TSTP Solution File: SEU544^1 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEU544^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n026.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 15:41:10 EDT 2024
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU544^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n026.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 16:02:24 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 % (6341)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 % (6342)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 % (6343)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.37 % (6340)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 % (6344)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 % (6345)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 % (6346)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.38 % (6343)Instruction limit reached!
% 0.12/0.38 % (6343)------------------------------
% 0.12/0.38 % (6343)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (6343)Termination reason: Unknown
% 0.12/0.38 % (6344)Instruction limit reached!
% 0.12/0.38 % (6344)------------------------------
% 0.12/0.38 % (6344)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (6343)Termination phase: shuffling
% 0.12/0.38
% 0.12/0.38 % (6343)Memory used [KB]: 1151
% 0.12/0.38 % (6343)Time elapsed: 0.004 s
% 0.12/0.38 % (6343)Instructions burned: 3 (million)
% 0.12/0.38 % (6343)------------------------------
% 0.12/0.38 % (6343)------------------------------
% 0.12/0.38 % (6344)Termination reason: Unknown
% 0.12/0.38 % (6344)Termination phase: shuffling
% 0.12/0.38
% 0.12/0.38 % (6344)Memory used [KB]: 1151
% 0.12/0.38 % (6344)Time elapsed: 0.004 s
% 0.12/0.38 % (6344)Instructions burned: 3 (million)
% 0.12/0.38 % (6344)------------------------------
% 0.12/0.38 % (6344)------------------------------
% 0.12/0.38 % (6341)Instruction limit reached!
% 0.12/0.38 % (6341)------------------------------
% 0.12/0.38 % (6341)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (6341)Termination reason: Unknown
% 0.12/0.38 % (6341)Termination phase: shuffling
% 0.12/0.38
% 0.12/0.38 % (6341)Memory used [KB]: 1151
% 0.12/0.38 % (6341)Time elapsed: 0.005 s
% 0.12/0.38 % (6341)Instructions burned: 5 (million)
% 0.12/0.38 % (6341)------------------------------
% 0.12/0.38 % (6341)------------------------------
% 0.12/0.38 % (6346)Instruction limit reached!
% 0.12/0.38 % (6346)------------------------------
% 0.12/0.38 % (6346)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (6346)Termination reason: Unknown
% 0.12/0.38 % (6346)Termination phase: Preprocessing 3
% 0.12/0.38
% 0.12/0.38 % (6346)Memory used [KB]: 1663
% 0.12/0.39 % (6346)Time elapsed: 0.013 s
% 0.12/0.39 % (6346)Instructions burned: 18 (million)
% 0.12/0.39 % (6346)------------------------------
% 0.12/0.39 % (6346)------------------------------
% 0.20/0.39 % (6342)Instruction limit reached!
% 0.20/0.39 % (6342)------------------------------
% 0.20/0.39 % (6342)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (6342)Termination reason: Unknown
% 0.20/0.39 % (6342)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (6342)Memory used [KB]: 5884
% 0.20/0.39 % (6342)Time elapsed: 0.016 s
% 0.20/0.39 % (6342)Instructions burned: 27 (million)
% 0.20/0.39 % (6342)------------------------------
% 0.20/0.39 % (6342)------------------------------
% 0.20/0.39 % (6347)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)
% 0.20/0.39 % (6348)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)
% 0.20/0.39 % (6349)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)
% 0.20/0.39 % (6347)Instruction limit reached!
% 0.20/0.39 % (6347)------------------------------
% 0.20/0.39 % (6347)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (6347)Termination reason: Unknown
% 0.20/0.39 % (6347)Termination phase: shuffling
% 0.20/0.39
% 0.20/0.39 % (6347)Memory used [KB]: 1151
% 0.20/0.39 % (6347)Time elapsed: 0.004 s
% 0.20/0.39 % (6347)Instructions burned: 4 (million)
% 0.20/0.39 % (6347)------------------------------
% 0.20/0.39 % (6347)------------------------------
% 0.20/0.40 % (6349)Instruction limit reached!
