TSTP Solution File: SEV289^5 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV289^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n001.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 16:02:38 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEV289^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.03/0.13 % Command : run_vampire %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 21 19:39:39 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.36 This is a TH0_THM_EQU_NAR problem
% 0.13/0.36 Running higher-order theorem proving
% 0.13/0.36 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
% 0.22/0.38 % (23817)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.39 % (23812)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)
% 0.22/0.39 % (23813)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.39 % (23814)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)
% 0.22/0.39 % (23815)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)
% 0.22/0.39 % (23813)Instruction limit reached!
% 0.22/0.39 % (23813)------------------------------
% 0.22/0.39 % (23813)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (23813)Termination reason: Unknown
% 0.22/0.39 % (23814)Instruction limit reached!
% 0.22/0.39 % (23814)------------------------------
% 0.22/0.39 % (23814)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (23813)Termination phase: Property scanning
% 0.22/0.39
% 0.22/0.39 % (23814)Termination reason: Unknown
% 0.22/0.39 % (23813)Memory used [KB]: 895
% 0.22/0.39 % (23814)Termination phase: Property scanning
% 0.22/0.39 % (23813)Time elapsed: 0.005 s
% 0.22/0.39
% 0.22/0.39 % (23813)Instructions burned: 2 (million)
% 0.22/0.39 % (23814)Memory used [KB]: 895
% 0.22/0.39 % (23813)------------------------------
% 0.22/0.39 % (23813)------------------------------
% 0.22/0.39 % (23814)Time elapsed: 0.005 s
% 0.22/0.39 % (23814)Instructions burned: 2 (million)
% 0.22/0.39 % (23814)------------------------------
% 0.22/0.39 % (23814)------------------------------
% 0.22/0.39 % (23810)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.39 % (23811)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)
% 0.22/0.39 % (23815)Refutation not found, incomplete strategy
% 0.22/0.39 % (23815)------------------------------
% 0.22/0.39 % (23815)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (23815)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.39
% 0.22/0.39
% 0.22/0.39 % (23815)Memory used [KB]: 5500
% 0.22/0.39 % (23815)Time elapsed: 0.005 s
% 0.22/0.39 % (23815)Instructions burned: 2 (million)
% 0.22/0.39 % (23815)------------------------------
% 0.22/0.39 % (23815)------------------------------
% 0.22/0.39 % (23811)Instruction limit reached!
% 0.22/0.39 % (23811)------------------------------
% 0.22/0.39 % (23811)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (23811)Termination reason: Unknown
% 0.22/0.39 % (23811)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (23811)Memory used [KB]: 5500
% 0.22/0.39 % (23811)Time elapsed: 0.007 s
% 0.22/0.39 % (23811)Instructions burned: 5 (million)
% 0.22/0.39 % (23811)------------------------------
% 0.22/0.39 % (23811)------------------------------
% 0.22/0.40 % (23817)Instruction limit reached!
% 0.22/0.40 % (23817)------------------------------
% 0.22/0.40 % (23817)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (23817)Termination reason: Unknown
% 0.22/0.40 % (23817)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (23817)Memory used [KB]: 5628
% 0.22/0.40 % (23817)Time elapsed: 0.015 s
% 0.22/0.40 % (23817)Instructions burned: 18 (million)
% 0.22/0.40 % (23817)------------------------------
% 0.22/0.40 % (23817)------------------------------
% 0.22/0.40 % (23812)First to succeed.
% 0.22/0.40 % (23812)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% 0.22/0.40 thf(func_def_0, type, cNAT: (($i > $o) > $o) > $o).
% 0.22/0.40 thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 0.22/0.40 thf(func_def_2, type, cZERO: ($i > $o) > $o).
% 0.22/0.40 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.22/0.40 thf(func_def_17, type, sK0: ($i > $o) > $o).
% 0.22/0.40 thf(func_def_19, type, sK2: ((($i > $o) > $o) > $o) > ($i > $o) > $o).
