TSTP Solution File: SEV282^5 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV282^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n019.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 16:02:37 EDT 2024
% Result : Theorem 0.18s 0.35s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEV282^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.03/0.11 % Command : run_vampire %s %d THM
% 0.10/0.31 % Computer : n019.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Jun 21 19:11:54 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.17/0.32 This is a TH0_THM_EQU_NAR problem
% 0.17/0.32 Running higher-order theorem proving
% 0.17/0.32 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
% 0.17/0.34 % (19862)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)
% 0.17/0.34 % (19861)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)
% 0.17/0.34 % (19865)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)
% 0.17/0.34 % (19863)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.17/0.34 % (19860)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.17/0.34 % (19864)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)
% 0.18/0.34 % (19866)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.34 % (19865)Refutation not found, incomplete strategy
% 0.18/0.34 % (19865)------------------------------
% 0.18/0.34 % (19865)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.34 % (19865)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.34
% 0.18/0.34
% 0.18/0.34 % (19865)Memory used [KB]: 5500
% 0.18/0.34 % (19865)Time elapsed: 0.002 s
% 0.18/0.34 % (19863)Instruction limit reached!
% 0.18/0.34 % (19863)------------------------------
% 0.18/0.34 % (19863)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.34 % (19865)Instructions burned: 1 (million)
% 0.18/0.34 % (19865)------------------------------
% 0.18/0.34 % (19865)------------------------------
% 0.18/0.34 % (19863)Termination reason: Unknown
% 0.18/0.34 % (19863)Termination phase: Saturation
% 0.18/0.34 % (19864)Instruction limit reached!
% 0.18/0.34 % (19864)------------------------------
% 0.18/0.34 % (19864)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.34 % (19864)Termination reason: Unknown
% 0.18/0.34 % (19864)Termination phase: Saturation
% 0.18/0.34
% 0.18/0.34 % (19864)Memory used [KB]: 5500
% 0.18/0.34 % (19864)Time elapsed: 0.003 s
% 0.18/0.34 % (19864)Instructions burned: 2 (million)
% 0.18/0.34 % (19864)------------------------------
% 0.18/0.34 % (19864)------------------------------
% 0.18/0.34
% 0.18/0.34 % (19863)Memory used [KB]: 5500
% 0.18/0.34 % (19863)Time elapsed: 0.003 s
% 0.18/0.34 % (19863)Instructions burned: 2 (million)
% 0.18/0.34 % (19863)------------------------------
% 0.18/0.34 % (19863)------------------------------
% 0.18/0.34 % (19866)First to succeed.
% 0.18/0.35 % (19860)Also succeeded, but the first one will report.
% 0.18/0.35 % (19861)Also succeeded, but the first one will report.
% 0.18/0.35 % (19866)Refutation found. Thanks to Tanya!
% 0.18/0.35 % SZS status Theorem for theBenchmark
% 0.18/0.35 % SZS output start Proof for theBenchmark
% 0.18/0.35 thf(func_def_0, type, cNAT: (($i > $o) > $o) > $o).
% 0.18/0.35 thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 0.18/0.35 thf(func_def_2, type, cZERO: ($i > $o) > $o).
% 0.18/0.35 thf(func_def_17, type, sK1: (($i > $o) > $o) > $o).
% 0.18/0.35 thf(f33,plain,(
% 0.18/0.35 $false),
% 0.18/0.35 inference(trivial_inequality_removal,[],[f32])).
% 0.18/0.35 thf(f32,plain,(
% 0.18/0.35 ($false = $true)),
% 0.18/0.35 inference(forward_demodulation,[],[f27,f25])).
% 0.18/0.35 thf(f25,plain,(
% 0.18/0.35 ((sK1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false)),
% 0.18/0.35 inference(binary_proxy_clausification,[],[f24])).
% 0.18/0.35 thf(f24,plain,(
% 0.18/0.35 ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ Y0) => (sK1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (sK1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (sK1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $false)),
% 0.18/0.35 inference(beta_eta_normalization,[],[f23])).
% 0.18/0.35 thf(f23,plain,(
% 0.18/0.35 (((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))) @ sK1) = $false)),
% 0.18/0.35 inference(sigma_clausification,[],[f22])).
% 0.18/0.35 thf(f22,plain,(
% 0.18/0.35 ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) != $true)),
% 0.18/0.35 inference(beta_eta_normalization,[],[f21])).
% 0.18/0.35 thf(f21,plain,(
% 0.18/0.35 (((^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) != $true)),
% 0.18/0.35 inference(definition_unfolding,[],[f16,f20,f18])).
% 0.18/0.35 thf(f18,plain,(
% 0.18/0.35 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.18/0.35 inference(cnf_transformation,[],[f10])).