% 0.20/0.40 % (6349)------------------------------
% 0.20/0.40 % (6349)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.40 % (6349)Termination reason: Unknown
% 0.20/0.40 % (6349)Termination phase: Preprocessing 3
% 0.20/0.40
% 0.20/0.40 % (6349)Memory used [KB]: 1535
% 0.20/0.40 % (6349)Time elapsed: 0.011 s
% 0.20/0.40 % (6349)Instructions burned: 15 (million)
% 0.20/0.40 % (6349)------------------------------
% 0.20/0.40 % (6349)------------------------------
% 0.20/0.40 % (6350)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 % (6351)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)
% 0.20/0.40 % (6350)Instruction limit reached!
% 0.20/0.40 % (6350)------------------------------
% 0.20/0.40 % (6350)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.40 % (6350)Termination reason: Unknown
% 0.20/0.40 % (6350)Termination phase: shuffling
% 0.20/0.40
% 0.20/0.40 % (6350)Memory used [KB]: 1151
% 0.20/0.40 % (6350)Time elapsed: 0.004 s
% 0.20/0.40 % (6350)Instructions burned: 4 (million)
% 0.20/0.40 % (6350)------------------------------
% 0.20/0.40 % (6350)------------------------------
% 0.20/0.41 % (6352)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 % (6348)Instruction limit reached!
% 0.20/0.41 % (6348)------------------------------
% 0.20/0.41 % (6348)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41 % (6348)Termination reason: Unknown
% 0.20/0.41 % (6348)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (6348)Memory used [KB]: 5884
% 0.20/0.41 % (6348)Time elapsed: 0.020 s
% 0.20/0.41 % (6348)Instructions burned: 37 (million)
% 0.20/0.41 % (6348)------------------------------
% 0.20/0.41 % (6348)------------------------------
% 0.20/0.41 % (6352)Instruction limit reached!
% 0.20/0.41 % (6352)------------------------------
% 0.20/0.41 % (6352)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41 % (6352)Termination reason: Unknown
% 0.20/0.41 % (6352)Termination phase: shuffling
% 0.20/0.41
% 0.20/0.41 % (6352)Memory used [KB]: 1279
% 0.20/0.41 % (6352)Time elapsed: 0.006 s
% 0.20/0.41 % (6352)Instructions burned: 7 (million)
% 0.20/0.41 % (6352)------------------------------
% 0.20/0.41 % (6352)------------------------------
% 0.20/0.42 % (6353)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 % (6354)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 % (6354)Instruction limit reached!
% 0.20/0.42 % (6354)------------------------------
% 0.20/0.42 % (6354)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.42 % (6354)Termination reason: Unknown
% 0.20/0.42 % (6354)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (6354)Memory used [KB]: 1151
% 0.20/0.42 % (6354)Time elapsed: 0.004 s
% 0.20/0.42 % (6354)Instructions burned: 3 (million)
% 0.20/0.42 % (6354)------------------------------
% 0.20/0.42 % (6354)------------------------------
% 0.20/0.43 % (6355)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)
% 0.20/0.43 % (6353)Instruction limit reached!
% 0.20/0.43 % (6353)------------------------------
% 0.20/0.43 % (6353)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43 % (6353)Termination reason: Unknown
% 0.20/0.43 % (6353)Termination phase: Property scanning
% 0.20/0.43
% 0.20/0.43 % (6353)Memory used [KB]: 1279
% 0.20/0.43 % (6353)Time elapsed: 0.011 s
% 0.20/0.43 % (6353)Instructions burned: 18 (million)
% 0.20/0.43 % (6353)------------------------------
% 0.20/0.43 % (6353)------------------------------
% 0.20/0.43 % (6340)First to succeed.
% 0.20/0.43 % (6355)Instruction limit reached!
% 0.20/0.43 % (6355)------------------------------
% 0.20/0.43 % (6355)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43 % (6355)Termination reason: Unknown
% 0.20/0.43 % (6355)Termination phase: shuffling
% 0.20/0.43
% 0.20/0.43 % (6355)Memory used [KB]: 1151
% 0.20/0.43 % (6355)Time elapsed: 0.004 s
% 0.20/0.43 % (6355)Instructions burned: 4 (million)
% 0.20/0.43 % (6355)------------------------------
% 0.20/0.43 % (6355)------------------------------
% 0.20/0.43 % (6356)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)
% 0.20/0.43 % (6340)Refutation found. Thanks to Tanya!