% 0.22/0.40 thf(func_def_20, type, sK3: (($i > $o) > $o) > $o).
% 0.22/0.40 thf(func_def_21, type, ph4: !>[X0: $tType]:(X0)).
% 0.22/0.40 thf(f92,plain,(
% 0.22/0.40 $false),
% 0.22/0.40 inference(avatar_sat_refutation,[],[f58,f69,f84,f87,f91])).
% 0.22/0.40 thf(f91,plain,(
% 0.22/0.40 ~spl1_3),
% 0.22/0.40 inference(avatar_contradiction_clause,[],[f90])).
% 0.22/0.40 thf(f90,plain,(
% 0.22/0.40 $false | ~spl1_3),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f89])).
% 0.22/0.40 thf(f89,plain,(
% 0.22/0.40 ($true = $false) | ~spl1_3),
% 0.22/0.40 inference(backward_demodulation,[],[f40,f76])).
% 0.22/0.40 thf(f76,plain,(
% 0.22/0.40 ((sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ~spl1_3),
% 0.22/0.40 inference(avatar_component_clause,[],[f74])).
% 0.22/0.40 thf(f74,plain,(
% 0.22/0.40 spl1_3 <=> ((sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false)),
% 0.22/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_3])])).
% 0.22/0.40 thf(f40,plain,(
% 0.22/0.40 ((sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $true)),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f39])).
% 0.22/0.40 thf(f39,plain,(
% 0.22/0.40 ($true = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))))),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f37])).
% 0.22/0.40 thf(f37,plain,(
% 0.22/0.40 ($false = (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK0 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))))),
% 0.22/0.40 inference(beta_eta_normalization,[],[f36])).
% 0.22/0.40 thf(f36,plain,(
% 0.22/0.40 (((^[Y0 : (($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 @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))) @ sK3) = $false)),
% 0.22/0.40 inference(sigma_clausification,[],[f35])).
% 0.22/0.40 thf(f35,plain,(
% 0.22/0.40 ((!! @ ((($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 @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) != $true)),
% 0.22/0.40 inference(beta_eta_normalization,[],[f25])).
% 0.22/0.40 thf(f25,plain,(
% 0.22/0.40 ($true != ((^[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) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))) @ sK0)))),
% 0.22/0.40 inference(definition_unfolding,[],[f21,f23,f20])).
% 0.22/0.40 thf(f20,plain,(
% 0.22/0.40 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))),
% 0.22/0.40 inference(cnf_transformation,[],[f14])).
% 0.22/0.40 thf(f14,plain,(
% 0.22/0.40 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))),
% 0.22/0.40 inference(fool_elimination,[],[f13])).
% 0.22/0.40 thf(f13,plain,(
% 0.22/0.40 ((^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2] : ((X0 @ (^[X3 : $i] : ((X2 != X3) & (X1 @ X3)))) & (X1 @ X2)))) = cSUCC)),
% 0.22/0.40 inference(rectify,[],[f2])).
% 0.22/0.40 thf(f2,axiom,(
% 0.22/0.40 ((^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1] : ((X2 @ (^[X3 : $i] : ((X1 != X3) & (X0 @ X3)))) & (X0 @ X1)))) = cSUCC)),
% 0.22/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSUCC_def)).
% 0.22/0.40 thf(f23,plain,(
% 0.22/0.40 (cNAT = (^[Y0 : ($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))))))),
% 0.22/0.40 inference(definition_unfolding,[],[f19,f20,f18])).
% 0.22/0.40 thf(f18,plain,(
% 0.22/0.40 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.22/0.40 inference(cnf_transformation,[],[f8])).
% 0.22/0.40 thf(f8,plain,(
% 0.22/0.40 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.22/0.40 inference(fool_elimination,[],[f7])).
% 0.22/0.40 thf(f7,plain,(
% 0.22/0.40 (cZERO = (^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))))),
% 0.22/0.40 inference(rectify,[],[f1])).
