TSTP Solution File: SEV300^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV300^5 : 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 16:02:41 EDT 2024
% Result : Theorem 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV300^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.07/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:05:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.35 Running higher-order theorem proving
% 0.12/0.35 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
% 0.12/0.37 % (14539)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.37 % (14541)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)
% 0.12/0.37 % (14542)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.37 % (14540)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)
% 0.12/0.37 % (14543)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)
% 0.12/0.37 % (14544)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)
% 0.12/0.37 % (14545)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.37 % (14542)Instruction limit reached!
% 0.12/0.37 % (14542)------------------------------
% 0.12/0.37 % (14542)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37 % (14543)Instruction limit reached!
% 0.12/0.37 % (14543)------------------------------
% 0.12/0.37 % (14543)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37 % (14542)Termination reason: Unknown
% 0.12/0.37 % (14542)Termination phase: Saturation
% 0.12/0.37
% 0.12/0.37 % (14542)Memory used [KB]: 5500
% 0.12/0.37 % (14542)Time elapsed: 0.003 s
% 0.12/0.37 % (14542)Instructions burned: 2 (million)
% 0.12/0.37 % (14542)------------------------------
% 0.12/0.37 % (14542)------------------------------
% 0.12/0.37 % (14543)Termination reason: Unknown
% 0.12/0.37 % (14543)Termination phase: Saturation
% 0.12/0.37
% 0.12/0.37 % (14543)Memory used [KB]: 895
% 0.12/0.37 % (14543)Time elapsed: 0.003 s
% 0.12/0.37 % (14543)Instructions burned: 2 (million)
% 0.12/0.37 % (14543)------------------------------
% 0.12/0.37 % (14543)------------------------------
% 0.12/0.37 % (14540)Instruction limit reached!
% 0.12/0.37 % (14540)------------------------------
% 0.12/0.37 % (14540)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37 % (14540)Termination reason: Unknown
% 0.12/0.37 % (14540)Termination phase: Saturation
% 0.12/0.37
% 0.12/0.37 % (14540)Memory used [KB]: 5500
% 0.12/0.37 % (14540)Time elapsed: 0.005 s
% 0.12/0.37 % (14540)Instructions burned: 4 (million)
% 0.12/0.37 % (14540)------------------------------
% 0.12/0.37 % (14540)------------------------------
% 0.12/0.38 % (14545)Instruction limit reached!
% 0.12/0.38 % (14545)------------------------------
% 0.12/0.38 % (14545)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (14545)Termination reason: Unknown
% 0.12/0.38 % (14545)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (14545)Memory used [KB]: 5500
% 0.12/0.38 % (14545)Time elapsed: 0.013 s
% 0.12/0.38 % (14545)Instructions burned: 19 (million)
% 0.12/0.38 % (14545)------------------------------
% 0.12/0.38 % (14545)------------------------------
% 0.12/0.39 % (14541)Instruction limit reached!
% 0.12/0.39 % (14541)------------------------------
% 0.12/0.39 % (14541)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (14541)Termination reason: Unknown
% 0.12/0.39 % (14541)Termination phase: Saturation
% 0.12/0.39
% 0.12/0.39 % (14541)Memory used [KB]: 5628
% 0.12/0.39 % (14541)Time elapsed: 0.020 s
% 0.12/0.39 % (14541)Instructions burned: 27 (million)
% 0.12/0.39 % (14541)------------------------------
% 0.12/0.39 % (14541)------------------------------
% 0.12/0.39 % (14546)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)
% 0.12/0.39 % (14547)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)
% 0.12/0.39 % (14548)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)
% 0.12/0.39 % (14546)Instruction limit reached!
% 0.12/0.39 % (14546)------------------------------
% 0.12/0.39 % (14546)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (14546)Termination reason: Unknown
% 0.12/0.39 % (14546)Termination phase: Saturation
% 0.12/0.39
% 0.12/0.39 % (14546)Memory used [KB]: 5500
% 0.12/0.39 % (14546)Time elapsed: 0.005 s
% 0.12/0.39 % (14546)Instructions burned: 3 (million)
% 0.12/0.39 % (14546)------------------------------
% 0.12/0.39 % (14546)------------------------------
% 0.20/0.40 % (14549)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)
% 0.20/0.40 % (14548)Instruction limit reached!