% 0.20/0.43 % SZS status Theorem for theBenchmark
% 0.20/0.43 % SZS output start Proof for theBenchmark
% 0.20/0.43 thf(func_def_0, type, in: $i > $i > $o).
% 0.20/0.43 thf(func_def_1, type, exu: ($i > $o) > $o).
% 0.20/0.43 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 0.20/0.43 thf(func_def_8, type, powerset: $i > $i).
% 0.20/0.43 thf(func_def_10, type, setunion: $i > $i).
% 0.20/0.43 thf(func_def_19, type, descr: ($i > $o) > $i).
% 0.20/0.43 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.43 thf(func_def_26, type, prop2set: $o > $i).
% 0.20/0.43 thf(func_def_36, type, nonempty: $i > $o).
% 0.20/0.43 thf(func_def_69, type, set2prop: $i > $o).
% 0.20/0.43 thf(func_def_89, type, sK0: $i > $o).
% 0.20/0.43 thf(func_def_92, type, sK3: $i > $i).
% 0.20/0.43 thf(func_def_93, type, sK4: $i > $i).
% 0.20/0.43 thf(func_def_94, type, sK5: $i > $i).
% 0.20/0.43 thf(func_def_95, type, sK6: $i > $i > $i > $i).
% 0.20/0.43 thf(func_def_96, type, sK7: $i > $i > $i).
% 0.20/0.43 thf(func_def_97, type, sK8: $i > $i > $i).
% 0.20/0.43 thf(func_def_98, type, sK9: $i > $i > $i).
% 0.20/0.43 thf(func_def_99, type, sK10: $i > $i > $i).
% 0.20/0.43 thf(func_def_100, type, sK11: $i > $i > $i).
% 0.20/0.43 thf(func_def_101, type, sK12: $i > $i).
% 0.20/0.43 thf(func_def_102, type, sK13: $o > $i > $i > $i).
% 0.20/0.43 thf(func_def_103, type, sK14: ($i > $o) > $i).
% 0.20/0.43 thf(func_def_104, type, sK15: ($i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_106, type, sK16: ($i > $i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_107, type, sK17: ($i > $i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_108, type, sK18: $i > ($i > $i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_109, type, sK19: ($i > $i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_110, type, sK20: $i > ($i > $i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_111, type, sK21: $i > ($i > $i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_112, type, sK22: $i > ($i > $i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_113, type, sK23: $i > $i).
% 0.20/0.43 thf(func_def_114, type, sK24: ($i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_115, type, sK25: ($i > $o) > $i).
% 0.20/0.43 thf(func_def_116, type, sK26: ($i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_117, type, sK27: ($i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_118, type, sK28: $i > ($i > $o) > $i).
% 0.20/0.43 thf(func_def_119, type, sK29: ($i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_120, type, sK30: $i > ($i > $o) > $i).
% 0.20/0.43 thf(func_def_121, type, sK31: $i > $i > $i).
% 0.20/0.43 thf(func_def_122, type, sK32: $i > $i > $i).
% 0.20/0.43 thf(func_def_123, type, sK33: $i > $i > $i).
% 0.20/0.43 thf(func_def_124, type, sK34: $i > $i).
% 0.20/0.43 thf(func_def_125, type, sK35: $i > $i > $i).
% 0.20/0.43 thf(func_def_126, type, sK36: ($i > $o) > $i).
% 0.20/0.43 thf(func_def_127, type, sK37: ($i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_128, type, sK38: ($i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_129, type, sK39: $i > $i > $i).
% 0.20/0.43 thf(func_def_130, type, sK40: $i > $i > $i).
% 0.20/0.43 thf(func_def_131, type, sK41: $i > $i).
% 0.20/0.43 thf(func_def_132, type, sK42: ($i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_133, type, sK43: ($i > $o) > $i > $i).