% 0.18/0.35 thf(f10,plain,(
% 0.18/0.35 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.18/0.35 inference(fool_elimination,[],[f9])).
% 0.18/0.35 thf(f9,plain,(
% 0.18/0.35 (cZERO = (^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))))),
% 0.18/0.35 inference(rectify,[],[f1])).
% 0.18/0.35 thf(f1,axiom,(
% 0.18/0.35 (cZERO = (^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))))),
% 0.18/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cZERO_def)).
% 0.18/0.35 thf(f20,plain,(
% 0.18/0.35 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))))),
% 0.18/0.35 inference(definition_unfolding,[],[f19,f17,f18])).
% 0.18/0.35 thf(f17,plain,(
% 0.18/0.35 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))),
% 0.18/0.35 inference(cnf_transformation,[],[f8])).
% 0.18/0.35 thf(f8,plain,(
% 0.18/0.35 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))),
% 0.18/0.35 inference(fool_elimination,[],[f7])).
% 0.18/0.35 thf(f7,plain,(
% 0.18/0.35 (cSUCC = (^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2] : ((X0 @ (^[X3 : $i] : ((X2 != X3) & (X1 @ X3)))) & (X1 @ X2)))))),
% 0.18/0.35 inference(rectify,[],[f2])).
% 0.18/0.35 thf(f2,axiom,(
% 0.18/0.35 (cSUCC = (^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1] : ((X2 @ (^[X3 : $i] : ((X1 != X3) & (X0 @ X3)))) & (X0 @ X1)))))),
% 0.18/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSUCC_def)).
% 0.18/0.35 thf(f19,plain,(
% 0.18/0.35 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 0.18/0.35 inference(cnf_transformation,[],[f12])).
% 0.18/0.35 thf(f12,plain,(
% 0.18/0.35 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 0.18/0.35 inference(fool_elimination,[],[f11])).
% 0.18/0.35 thf(f11,plain,(
% 0.18/0.35 (cNAT = (^[X0 : ($i > $o) > $o] : (! [X1 : (($i > $o) > $o) > $o] : (((X1 @ cZERO) & ! [X2 : ($i > $o) > $o] : ((X1 @ X2) => (X1 @ (cSUCC @ X2)))) => (X1 @ X0)))))),
% 0.18/0.35 inference(rectify,[],[f3])).
% 0.18/0.35 thf(f3,axiom,(
% 0.18/0.35 (cNAT = (^[X2 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : (((X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) => (X0 @ X2)))))),
% 0.18/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cNAT_def)).
% 0.18/0.35 thf(f16,plain,(
% 0.18/0.35 ((cNAT @ cZERO) != $true)),
% 0.18/0.35 inference(cnf_transformation,[],[f15])).
% 0.18/0.35 thf(f15,plain,(
% 0.18/0.35 ((cNAT @ cZERO) != $true)),
% 0.18/0.35 inference(flattening,[],[f14])).
% 0.18/0.35 thf(f14,plain,(
% 0.18/0.35 ~((cNAT @ cZERO) = $true)),
% 0.18/0.35 inference(fool_elimination,[],[f13])).
% 0.18/0.35 thf(f13,plain,(
% 0.18/0.35 ~(cNAT @ cZERO)),
% 0.18/0.35 inference(rectify,[],[f5])).
% 0.18/0.35 thf(f5,negated_conjecture,(
% 0.18/0.35 ~(cNAT @ cZERO)),
% 0.18/0.35 inference(negated_conjecture,[],[f4])).
% 0.18/0.35 thf(f4,conjecture,(
% 0.18/0.35 (cNAT @ cZERO)),
% 0.18/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTTTP6100)).
% 0.18/0.35 thf(f27,plain,(
% 0.18/0.35 ((sK1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $true)),
% 0.18/0.35 inference(binary_proxy_clausification,[],[f26])).
% 0.18/0.35 thf(f26,plain,(
% 0.18/0.35 (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ Y0) => (sK1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (sK1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $true)),
% 0.18/0.35 inference(binary_proxy_clausification,[],[f24])).
% 0.18/0.35 % SZS output end Proof for theBenchmark
% 0.18/0.35 % (19866)------------------------------
% 0.18/0.35 % (19866)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.35 % (19866)Termination reason: Refutation
% 0.18/0.35
% 0.18/0.35 % (19866)Memory used [KB]: 5500
% 0.18/0.35 % (19866)Time elapsed: 0.004 s
% 0.18/0.35 % (19866)Instructions burned: 3 (million)
% 0.18/0.35 % (19866)------------------------------
% 0.18/0.35 % (19866)------------------------------
% 0.18/0.35 % (19859)Success in time 0.017 s
%------------------------------------------------------------------------------