% 0.20/0.40 % (14548)------------------------------
% 0.20/0.40 % (14548)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.40 % (14548)Termination reason: Unknown
% 0.20/0.40 % (14548)Termination phase: Saturation
% 0.20/0.40
% 0.20/0.40 % (14548)Memory used [KB]: 5628
% 0.20/0.40 % (14548)Time elapsed: 0.011 s
% 0.20/0.40 % (14548)Instructions burned: 16 (million)
% 0.20/0.40 % (14548)------------------------------
% 0.20/0.40 % (14548)------------------------------
% 0.20/0.40 % (14549)Instruction limit reached!
% 0.20/0.40 % (14549)------------------------------
% 0.20/0.40 % (14549)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.40 % (14549)Termination reason: Unknown
% 0.20/0.40 % (14549)Termination phase: Saturation
% 0.20/0.40
% 0.20/0.40 % (14549)Memory used [KB]: 5500
% 0.20/0.40 % (14549)Time elapsed: 0.005 s
% 0.20/0.40 % (14549)Instructions burned: 3 (million)
% 0.20/0.40 % (14549)------------------------------
% 0.20/0.40 % (14549)------------------------------
% 0.20/0.40 % (14550)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)
% 0.20/0.41 % (14551)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.41 % (14547)Instruction limit reached!
% 0.20/0.41 % (14547)------------------------------
% 0.20/0.41 % (14547)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41 % (14547)Termination reason: Unknown
% 0.20/0.41 % (14547)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (14547)Memory used [KB]: 5628
% 0.20/0.41 % (14547)Time elapsed: 0.048 s
% 0.20/0.41 % (14547)Instructions burned: 37 (million)
% 0.20/0.41 % (14547)------------------------------
% 0.20/0.41 % (14547)------------------------------
% 0.20/0.41 % (14551)Instruction limit reached!
% 0.20/0.41 % (14551)------------------------------
% 0.20/0.41 % (14551)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41 % (14551)Termination reason: Unknown
% 0.20/0.41 % (14551)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (14551)Memory used [KB]: 1023
% 0.20/0.41 % (14551)Time elapsed: 0.008 s
% 0.20/0.41 % (14551)Instructions burned: 8 (million)
% 0.20/0.41 % (14551)------------------------------
% 0.20/0.41 % (14551)------------------------------
% 0.20/0.42 % (14552)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.42 % (14553)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)
% 0.20/0.42 % (14553)Instruction limit reached!
% 0.20/0.42 % (14553)------------------------------
% 0.20/0.42 % (14553)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.42 % (14553)Termination reason: Unknown
% 0.20/0.42 % (14553)Termination phase: Saturation
% 0.20/0.42
% 0.20/0.42 % (14553)Memory used [KB]: 5500
% 0.20/0.42 % (14553)Time elapsed: 0.005 s
% 0.20/0.42 % (14553)Instructions burned: 3 (million)
% 0.20/0.42 % (14553)------------------------------
% 0.20/0.42 % (14553)------------------------------
% 0.20/0.42 % (14550)First to succeed.
% 0.20/0.42 % (14550)Refutation found. Thanks to Tanya!
% 0.20/0.42 % SZS status Theorem for theBenchmark
% 0.20/0.42 % SZS output start Proof for theBenchmark
% 0.20/0.42 thf(func_def_0, type, cONE: ($i > $o) > $o).
% 0.20/0.42 thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 0.20/0.42 thf(func_def_2, type, cZERO: ($i > $o) > $o).
% 0.20/0.42 thf(func_def_18, type, ph1: !>[X0: $tType]:(X0)).
% 0.20/0.42 thf(func_def_19, type, sK2: $i > $o).
% 0.20/0.42 thf(func_def_21, type, sK4: $i > $i).
% 0.20/0.42 thf(func_def_23, type, sK6: $i > $i).
% 0.20/0.42 thf(func_def_24, type, sK7: ($i > $i) > ($i > $i) > $i).
% 0.20/0.42 thf(f191,plain,(
% 0.20/0.42 $false),
% 0.20/0.42 inference(avatar_sat_refutation,[],[f51,f97,f153,f180,f190])).
% 0.20/0.42 thf(f190,plain,(
% 0.20/0.42 ~spl0_4 | ~spl0_6),
% 0.20/0.42 inference(avatar_contradiction_clause,[],[f189])).