% 0.20/0.43 thf(func_def_134, type, sK44: $i > $i > $i).
% 0.20/0.43 thf(func_def_135, type, sK45: $i > $i).
% 0.20/0.43 thf(f1184,plain,(
% 0.20/0.43 $false),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f1182])).
% 0.20/0.43 thf(f1182,plain,(
% 0.20/0.43 ($true = $false)),
% 0.20/0.43 inference(superposition,[],[f285,f1180])).
% 0.20/0.43 thf(f1180,plain,(
% 0.20/0.43 ((sK0 @ sK1) = $false)),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f1178])).
% 0.20/0.43 thf(f1178,plain,(
% 0.20/0.43 (sK1 != sK1) | ((sK0 @ sK1) = $false)),
% 0.20/0.43 inference(superposition,[],[f1143,f1162])).
% 0.20/0.43 thf(f1162,plain,(
% 0.20/0.43 ( ! [X0 : $i] : ((sK1 = (sK34 @ X0)) | ((sK0 @ X0) = $false)) )),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f1158])).
% 0.20/0.43 thf(f1158,plain,(
% 0.20/0.43 ( ! [X0 : $i] : ((sK1 = (sK34 @ X0)) | ($true != $true) | ((sK0 @ X0) = $false)) )),
% 0.20/0.43 inference(superposition,[],[f284,f894])).
% 0.20/0.43 thf(f894,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = (sK0 @ (sK34 @ X1))) | ((sK0 @ X1) = $false)) )),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f892])).
% 0.20/0.43 thf(f892,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (((sK0 @ X1) = $false) | (((sK0 @ (sK34 @ X1)) => (X1 = (sK34 @ X1))) = $false)) )),
% 0.20/0.43 inference(beta_eta_normalization,[],[f891])).
% 0.20/0.43 thf(f891,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (((sK0 @ X1) = $false) | (((^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0))) @ (sK34 @ X1)) = $false)) )),
% 0.20/0.43 inference(sigma_clausification,[],[f890])).
% 0.20/0.43 thf(f890,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (((sK0 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0)))) = $false)) )),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f889])).
% 0.20/0.43 thf(f889,plain,(
% 0.20/0.43 ( ! [X1 : $i] : ((((sK0 @ X1) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0))))) = $false)) )),
% 0.20/0.43 inference(beta_eta_normalization,[],[f888])).
% 0.20/0.43 thf(f888,plain,(
% 0.20/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ X1) = $false)) )),
% 0.20/0.43 inference(pi_clausification,[],[f887])).
% 0.20/0.43 thf(f887,plain,(
% 0.20/0.43 ($true != (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))))),
% 0.20/0.43 inference(beta_eta_normalization,[],[f330])).
% 0.20/0.43 thf(f330,plain,(
% 0.20/0.43 ($true != ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 0.20/0.43 inference(definition_unfolding,[],[f283,f229])).
% 0.20/0.43 thf(f229,plain,(
% 0.20/0.43 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.20/0.43 inference(cnf_transformation,[],[f95])).
% 0.20/0.43 thf(f95,plain,(
% 0.20/0.43 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.20/0.43 inference(fool_elimination,[],[f94])).
% 0.20/0.43 thf(f94,plain,(
% 0.20/0.43 (exu = (^[X0 : $i > $o] : (? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.20/0.43 inference(rectify,[],[f1])).
% 0.20/0.43 thf(f1,axiom,(
% 0.20/0.43 (exu = (^[X0 : $i > $o] : (? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.20/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu)).
% 0.20/0.43 thf(f283,plain,(
% 0.20/0.43 ($true != (exu @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 0.20/0.43 inference(cnf_transformation,[],[f192])).
