0.36 % (21258)------------------------------
% 0.17/0.36 % (21258)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.36 % (21258)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.36
% 0.17/0.36
% 0.17/0.36 % (21258)Memory used [KB]: 5500
% 0.17/0.36 % (21258)Time elapsed: 0.003 s
% 0.17/0.36 % (21258)Instructions burned: 1 (million)
% 0.17/0.36 % (21258)------------------------------
% 0.17/0.36 % (21258)------------------------------
% 0.17/0.36 % (21256)Instruction limit reached!
% 0.17/0.36 % (21256)------------------------------
% 0.17/0.36 % (21256)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.36 % (21256)Termination reason: Unknown
% 0.17/0.36 % (21256)Termination phase: Saturation
% 0.17/0.36
% 0.17/0.36 % (21256)Memory used [KB]: 5500
% 0.17/0.36 % (21256)Time elapsed: 0.004 s
% 0.17/0.36 % (21256)Instructions burned: 2 (million)
% 0.17/0.36 % (21256)------------------------------
% 0.17/0.36 % (21256)------------------------------
% 0.17/0.36 % (21255)Refutation not found, incomplete strategy
% 0.17/0.36 % (21255)------------------------------
% 0.17/0.36 % (21255)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.36 % (21255)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.36
% 0.17/0.36
% 0.17/0.36 % (21255)Memory used [KB]: 5500
% 0.17/0.36 % (21255)Time elapsed: 0.004 s
% 0.17/0.36 % (21255)Instructions burned: 2 (million)
% 0.17/0.36 % (21255)------------------------------
% 0.17/0.36 % (21255)------------------------------
% 0.17/0.36 % (21254)Instruction limit reached!
% 0.17/0.36 % (21254)------------------------------
% 0.17/0.36 % (21254)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.36 % (21254)Termination reason: Unknown
% 0.17/0.36 % (21254)Termination phase: Saturation
% 0.17/0.36
% 0.17/0.36 % (21254)Memory used [KB]: 5500
% 0.17/0.36 % (21254)Time elapsed: 0.005 s
% 0.17/0.36 % (21254)Instructions burned: 4 (million)
% 0.17/0.36 % (21254)------------------------------
% 0.17/0.36 % (21254)------------------------------
% 0.17/0.37 % (21259)Instruction limit reached!
% 0.17/0.37 % (21259)------------------------------
% 0.17/0.37 % (21259)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.37 % (21259)Termination reason: Unknown
% 0.17/0.37 % (21259)Termination phase: Saturation
% 0.17/0.37
% 0.17/0.37 % (21259)Memory used [KB]: 5500
% 0.17/0.37 % (21259)Time elapsed: 0.012 s
% 0.17/0.37 % (21259)Instructions burned: 18 (million)
% 0.17/0.37 % (21259)------------------------------
% 0.17/0.37 % (21259)------------------------------
% 0.17/0.37 % (21253)First to succeed.
% 0.17/0.37 % (21260)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)
% 0.17/0.37 % (21263)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)
% 0.17/0.37 % (21261)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)
% 0.17/0.37 % (21264)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)
% 0.17/0.37 % (21262)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)
% 0.17/0.37 % (21253)Refutation found. Thanks to Tanya!
% 0.17/0.37 % SZS status Theorem for theBenchmark
% 0.17/0.37 % SZS output start Proof for theBenchmark
% 0.17/0.37 thf(func_def_1, type, cS: $i > $i).
% 0.17/0.37 thf(func_def_2, type, cEVEN1: $i > $o).
% 0.17/0.37 thf(func_def_3, type, cODD1: $i > $o).
% 0.17/0.37 thf(func_def_15, type, sK1: ($i > $o) > $i).
% 0.17/0.37 thf(func_def_16, type, ph2: !>[X0: $tType]:(X0)).
% 0.17/0.37 thf(f391,plain,(
% 0.17/0.37 $false),
% 0.17/0.37 inference(trivial_inequality_removal,[],[f388])).
% 0.17/0.37 thf(f388,plain,(
% 0.17/0.37 ((cS @ c0) != (cS @ c0))),
% 0.17/0.37 inference(superposition,[],[f387,f105])).