% 0.22/0.40 thf(f1,axiom,(
% 0.22/0.40 (cZERO = (^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))))),
% 0.22/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cZERO_def)).
% 0.22/0.40 thf(f19,plain,(
% 0.22/0.40 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 0.22/0.40 inference(cnf_transformation,[],[f10])).
% 0.22/0.40 thf(f10,plain,(
% 0.22/0.40 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 0.22/0.40 inference(fool_elimination,[],[f9])).
% 0.22/0.40 thf(f9,plain,(
% 0.22/0.40 ((^[X0 : ($i > $o) > $o] : (! [X1 : (($i > $o) > $o) > $o] : (((X1 @ cZERO) & ! [X2 : ($i > $o) > $o] : ((X1 @ X2) => (X1 @ (cSUCC @ X2)))) => (X1 @ X0)))) = cNAT)),
% 0.22/0.40 inference(rectify,[],[f3])).
% 0.22/0.40 thf(f3,axiom,(
% 0.22/0.40 ((^[X2 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : (((X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) => (X0 @ X2)))) = cNAT)),
% 0.22/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cNAT_def)).
% 0.22/0.40 thf(f21,plain,(
% 0.22/0.40 ($true != (cNAT @ (cSUCC @ sK0)))),
% 0.22/0.40 inference(cnf_transformation,[],[f17])).
% 0.22/0.40 thf(f17,plain,(
% 0.22/0.40 ($true = (cNAT @ sK0)) & ($true != (cNAT @ (cSUCC @ sK0)))),
% 0.22/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f16])).
% 0.22/0.40 thf(f16,plain,(
% 0.22/0.40 ? [X0 : ($i > $o) > $o] : (($true = (cNAT @ X0)) & ($true != (cNAT @ (cSUCC @ X0)))) => (($true = (cNAT @ sK0)) & ($true != (cNAT @ (cSUCC @ sK0))))),
% 0.22/0.40 introduced(choice_axiom,[])).
% 0.22/0.40 thf(f15,plain,(
% 0.22/0.40 ? [X0 : ($i > $o) > $o] : (($true = (cNAT @ X0)) & ($true != (cNAT @ (cSUCC @ X0))))),
% 0.22/0.40 inference(ennf_transformation,[],[f12])).
% 0.22/0.40 thf(f12,plain,(
% 0.22/0.40 ~! [X0 : ($i > $o) > $o] : (($true = (cNAT @ X0)) => ($true = (cNAT @ (cSUCC @ X0))))),
% 0.22/0.40 inference(fool_elimination,[],[f11])).
% 0.22/0.40 thf(f11,plain,(
% 0.22/0.40 ~! [X0 : ($i > $o) > $o] : ((cNAT @ X0) => (cNAT @ (cSUCC @ X0)))),
% 0.22/0.40 inference(rectify,[],[f5])).
% 0.22/0.40 thf(f5,negated_conjecture,(
% 0.22/0.40 ~! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => (cNAT @ (cSUCC @ X1)))),
% 0.22/0.40 inference(negated_conjecture,[],[f4])).
% 0.22/0.40 thf(f4,conjecture,(
% 0.22/0.40 ! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => (cNAT @ (cSUCC @ X1)))),
% 0.22/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTTTP6101)).
% 0.22/0.40 thf(f87,plain,(
% 0.22/0.40 ~spl1_1 | ~spl1_4),
% 0.22/0.40 inference(avatar_contradiction_clause,[],[f86])).
% 0.22/0.40 thf(f86,plain,(
% 0.22/0.40 $false | (~spl1_1 | ~spl1_4)),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f85])).
% 0.22/0.40 thf(f85,plain,(
% 0.22/0.40 ($true = $false) | (~spl1_1 | ~spl1_4)),
% 0.22/0.40 inference(backward_demodulation,[],[f52,f80])).