% 0.20/0.43 thf(f192,plain,(
% 0.20/0.43 (nonemptyI1 = $true) & (emptyinunitempty = $true) & (notdallE = $true) & (quantDeMorgan3 = $true) & (setbeta = $true) & (subPowSU = $true) & (setextAx = $true) & (quantDeMorgan4 = $true) & ((($true = (sK0 @ sK1)) & ! [X2] : (($true != (sK0 @ X2)) | (sK1 = X2))) & ($true != (exu @ (^[Y0 : $i]: (sK0 @ Y0))))) & (prop2setI = $true) & (exuE1 = $true) & (emptyE1 = $true) & (setadjoinIR = $true) & (omegaIndAx = $true) & (setadjoinAx = $true) & (emptysetimpfalse = $true) & (quantDeMorgan1 = $true) & (wellorderingAx = $true) & (nonemptyE1 = $true) & (notinemptyset = $true) & (omegaSAx = $true) & (nonemptyI = $true) & (prop2setE = $true) & (uniqinunit = $true) & (powersetAx = $true) & (notdexE = $true) & (upairsetIL = $true) & (emptyI = $true) & (omega0Ax = $true) & (notinsingleton = $true) & (vacuousDall = $true) & (exuE3e = $true) & (emptyInPowerset = $true) & (replAx = $true) & (quantDeMorgan2 = $true) & (emptysetE = $true) & (setadjoinE = $true) & (setunionE = $true) & (descrp = $true) & (exuE2 = $true) & (dsetconstrEL = $true) & (upairsetIR = $true) & (powersetE = $true) & (dsetconstrER = $true) & (foundationAx = $true) & (emptysetAx = $true) & (powersetI = $true) & (upairsetE = $true) & (prop2set2propI = $true) & (setunionAx = $true) & (dsetconstrI = $true) & (setunionI = $true) & (setadjoinOr = $true) & (setext = $true) & (nonemptyImpWitness = $true) & (noeltsimpempty = $true) & (setadjoinIL = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (emptyinPowerset = $true) & (setoftrueEq = $true)),
% 0.20/0.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f189,f191,f190])).
% 0.20/0.43 thf(f190,plain,(
% 0.20/0.43 ? [X0 : $i > $o] : (? [X1] : (((X0 @ X1) = $true) & ! [X2] : (((X0 @ X2) != $true) | (X1 = X2))) & ($true != (exu @ (^[Y0 : $i]: (X0 @ Y0))))) => (? [X1] : (($true = (sK0 @ X1)) & ! [X2] : (($true != (sK0 @ X2)) | (X1 = X2))) & ($true != (exu @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 0.20/0.43 introduced(choice_axiom,[])).
% 0.20/0.43 thf(f191,plain,(
% 0.20/0.43 ? [X1] : (($true = (sK0 @ X1)) & ! [X2] : (($true != (sK0 @ X2)) | (X1 = X2))) => (($true = (sK0 @ sK1)) & ! [X2] : (($true != (sK0 @ X2)) | (sK1 = X2)))),
% 0.20/0.43 introduced(choice_axiom,[])).
% 0.20/0.43 thf(f189,plain,(
% 0.20/0.43 (nonemptyI1 = $true) & (emptyinunitempty = $true) & (notdallE = $true) & (quantDeMorgan3 = $true) & (setbeta = $true) & (subPowSU = $true) & (setextAx = $true) & (quantDeMorgan4 = $true) & ? [X0 : $i > $o] : (? [X1] : (((X0 @ X1) = $true) & ! [X2] : (((X0 @ X2) != $true) | (X1 = X2))) & ($true != (exu @ (^[Y0 : $i]: (X0 @ Y0))))) & (prop2setI = $true) & (exuE1 = $true) & (emptyE1 = $true) & (setadjoinIR = $true) & (omegaIndAx = $true) & (setadjoinAx = $true) & (emptysetimpfalse = $true) & (quantDeMorgan1 = $true) & (wellorderingAx = $true) & (nonemptyE1 = $true) & (notinemptyset = $true) & (omegaSAx = $true) & (nonemptyI = $true) & (prop2setE = $true) & (uniqinunit = $true) & (powersetAx = $true) & (notdexE = $true) & (upairsetIL = $true) & (emptyI = $true) & (omega0Ax = $true) & (notinsingleton = $true) & (vacuousDall = $true) & (exuE3e = $true) & (emptyInPowerset = $true) & (replAx = $true) & (quantDeMorgan2 = $true) & (emptysetE = $true) & (setadjoinE = $true) & (setunionE = $true) & (descrp = $true) & (exuE2 = $true) & (dsetconstrEL = $true) & (upairsetIR = $true) & (powersetE = $true) & (dsetconstrER = $true) & (foundationAx = $true) & (emptysetAx = $true) & (powersetI = $true) & (upairsetE = $true) & (prop2set2propI = $true) & (setunionAx = $true) & (dsetconstrI = $true) & (setunionI = $true) & (setadjoinOr = $true) & (setext = $true) & (nonemptyImpWitness = $true) & (noeltsimpempty = $true) & (setadjoinIL = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (emptyinPowerset = $true) & (setoftrueEq = $true)),
% 0.20/0.43 inference(flattening,[],[f188])).