% 0.17/0.37 thf(f105,plain,(
% 0.17/0.37 ((cS @ c0) = (cS @ (cS @ (sK1 @ (^[Y0 : $i]: (~ ((cS @ c0) = Y0)))))))),
% 0.17/0.37 inference(subsumption_resolution,[],[f76,f17])).
% 0.17/0.37 thf(f17,plain,(
% 0.17/0.37 ( ! [X0 : $i] : ((c0 != (cS @ X0))) )),
% 0.17/0.37 inference(cnf_transformation,[],[f13])).
% 0.17/0.37 thf(f13,plain,(
% 0.17/0.37 ((cODD1 @ (cS @ c0)) != $true) & ! [X0] : (c0 != (cS @ X0)) & ! [X1,X2] : (((cS @ X2) != (cS @ X1)) | (X1 = X2))),
% 0.17/0.37 inference(flattening,[],[f12])).
% 0.17/0.37 thf(f12,plain,(
% 0.17/0.37 ((cODD1 @ (cS @ c0)) != $true) & (! [X1,X2] : (((cS @ X2) != (cS @ X1)) | (X1 = X2)) & ! [X0] : (c0 != (cS @ X0)))),
% 0.17/0.37 inference(ennf_transformation,[],[f9])).
% 0.17/0.37 thf(f9,plain,(
% 0.17/0.37 ~((! [X1,X2] : (((cS @ X2) = (cS @ X1)) => (X1 = X2)) & ! [X0] : (c0 != (cS @ X0))) => ((cODD1 @ (cS @ c0)) = $true))),
% 0.17/0.37 inference(fool_elimination,[],[f8])).
% 0.17/0.37 thf(f8,plain,(
% 0.17/0.37 ~((! [X0] : (c0 != (cS @ X0)) & ! [X1,X2] : (((cS @ X2) = (cS @ X1)) => (X1 = X2))) => (cODD1 @ (cS @ c0)))),
% 0.17/0.37 inference(rectify,[],[f4])).
% 0.17/0.37 thf(f4,negated_conjecture,(
% 0.17/0.37 ~((! [X3] : (c0 != (cS @ X3)) & ! [X5,X4] : (((cS @ X4) = (cS @ X5)) => (X4 = X5))) => (cODD1 @ (cS @ c0)))),
% 0.17/0.37 inference(negated_conjecture,[],[f3])).
% 0.17/0.37 thf(f3,conjecture,(
% 0.17/0.37 (! [X3] : (c0 != (cS @ X3)) & ! [X5,X4] : (((cS @ X4) = (cS @ X5)) => (X4 = X5))) => (cODD1 @ (cS @ c0))),
% 0.17/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM406)).
% 0.17/0.37 thf(f76,plain,(
% 0.17/0.37 (c0 = (cS @ c0)) | ((cS @ c0) = (cS @ (cS @ (sK1 @ (^[Y0 : $i]: (~ ((cS @ c0) = Y0)))))))),
% 0.17/0.37 inference(equality_proxy_clausification,[],[f75])).
% 0.17/0.37 thf(f75,plain,(
% 0.17/0.37 ((cS @ c0) = (cS @ (cS @ (sK1 @ (^[Y0 : $i]: (~ ((cS @ c0) = Y0))))))) | ($true = ((cS @ c0) = c0))),
% 0.17/0.37 inference(not_proxy_clausification,[],[f74])).
% 0.17/0.37 thf(f74,plain,(
% 0.17/0.37 ((cS @ c0) = (cS @ (cS @ (sK1 @ (^[Y0 : $i]: (~ ((cS @ c0) = Y0))))))) | ((~ ((cS @ c0) = c0)) = $false)),
% 0.17/0.37 inference(beta_eta_normalization,[],[f62])).
% 0.17/0.37 thf(f62,plain,(
% 0.17/0.37 ((cS @ c0) = (cS @ (cS @ (sK1 @ (^[Y0 : $i]: (~ ((cS @ c0) = Y0))))))) | (((^[Y0 : $i]: (~ ((cS @ c0) = Y0))) @ c0) = $false)),
% 0.17/0.37 inference(leibniz_equality_elimination,[],[f29])).