% 0.20/0.42 thf(f189,plain,(
% 0.20/0.42 $false | (~spl0_4 | ~spl0_6)),
% 0.20/0.42 inference(trivial_inequality_removal,[],[f188])).
% 0.20/0.42 thf(f188,plain,(
% 0.20/0.42 ($false = $true) | (~spl0_4 | ~spl0_6)),
% 0.20/0.42 inference(backward_demodulation,[],[f113,f187])).
% 0.20/0.42 thf(f187,plain,(
% 0.20/0.42 ($false = (sK2 @ sK5)) | (~spl0_4 | ~spl0_6)),
% 0.20/0.42 inference(backward_demodulation,[],[f152,f185])).
% 0.20/0.42 thf(f185,plain,(
% 0.20/0.42 ((sK6 @ sK5) = sK5) | (~spl0_4 | ~spl0_6)),
% 0.20/0.42 inference(trivial_inequality_removal,[],[f182])).
% 0.20/0.42 thf(f182,plain,(
% 0.20/0.42 ($false = $true) | ((sK6 @ sK5) = sK5) | (~spl0_4 | ~spl0_6)),
% 0.20/0.42 inference(superposition,[],[f159,f152])).
% 0.20/0.42 thf(f159,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = (sK2 @ (sK6 @ X1))) | ((sK6 @ X1) = X1)) ) | ~spl0_4),
% 0.20/0.42 inference(equality_proxy_clausification,[],[f122])).
% 0.20/0.42 thf(f122,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (((X1 = (sK6 @ X1)) = $true) | ($true = (sK2 @ (sK6 @ X1)))) ) | ~spl0_4),
% 0.20/0.42 inference(binary_proxy_clausification,[],[f119])).
% 0.20/0.42 thf(f119,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (((X1 = (sK6 @ X1)) != (sK2 @ (sK6 @ X1)))) ) | ~spl0_4),
% 0.20/0.42 inference(negative_extensionality,[],[f111])).
% 0.20/0.42 thf(f111,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (((= @ X1) != sK2)) ) | ~spl0_4),
% 0.20/0.42 inference(equality_proxy_clausification,[],[f108])).
% 0.20/0.42 thf(f108,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($false = (sK2 = (= @ X1)))) ) | ~spl0_4),
% 0.20/0.42 inference(beta_eta_normalization,[],[f107])).
% 0.20/0.42 thf(f107,plain,(
% 0.20/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: (sK2 = (= @ Y0))) @ X1) = $false)) ) | ~spl0_4),
% 0.20/0.42 inference(pi_clausification,[],[f50])).
% 0.20/0.42 thf(f50,plain,(
% 0.20/0.42 ($false = (?? @ $i @ (^[Y0 : $i]: (sK2 = (= @ Y0))))) | ~spl0_4),
% 0.20/0.42 inference(avatar_component_clause,[],[f49])).
% 0.20/0.42 thf(f49,plain,(
% 0.20/0.42 spl0_4 <=> ($false = (?? @ $i @ (^[Y0 : $i]: (sK2 = (= @ Y0)))))),
% 0.20/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.20/0.42 thf(f152,plain,(
% 0.20/0.42 ($false = (sK2 @ (sK6 @ sK5))) | ~spl0_6),
% 0.20/0.42 inference(avatar_component_clause,[],[f151])).
% 0.20/0.42 thf(f151,plain,(
% 0.20/0.42 spl0_6 <=> ($false = (sK2 @ (sK6 @ sK5)))),
% 0.20/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.20/0.42 thf(f113,plain,(
% 0.20/0.42 ($true = (sK2 @ sK5)) | ~spl0_4),
% 0.20/0.42 inference(binary_proxy_clausification,[],[f110])).
% 0.20/0.42 thf(f110,plain,(
% 0.20/0.42 ($true = ((sK2 @ sK5) & (~ (?? @ $i @ (^[Y0 : $i]: ((~ (sK5 = Y0)) & (sK2 @ Y0))))))) | ~spl0_4),
% 0.20/0.42 inference(beta_eta_normalization,[],[f109])).