% 0.20/0.43 thf(f188,plain,(
% 0.20/0.43 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i > $o] : (? [X1] : (((X0 @ X1) = $true) & ! [X2] : (((X0 @ X2) != $true) | (X1 = X2))) & ($true != (exu @ (^[Y0 : $i]: (X0 @ Y0))))) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 0.20/0.43 inference(ennf_transformation,[],[f135])).
% 0.20/0.43 thf(f135,plain,(
% 0.20/0.43 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ! [X0 : $i > $o] : (? [X1] : (((X0 @ X1) = $true) & ! [X2] : (((X0 @ X2) = $true) => (X1 = X2))) => ($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.20/0.43 inference(fool_elimination,[],[f134])).
% 0.20/0.43 thf(f134,plain,(
% 0.20/0.43 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => ! [X0 : $i > $o] : (? [X1] : ((X0 @ X1) & ! [X2] : ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X3 : $i] : (X0 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.20/0.43 inference(rectify,[],[f64])).
% 0.20/0.43 thf(f64,negated_conjecture,(
% 0.20/0.43 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => ! [X0 : $i > $o] : (? [X1] : ((X0 @ X1) & ! [X2] : ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : (X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.20/0.43 inference(negated_conjecture,[],[f63])).
% 0.20/0.43 thf(f63,conjecture,(
% 0.20/0.43 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => ! [X0 : $i > $o] : (? [X1] : ((X0 @ X1) & ! [X2] : ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : (X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.20/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1)).
% 0.20/0.43 thf(f284,plain,(
% 0.20/0.43 ( ! [X2 : $i] : (($true != (sK0 @ X2)) | (sK1 = X2)) )),
% 0.20/0.43 inference(cnf_transformation,[],[f192])).
% 0.20/0.43 thf(f1143,plain,(
% 0.20/0.43 (sK1 != (sK34 @ sK1))),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f1137])).
% 0.20/0.43 thf(f1137,plain,(
% 0.20/0.43 (sK1 != (sK34 @ sK1)) | ($true = $false)),
% 0.20/0.43 inference(superposition,[],[f895,f285])).
% 0.20/0.43 thf(f895,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (((sK0 @ X1) = $false) | ((sK34 @ X1) != X1)) )),
% 0.20/0.43 inference(equality_proxy_clausification,[],[f893])).
% 0.20/0.43 thf(f893,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (((X1 = (sK34 @ X1)) = $false) | ((sK0 @ X1) = $false)) )),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f892])).
% 0.20/0.43 thf(f285,plain,(
% 0.20/0.43 ($true = (sK0 @ sK1))),
% 0.20/0.43 inference(cnf_transformation,[],[f192])).
% 0.20/0.43 % SZS output end Proof for theBenchmark
% 0.20/0.43 % (6340)------------------------------
% 0.20/0.43 % (6340)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43 % (6340)Termination reason: Refutation
% 0.20/0.43
% 0.20/0.43 % (6340)Memory used [KB]: 6396
% 0.20/0.43 % (6340)Time elapsed: 0.056 s
% 0.20/0.43 % (6340)Instructions burned: 89 (million)
% 0.20/0.43 % (6340)------------------------------
% 0.20/0.43 % (6340)------------------------------
% 0.20/0.43 % (6339)Success in time 0.078 s
%------------------------------------------------------------------------------