% 0.17/0.37 thf(f29,plain,(
% 0.17/0.37 ( ! [X1 : $i > $o] : (((X1 @ (cS @ (cS @ (sK1 @ X1)))) = $false) | ($true = (X1 @ (cS @ c0))) | ((X1 @ c0) = $false)) )),
% 0.17/0.37 inference(binary_proxy_clausification,[],[f28])).
% 0.17/0.37 thf(f28,plain,(
% 0.17/0.37 ( ! [X1 : $i > $o] : (((X1 @ c0) = $false) | ($true = (X1 @ (cS @ c0))) | (((X1 @ (sK1 @ X1)) => (X1 @ (cS @ (cS @ (sK1 @ X1))))) = $false)) )),
% 0.17/0.37 inference(beta_eta_normalization,[],[f27])).
% 0.17/0.37 thf(f27,plain,(
% 0.17/0.37 ( ! [X1 : $i > $o] : (((X1 @ c0) = $false) | (((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ (cS @ Y0))))) @ (sK1 @ X1)) = $false) | ($true = (X1 @ (cS @ c0)))) )),
% 0.17/0.37 inference(sigma_clausification,[],[f26])).
% 0.17/0.37 thf(f26,plain,(
% 0.17/0.37 ( ! [X1 : $i > $o] : (((X1 @ c0) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ (cS @ Y0)))))) = $false) | ($true = (X1 @ (cS @ c0)))) )),
% 0.17/0.37 inference(binary_proxy_clausification,[],[f25])).
% 0.17/0.37 thf(f25,plain,(
% 0.17/0.37 ( ! [X1 : $i > $o] : ((((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ (cS @ Y0)))))) & (X1 @ c0)) = $false) | ($true = (X1 @ (cS @ c0)))) )),
% 0.17/0.37 inference(binary_proxy_clausification,[],[f24])).
% 0.17/0.37 thf(f24,plain,(
% 0.17/0.37 ( ! [X1 : $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ (cS @ Y0)))))) & (X1 @ c0)) => (X1 @ (cS @ c0))))) )),
% 0.17/0.37 inference(beta_eta_normalization,[],[f23])).
% 0.17/0.37 thf(f23,plain,(
% 0.17/0.37 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ (cS @ Y1)))))) & (Y0 @ c0)) => (Y0 @ (cS @ c0)))) @ X1) = $true)) )),
% 0.17/0.37 inference(pi_clausification,[],[f22])).
% 0.17/0.37 thf(f22,plain,(
% 0.17/0.37 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ (cS @ Y1)))))) & (Y0 @ c0)) => (Y0 @ (cS @ c0))))) = $true)),
% 0.17/0.37 inference(not_proxy_clausification,[],[f21])).
% 0.17/0.37 thf(f21,plain,(
% 0.17/0.37 ($true != (~ (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ (cS @ Y1)))))) & (Y0 @ c0)) => (Y0 @ (cS @ c0)))))))),
% 0.17/0.37 inference(beta_eta_normalization,[],[f20])).
% 0.17/0.37 thf(f20,plain,(
% 0.17/0.37 (((^[Y0 : $i]: (~ ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (cS @ (cS @ Y3)))))) & (Y2 @ c0)) => (Y2 @ Y1))))) @ Y0))) @ (cS @ c0)) != $true)),
% 0.17/0.37 inference(definition_unfolding,[],[f18,f19])).
% 0.17/0.37 thf(f19,plain,(
% 0.17/0.37 (cODD1 = (^[Y0 : $i]: (~ ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (cS @ (cS @ Y3)))))) & (Y2 @ c0)) => (Y2 @ Y1))))) @ Y0))))),
% 0.17/0.37 inference(definition_unfolding,[],[f14,f15])).
% 0.17/0.37 thf(f15,plain,(
% 0.17/0.37 (cEVEN1 = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (cS @ (cS @ Y2)))))) & (Y1 @ c0)) => (Y1 @ Y0))))))),
% 0.17/0.37 inference(cnf_transformation,[],[f11])).