% 0.20/0.42 thf(f109,plain,(
% 0.20/0.42 (((^[Y0 : $i]: ((sK2 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK2 @ Y1))))))) @ sK5) = $true) | ~spl0_4),
% 0.20/0.42 inference(sigma_clausification,[],[f106])).
% 0.20/0.42 thf(f106,plain,(
% 0.20/0.42 ($false != (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK2 @ Y1))))))))) | ~spl0_4),
% 0.20/0.42 inference(forward_demodulation,[],[f32,f50])).
% 0.20/0.42 thf(f32,plain,(
% 0.20/0.42 ((?? @ $i @ (^[Y0 : $i]: (sK2 = (= @ Y0)))) != (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK2 @ Y1)))))))))),
% 0.20/0.42 inference(beta_eta_normalization,[],[f31])).
% 0.20/0.42 thf(f31,plain,(
% 0.20/0.42 (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = (= @ Y1))))) @ sK2) != ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ sK2))),
% 0.20/0.42 inference(negative_extensionality,[],[f28])).
% 0.20/0.42 thf(f28,plain,(
% 0.20/0.42 ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = (= @ Y1))))))),
% 0.20/0.42 inference(equality_proxy_clausification,[],[f27])).
% 0.20/0.42 thf(f27,plain,(
% 0.20/0.42 ($false = ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = (= @ Y1))))) = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))),
% 0.20/0.42 inference(boolean_simplification,[],[f26])).
% 0.20/0.42 thf(f26,plain,(
% 0.20/0.42 ($false = ($true => ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = (= @ Y1))))) = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))),
% 0.20/0.42 inference(backward_demodulation,[],[f21,f25])).
% 0.20/0.42 thf(f25,plain,(
% 0.20/0.42 ($true = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 @ Y2)))) => (Y1 = Y0)))))))),
% 0.20/0.42 inference(binary_proxy_clausification,[],[f21])).
% 0.20/0.42 thf(f21,plain,(
% 0.20/0.42 (((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 @ Y2)))) => (Y1 = Y0)))))) => ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = (= @ Y1))))) = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) = $false)),
% 0.20/0.42 inference(not_proxy_clausification,[],[f20])).
% 0.20/0.42 thf(f20,plain,(
% 0.20/0.42 ((~ ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 @ Y2)))) => (Y1 = Y0)))))) => ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = (= @ Y1))))) = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) = $true)),
% 0.20/0.42 inference(beta_eta_normalization,[],[f19])).
% 0.20/0.42 thf(f19,plain,(
% 0.20/0.42 ($true = (~ ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 @ Y2)))) => (Y1 = Y0)))))) => ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1))))) = ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))))))),
% 0.20/0.42 inference(definition_unfolding,[],[f17,f18])).
% 0.20/0.42 thf(f18,plain,(
% 0.20/0.42 (cONE = ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 0.20/0.42 inference(definition_unfolding,[],[f14,f16,f15])).
% 0.20/0.42 thf(f15,plain,(
% 0.20/0.42 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f8])).
% 0.20/0.42 thf(f8,plain,(
% 0.20/0.42 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.20/0.42 inference(fool_elimination,[],[f7])).
% 0.20/0.42 thf(f7,plain,(
% 0.20/0.42 (cZERO = (^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))))),
% 0.20/0.42 inference(rectify,[],[f1])).
% 0.20/0.42 thf(f1,axiom,(
% 0.20/0.42 (cZERO = (^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cZERO_def)).
% 0.20/0.42 thf(f16,plain,(
% 0.20/0.42 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f13])).
% 0.20/0.42 thf(f13,plain,(
% 0.20/0.42 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 0.20/0.43 inference(fool_elimination,[],[f12])).
% 0.20/0.43 thf(f12,plain,(
% 0.20/0.43 (cSUCC = (^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2] : ((X0 @ (^[X3 : $i] : ((X1 @ X3) & (X2 != X3)))) & (X1 @ X2)))))),
% 0.20/0.43 inference(rectify,[],[f2])).
% 0.20/0.43 thf(f2,axiom,(
% 0.20/0.43 (cSUCC = (^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1] : ((X2 @ (^[X3 : $i] : ((X0 @ X3) & (X1 != X3)))) & (X0 @ X1)))))),
% 0.20/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSUCC_def)).