% 0.22/0.40 thf(f80,plain,(
% 0.22/0.40 ($false = (sK3 @ (sK2 @ sK3))) | ~spl1_4),
% 0.22/0.40 inference(avatar_component_clause,[],[f78])).
% 0.22/0.40 thf(f78,plain,(
% 0.22/0.40 spl1_4 <=> ($false = (sK3 @ (sK2 @ sK3)))),
% 0.22/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 0.22/0.40 thf(f52,plain,(
% 0.22/0.40 ($true = (sK3 @ (sK2 @ sK3))) | ~spl1_1),
% 0.22/0.40 inference(avatar_component_clause,[],[f50])).
% 0.22/0.40 thf(f50,plain,(
% 0.22/0.40 spl1_1 <=> ($true = (sK3 @ (sK2 @ sK3)))),
% 0.22/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.22/0.40 thf(f84,plain,(
% 0.22/0.40 spl1_4 | spl1_3),
% 0.22/0.40 inference(avatar_split_clause,[],[f83,f74,f78])).
% 0.22/0.40 thf(f83,plain,(
% 0.22/0.40 ((sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($false = (sK3 @ (sK2 @ sK3)))),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f82])).
% 0.22/0.40 thf(f82,plain,(
% 0.22/0.40 ($true = $false) | ((sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($false = (sK3 @ (sK2 @ sK3)))),
% 0.22/0.40 inference(forward_demodulation,[],[f64,f63])).
% 0.22/0.40 thf(f63,plain,(
% 0.22/0.40 ((sK3 @ sK0) = $false)),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f61])).
% 0.22/0.40 thf(f61,plain,(
% 0.22/0.40 ((sK3 @ sK0) = $false) | ($true = $false)),
% 0.22/0.40 inference(superposition,[],[f38,f44])).
% 0.22/0.40 thf(f44,plain,(
% 0.22/0.40 ( ! [X1 : ($i > $o) > $o] : (($true = (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))) | ((sK3 @ X1) = $false)) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f43])).
% 0.22/0.40 thf(f43,plain,(
% 0.22/0.40 ( ! [X1 : ($i > $o) > $o] : (($true = ((sK3 @ X1) => (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))))) )),
% 0.22/0.40 inference(beta_eta_normalization,[],[f42])).
% 0.22/0.40 thf(f42,plain,(
% 0.22/0.40 ( ! [X1 : ($i > $o) > $o] : (($true = ((^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))) @ X1))) )),
% 0.22/0.40 inference(pi_clausification,[],[f41])).
% 0.22/0.40 thf(f41,plain,(
% 0.22/0.40 ($true = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))))),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f39])).
% 0.22/0.40 thf(f38,plain,(
% 0.22/0.40 ((sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK0 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))))))) = $false)),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f37])).
% 0.22/0.40 thf(f64,plain,(
% 0.22/0.40 ((sK3 @ sK0) = $true) | ($false = (sK3 @ (sK2 @ sK3))) | ((sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false)),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f60])).
% 0.22/0.40 thf(f60,plain,(
% 0.22/0.40 ((sK3 @ sK0) = $true) | ($false = (sK3 @ (sK2 @ sK3))) | ($true = $false) | ((sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false)),
% 0.22/0.40 inference(superposition,[],[f44,f33])).
% 0.22/0.40 thf(f33,plain,(
% 0.22/0.40 ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK2 @ X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))))))) = $false) | ($true = (X1 @ sK0)) | ((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false)) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f32])).
% 0.22/0.40 thf(f32,plain,(
% 0.22/0.40 ( ! [X1 : (($i > $o) > $o) > $o] : ((((X1 @ (sK2 @ X1)) => (X1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK2 @ X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))) = $false) | ((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($true = (X1 @ sK0))) )),
% 0.22/0.40 inference(beta_eta_normalization,[],[f31])).