% 0.17/0.37 thf(f11,plain,(
% 0.17/0.37 (cEVEN1 = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (cS @ (cS @ Y2)))))) & (Y1 @ c0)) => (Y1 @ Y0))))))),
% 0.17/0.37 inference(fool_elimination,[],[f10])).
% 0.17/0.37 thf(f10,plain,(
% 0.17/0.37 (cEVEN1 = (^[X0 : $i] : (! [X1 : $i > $o] : (((X1 @ c0) & ! [X2] : ((X1 @ X2) => (X1 @ (cS @ (cS @ X2))))) => (X1 @ X0)))))),
% 0.17/0.37 inference(rectify,[],[f1])).
% 0.17/0.37 thf(f1,axiom,(
% 0.17/0.37 (cEVEN1 = (^[X0 : $i] : (! [X1 : $i > $o] : (((X1 @ c0) & ! [X2] : ((X1 @ X2) => (X1 @ (cS @ (cS @ X2))))) => (X1 @ X0)))))),
% 0.17/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEVEN1_def)).
% 0.17/0.37 thf(f14,plain,(
% 0.17/0.37 (cODD1 = (^[Y0 : $i]: (~ (cEVEN1 @ Y0))))),
% 0.17/0.37 inference(cnf_transformation,[],[f7])).
% 0.17/0.37 thf(f7,plain,(
% 0.17/0.37 (cODD1 = (^[Y0 : $i]: (~ (cEVEN1 @ Y0))))),
% 0.17/0.37 inference(fool_elimination,[],[f6])).
% 0.17/0.37 thf(f6,plain,(
% 0.17/0.37 ((^[X0 : $i] : (~(cEVEN1 @ X0))) = cODD1)),
% 0.17/0.37 inference(rectify,[],[f2])).
% 0.17/0.37 thf(f2,axiom,(
% 0.17/0.37 ((^[X0 : $i] : (~(cEVEN1 @ X0))) = cODD1)),
% 0.17/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cODD1_def)).
% 0.17/0.37 thf(f18,plain,(
% 0.17/0.37 ((cODD1 @ (cS @ c0)) != $true)),
% 0.17/0.37 inference(cnf_transformation,[],[f13])).
% 0.17/0.37 thf(f387,plain,(
% 0.17/0.37 ( ! [X0 : $i] : (((cS @ c0) != (cS @ X0))) )),
% 0.17/0.37 inference(subsumption_resolution,[],[f369,f16])).
% 0.17/0.37 thf(f16,plain,(
% 0.17/0.37 ( ! [X2 : $i,X1 : $i] : (((cS @ X2) != (cS @ X1)) | (X1 = X2)) )),
% 0.17/0.37 inference(cnf_transformation,[],[f13])).
% 0.17/0.37 thf(f369,plain,(
% 0.17/0.37 ( ! [X0 : $i] : (((cS @ c0) != (cS @ X0)) | (c0 != X0)) )),
% 0.17/0.37 inference(superposition,[],[f17,f204])).
% 0.17/0.37 thf(f204,plain,(
% 0.17/0.37 ( ! [X0 : $i] : (((cS @ (sK1 @ (^[Y0 : $i]: (~ ((cS @ c0) = Y0))))) = X0) | ((cS @ c0) != (cS @ X0))) )),
% 0.17/0.37 inference(superposition,[],[f16,f105])).
% 0.17/0.37 % SZS output end Proof for theBenchmark
% 0.17/0.37 % (21253)------------------------------
% 0.17/0.37 % (21253)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.37 % (21253)Termination reason: Refutation
% 0.17/0.37
% 0.17/0.37 % (21253)Memory used [KB]: 5628
% 0.17/0.37 % (21253)Time elapsed: 0.019 s
% 0.17/0.37 % (21253)Instructions burned: 27 (million)
% 0.17/0.37 % (21253)------------------------------
% 0.17/0.37 % (21253)------------------------------
% 0.17/0.37 % (21252)Success in time 0.03 s
%------------------------------------------------------------------------------