% 0.20/0.43 thf(f14,plain,(
% 0.20/0.43 (cONE = (cSUCC @ cZERO))),
% 0.20/0.43 inference(cnf_transformation,[],[f9])).
% 0.20/0.43 thf(f9,plain,(
% 0.20/0.43 (cONE = (cSUCC @ cZERO))),
% 0.20/0.43 inference(fool_elimination,[],[f3])).
% 0.20/0.43 thf(f3,axiom,(
% 0.20/0.43 (cONE = (cSUCC @ cZERO))),
% 0.20/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cONE_def)).
% 0.20/0.43 thf(f17,plain,(
% 0.20/0.43 ((~ ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 @ Y2)))) => (Y1 = Y0)))))) => ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1))))) = cONE))) = $true)),
% 0.20/0.43 inference(cnf_transformation,[],[f11])).
% 0.20/0.43 thf(f11,plain,(
% 0.20/0.43 ((~ ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 @ Y2)))) => (Y1 = Y0)))))) => ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1))))) = cONE))) = $true)),
% 0.20/0.43 inference(fool_elimination,[],[f10])).
% 0.20/0.43 thf(f10,plain,(
% 0.20/0.43 ~(! [X0 : $i > $i,X1 : $i > $i] : (! [X2] : ((X1 @ X2) = (X0 @ X2)) => (X0 = X1)) => ((^[X3 : $i > $o] : (? [X4] : (X3 = ((^[X5 : $i, X6 : $i] : ((X5 = X6))) @ X4)))) = cONE))),
% 0.20/0.43 inference(rectify,[],[f5])).
% 0.20/0.43 thf(f5,negated_conjecture,(
% 0.20/0.43 ~(! [X4 : $i > $i,X5 : $i > $i] : (! [X1] : ((X4 @ X1) = (X5 @ X1)) => (X4 = X5)) => ((^[X6 : $i > $o] : (? [X7] : (X6 = ((^[X1 : $i, X7 : $i] : ((X1 = X7))) @ X7)))) = cONE))),
% 0.20/0.43 inference(negated_conjecture,[],[f4])).
% 0.20/0.43 thf(f4,conjecture,(
% 0.20/0.43 ! [X4 : $i > $i,X5 : $i > $i] : (! [X1] : ((X4 @ X1) = (X5 @ X1)) => (X4 = X5)) => ((^[X6 : $i > $o] : (? [X7] : (X6 = ((^[X1 : $i, X7 : $i] : ((X1 = X7))) @ X7)))) = cONE)),
% 0.20/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX6101_EXT_pme)).
% 0.20/0.43 thf(f180,plain,(
% 0.20/0.43 ~spl0_4 | spl0_5),
% 0.20/0.43 inference(avatar_contradiction_clause,[],[f179])).
% 0.20/0.43 thf(f179,plain,(
% 0.20/0.43 $false | (~spl0_4 | spl0_5)),
% 0.20/0.43 inference(subsumption_resolution,[],[f178,f113])).
% 0.20/0.43 thf(f178,plain,(
% 0.20/0.43 ($true != (sK2 @ sK5)) | (~spl0_4 | spl0_5)),
% 0.20/0.43 inference(backward_demodulation,[],[f149,f174])).
% 0.20/0.43 thf(f174,plain,(
% 0.20/0.43 ((sK6 @ sK5) = sK5) | (~spl0_4 | spl0_5)),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f171])).
% 0.20/0.43 thf(f171,plain,(
% 0.20/0.43 ((sK6 @ sK5) = sK5) | ($true != $true) | (~spl0_4 | spl0_5)),
% 0.20/0.43 inference(superposition,[],[f149,f159])).
% 0.20/0.43 thf(f149,plain,(
% 0.20/0.43 ($true != (sK2 @ (sK6 @ sK5))) | spl0_5),
% 0.20/0.43 inference(avatar_component_clause,[],[f148])).
% 0.20/0.43 thf(f148,plain,(
% 0.20/0.43 spl0_5 <=> ($true = (sK2 @ (sK6 @ sK5)))),
% 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.20/0.43 thf(f153,plain,(
% 0.20/0.43 ~spl0_5 | spl0_6 | ~spl0_4),
% 0.20/0.43 inference(avatar_split_clause,[],[f140,f49,f151,f148])).