% 0.22/0.40 thf(f31,plain,(
% 0.22/0.40 ( ! [X1 : (($i > $o) > $o) > $o] : (($false = ((^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))) @ (sK2 @ X1))) | ($true = (X1 @ sK0)) | ((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false)) )),
% 0.22/0.40 inference(sigma_clausification,[],[f30])).
% 0.22/0.40 thf(f30,plain,(
% 0.22/0.40 ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($false = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) | ($true = (X1 @ sK0))) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f29])).
% 0.22/0.40 thf(f29,plain,(
% 0.22/0.40 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = (X1 @ sK0)) | (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $false)) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f28])).
% 0.22/0.40 thf(f28,plain,(
% 0.22/0.40 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (X1 @ sK0)))) )),
% 0.22/0.40 inference(beta_eta_normalization,[],[f27])).
% 0.22/0.40 thf(f27,plain,(
% 0.22/0.40 ( ! [X1 : (($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 @ sK0))) @ X1) = $true)) )),
% 0.22/0.40 inference(pi_clausification,[],[f26])).
% 0.22/0.40 thf(f26,plain,(
% 0.22/0.40 ($true = (!! @ ((($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]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK0)))))),
% 0.22/0.40 inference(beta_eta_normalization,[],[f24])).
% 0.22/0.40 thf(f24,plain,(
% 0.22/0.40 ($true = ((^[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 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))) @ sK0))),
% 0.22/0.40 inference(definition_unfolding,[],[f22,f23])).
% 0.22/0.40 thf(f22,plain,(
% 0.22/0.40 ($true = (cNAT @ sK0))),
% 0.22/0.40 inference(cnf_transformation,[],[f17])).
% 0.22/0.40 thf(f69,plain,(
% 0.22/0.40 ~spl1_2),
% 0.22/0.40 inference(avatar_contradiction_clause,[],[f68])).
% 0.22/0.40 thf(f68,plain,(
% 0.22/0.40 $false | ~spl1_2),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f67])).
% 0.22/0.40 thf(f67,plain,(
% 0.22/0.40 ($true = $false) | ~spl1_2),
% 0.22/0.40 inference(backward_demodulation,[],[f56,f63])).
% 0.22/0.40 thf(f56,plain,(
% 0.22/0.40 ((sK3 @ sK0) = $true) | ~spl1_2),
% 0.22/0.40 inference(avatar_component_clause,[],[f54])).
% 0.22/0.40 thf(f54,plain,(
% 0.22/0.40 spl1_2 <=> ((sK3 @ sK0) = $true)),
% 0.22/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.22/0.40 thf(f58,plain,(
% 0.22/0.40 spl1_2 | spl1_1),
% 0.22/0.40 inference(avatar_split_clause,[],[f47,f50,f54])).
% 0.22/0.40 thf(f47,plain,(
% 0.22/0.40 ($true = (sK3 @ (sK2 @ sK3))) | ((sK3 @ sK0) = $true)),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f45])).
% 0.22/0.40 thf(f45,plain,(
% 0.22/0.40 ((sK3 @ sK0) = $true) | ($true = $false) | ($true = (sK3 @ (sK2 @ sK3)))),
% 0.22/0.40 inference(superposition,[],[f34,f40])).
% 0.22/0.40 thf(f34,plain,(
% 0.22/0.40 ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($true = (X1 @ (sK2 @ X1))) | ($true = (X1 @ sK0))) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f32])).
% 0.22/0.40 % SZS output end Proof for theBenchmark
% 0.22/0.40 % (23812)------------------------------
% 0.22/0.40 % (23812)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (23812)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (23812)Memory used [KB]: 5628
% 0.22/0.40 % (23812)Time elapsed: 0.014 s
% 0.22/0.40 % (23812)Instructions burned: 9 (million)
% 0.22/0.40 % (23812)------------------------------
% 0.22/0.40 % (23812)------------------------------
% 0.22/0.40 % (23807)Success in time 0.032 s
%------------------------------------------------------------------------------