% 0.20/0.43 thf(f140,plain,(
% 0.20/0.43 ($false = (sK2 @ (sK6 @ sK5))) | ($true != (sK2 @ (sK6 @ sK5))) | ~spl0_4),
% 0.20/0.43 inference(superposition,[],[f119,f136])).
% 0.20/0.43 thf(f136,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = (sK5 = X1)) | ($false = (sK2 @ X1))) ) | ~spl0_4),
% 0.20/0.43 inference(not_proxy_clausification,[],[f124])).
% 0.20/0.43 thf(f124,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (((~ (sK5 = X1)) = $false) | ($false = (sK2 @ X1))) ) | ~spl0_4),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f121])).
% 0.20/0.43 thf(f121,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($false = ((~ (sK5 = X1)) & (sK2 @ X1)))) ) | ~spl0_4),
% 0.20/0.43 inference(beta_eta_normalization,[],[f120])).
% 0.20/0.43 thf(f120,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((~ (sK5 = Y0)) & (sK2 @ Y0))) @ X1))) ) | ~spl0_4),
% 0.20/0.43 inference(pi_clausification,[],[f116])).
% 0.20/0.43 thf(f116,plain,(
% 0.20/0.43 ($false = (?? @ $i @ (^[Y0 : $i]: ((~ (sK5 = Y0)) & (sK2 @ Y0))))) | ~spl0_4),
% 0.20/0.43 inference(not_proxy_clausification,[],[f115])).
% 0.20/0.43 thf(f115,plain,(
% 0.20/0.43 ((~ (?? @ $i @ (^[Y0 : $i]: ((~ (sK5 = Y0)) & (sK2 @ Y0))))) = $true) | ~spl0_4),
% 0.20/0.43 inference(boolean_simplification,[],[f114])).
% 0.20/0.43 thf(f114,plain,(
% 0.20/0.43 ($true = ($true & (~ (?? @ $i @ (^[Y0 : $i]: ((~ (sK5 = Y0)) & (sK2 @ Y0))))))) | ~spl0_4),
% 0.20/0.43 inference(backward_demodulation,[],[f110,f113])).
% 0.20/0.43 thf(f97,plain,(
% 0.20/0.43 ~spl0_3),
% 0.20/0.43 inference(avatar_contradiction_clause,[],[f96])).
% 0.20/0.43 thf(f96,plain,(
% 0.20/0.43 $false | ~spl0_3),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f95])).
% 0.20/0.43 thf(f95,plain,(
% 0.20/0.43 ($false = $true) | ~spl0_3),
% 0.20/0.43 inference(boolean_simplification,[],[f94])).
% 0.20/0.43 thf(f94,plain,(
% 0.20/0.43 ($true = ((~ (sK2 @ (sK4 @ sK3))) & (sK2 @ (sK4 @ sK3)))) | ~spl0_3),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f93])).
% 0.20/0.43 thf(f93,plain,(
% 0.20/0.43 (sK3 != sK3) | ($true = ((~ (sK2 @ (sK4 @ sK3))) & (sK2 @ (sK4 @ sK3)))) | ~spl0_3),
% 0.20/0.43 inference(superposition,[],[f86,f62])).
% 0.20/0.43 thf(f62,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (((sK2 @ X1) = (sK3 = X1))) ) | ~spl0_3),
% 0.20/0.43 inference(argument_congruence,[],[f59])).
% 0.20/0.43 thf(f59,plain,(
% 0.20/0.43 (sK2 = (= @ sK3)) | ~spl0_3),
% 0.20/0.43 inference(equality_proxy_clausification,[],[f58])).
% 0.20/0.43 thf(f58,plain,(
% 0.20/0.43 ($true = (sK2 = (= @ sK3))) | ~spl0_3),
% 0.20/0.43 inference(beta_eta_normalization,[],[f57])).
% 0.20/0.43 thf(f57,plain,(
% 0.20/0.43 ($true = ((^[Y0 : $i]: (sK2 = (= @ Y0))) @ sK3)) | ~spl0_3),
% 0.20/0.43 inference(sigma_clausification,[],[f56])).
% 0.20/0.43 thf(f56,plain,(
% 0.20/0.43 ($false != (?? @ $i @ (^[Y0 : $i]: (sK2 = (= @ Y0))))) | ~spl0_3),
% 0.20/0.43 inference(forward_demodulation,[],[f32,f47])).
% 0.20/0.43 thf(f47,plain,(
% 0.20/0.43 ($false = (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK2 @ Y1))))))))) | ~spl0_3),
% 0.20/0.43 inference(avatar_component_clause,[],[f46])).
% 0.20/0.43 thf(f46,plain,(
% 0.20/0.43 spl0_3 <=> ($false = (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK2 @ Y1)))))))))),
% 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.20/0.43 thf(f86,plain,(
% 0.20/0.43 ( ! [X0 : $i] : (($true = ((~ (X0 = (sK4 @ X0))) & (sK2 @ (sK4 @ X0)))) | (sK3 != X0)) ) | ~spl0_3),
% 0.20/0.43 inference(beta_eta_normalization,[],[f81])).
% 0.20/0.43 thf(f81,plain,(
% 0.20/0.43 ( ! [X0 : $i] : (($true = ((^[Y0 : $i]: ((~ (X0 = Y0)) & (sK2 @ Y0))) @ (sK4 @ X0))) | (sK3 != X0)) ) | ~spl0_3),
% 0.20/0.43 inference(sigma_clausification,[],[f78])).
% 0.20/0.43 thf(f78,plain,(
% 0.20/0.43 ( ! [X0 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: ((~ (X0 = Y0)) & (sK2 @ Y0))))) | (sK3 != X0)) ) | ~spl0_3),
% 0.20/0.43 inference(not_proxy_clausification,[],[f77])).
% 0.20/0.43 thf(f77,plain,(
% 0.20/0.43 ( ! [X0 : $i] : (($false = (~ (?? @ $i @ (^[Y0 : $i]: ((~ (X0 = Y0)) & (sK2 @ Y0)))))) | (sK3 != X0)) ) | ~spl0_3),
% 0.20/0.43 inference(boolean_simplification,[],[f76])).
% 0.20/0.43 thf(f76,plain,(
% 0.20/0.43 ( ! [X0 : $i] : (($false = ($true & (~ (?? @ $i @ (^[Y0 : $i]: ((~ (X0 = Y0)) & (sK2 @ Y0))))))) | (sK3 != X0)) ) | ~spl0_3),
% 0.20/0.43 inference(superposition,[],[f71,f73])).
% 0.20/0.43 thf(f73,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = (sK2 @ X1)) | (sK3 != X1)) ) | ~spl0_3),
% 0.20/0.43 inference(equality_proxy_clausification,[],[f63])).
% 0.20/0.43 thf(f63,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($false = (sK3 = X1)) | ($true = (sK2 @ X1))) ) | ~spl0_3),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f62])).
% 0.20/0.43 thf(f71,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($false = ((sK2 @ X1) & (~ (?? @ $i @ (^[Y0 : $i]: ((~ (X1 = Y0)) & (sK2 @ Y0)))))))) ) | ~spl0_3),
% 0.20/0.43 inference(beta_eta_normalization,[],[f70])).
% 0.20/0.43 thf(f70,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((sK2 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK2 @ Y1))))))) @ X1))) ) | ~spl0_3),
% 0.20/0.43 inference(pi_clausification,[],[f47])).
% 0.20/0.43 thf(f51,plain,(
% 0.20/0.43 spl0_3 | spl0_4),
% 0.20/0.43 inference(avatar_split_clause,[],[f37,f49,f46])).
% 0.20/0.43 thf(f37,plain,(
% 0.20/0.43 ($false = (?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) & (~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK2 @ Y1))))))))) | ($false = (?? @ $i @ (^[Y0 : $i]: (sK2 = (= @ Y0)))))),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f32])).
% 0.20/0.43 % SZS output end Proof for theBenchmark
% 0.20/0.43 % (14550)------------------------------
% 0.20/0.43 % (14550)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43 % (14550)Termination reason: Refutation
% 0.20/0.43
% 0.20/0.43 % (14550)Memory used [KB]: 5628
% 0.20/0.43 % (14550)Time elapsed: 0.021 s
% 0.20/0.43 % (14550)Instructions burned: 22 (million)
% 0.20/0.43 % (14550)------------------------------
% 0.20/0.43 % (14550)------------------------------
% 0.20/0.43 % (14538)Success in time 0.074 s
%------------------------------------------------------------------------------