TSTP Solution File: SEU643^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU643^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 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 : Tue May 21 03:50:16 EDT 2024
% Result : Theorem 0.21s 0.46s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU643^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n019.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 15:47:23 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.37 % (1569)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.37 % (1572)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (1571)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)
% 0.21/0.37 % (1570)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)
% 0.21/0.37 % (1574)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)
% 0.21/0.37 % (1575)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.37 % (1572)Instruction limit reached!
% 0.21/0.37 % (1572)------------------------------
% 0.21/0.37 % (1572)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (1572)Termination reason: Unknown
% 0.21/0.37 % (1572)Termination phase: shuffling
% 0.21/0.37
% 0.21/0.37 % (1572)Memory used [KB]: 1023
% 0.21/0.37 % (1572)Time elapsed: 0.003 s
% 0.21/0.37 % (1572)Instructions burned: 2 (million)
% 0.21/0.37 % (1572)------------------------------
% 0.21/0.37 % (1572)------------------------------
% 0.21/0.38 % (1570)Instruction limit reached!
% 0.21/0.38 % (1570)------------------------------
% 0.21/0.38 % (1570)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (1570)Termination reason: Unknown
% 0.21/0.38 % (1570)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (1570)Memory used [KB]: 5500
% 0.21/0.38 % (1570)Time elapsed: 0.005 s
% 0.21/0.38 % (1570)Instructions burned: 5 (million)
% 0.21/0.38 % (1570)------------------------------
% 0.21/0.38 % (1570)------------------------------
% 0.21/0.38 % (1574)Refutation not found, incomplete strategy
% 0.21/0.38 % (1574)------------------------------
% 0.21/0.38 % (1574)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (1574)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38
% 0.21/0.38
% 0.21/0.38 % (1574)Memory used [KB]: 5628
% 0.21/0.38 % (1574)Time elapsed: 0.010 s
% 0.21/0.38 % (1574)Instructions burned: 12 (million)
% 0.21/0.38 % (1574)------------------------------
% 0.21/0.38 % (1574)------------------------------
% 0.21/0.38 % (1573)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)
% 0.21/0.38 % (1573)Instruction limit reached!
% 0.21/0.38 % (1573)------------------------------
% 0.21/0.38 % (1573)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (1573)Termination reason: Unknown
% 0.21/0.38 % (1573)Termination phase: Property scanning
% 0.21/0.38
% 0.21/0.38 % (1573)Memory used [KB]: 1023
% 0.21/0.38 % (1573)Time elapsed: 0.003 s
% 0.21/0.38 % (1573)Instructions burned: 2 (million)
% 0.21/0.38 % (1573)------------------------------
% 0.21/0.38 % (1573)------------------------------
% 0.21/0.38 % (1575)Instruction limit reached!
% 0.21/0.38 % (1575)------------------------------
% 0.21/0.38 % (1575)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (1576)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)
% 0.21/0.38 % (1575)Termination reason: Unknown
% 0.21/0.39 % (1575)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (1575)Memory used [KB]: 5628
% 0.21/0.39 % (1575)Time elapsed: 0.014 s
% 0.21/0.39 % (1575)Instructions burned: 19 (million)
% 0.21/0.39 % (1575)------------------------------
% 0.21/0.39 % (1575)------------------------------
% 0.21/0.39 % (1576)Instruction limit reached!
% 0.21/0.39 % (1576)------------------------------
% 0.21/0.39 % (1576)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (1576)Termination reason: Unknown
% 0.21/0.39 % (1576)Termination phase: Property scanning
% 0.21/0.39
% 0.21/0.39 % (1576)Memory used [KB]: 1023
% 0.21/0.39 % (1576)Time elapsed: 0.004 s
% 0.21/0.39 % (1576)Instructions burned: 4 (million)
% 0.21/0.39 % (1576)------------------------------
% 0.21/0.39 % (1576)------------------------------
% 0.21/0.39 % (1577)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)
% 0.21/0.39 % (1571)Instruction limit reached!
% 0.21/0.39 % (1571)------------------------------
% 0.21/0.39 % (1571)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (1571)Termination reason: Unknown
% 0.21/0.39 % (1571)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (1571)Memory used [KB]: 5628
% 0.21/0.39 % (1571)Time elapsed: 0.019 s
% 0.21/0.39 % (1571)Instructions burned: 27 (million)
% 0.21/0.39 % (1571)------------------------------
% 0.21/0.39 % (1571)------------------------------
% 0.21/0.39 % (1578)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)
% 0.21/0.40 % (1579)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)
% 0.21/0.40 % (1580)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)
% 0.21/0.40 % (1579)Instruction limit reached!
% 0.21/0.40 % (1579)------------------------------
% 0.21/0.40 % (1579)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (1579)Termination reason: Unknown
% 0.21/0.40 % (1579)Termination phase: Property scanning
% 0.21/0.40
% 0.21/0.40 % (1579)Memory used [KB]: 1023
% 0.21/0.40 % (1579)Time elapsed: 0.004 s
% 0.21/0.40 % (1579)Instructions burned: 4 (million)
% 0.21/0.40 % (1579)------------------------------
% 0.21/0.40 % (1579)------------------------------
% 0.21/0.40 % (1581)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.40 % (1578)Instruction limit reached!
% 0.21/0.40 % (1578)------------------------------
% 0.21/0.40 % (1578)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (1578)Termination reason: Unknown
% 0.21/0.40 % (1578)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (1578)Memory used [KB]: 5628
% 0.21/0.40 % (1578)Time elapsed: 0.012 s
% 0.21/0.40 % (1578)Instructions burned: 15 (million)
% 0.21/0.40 % (1578)------------------------------
% 0.21/0.40 % (1578)------------------------------
% 0.21/0.40 % (1582)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.40 % (1581)Instruction limit reached!
% 0.21/0.40 % (1581)------------------------------
% 0.21/0.40 % (1581)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (1581)Termination reason: Unknown
% 0.21/0.40 % (1581)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (1581)Memory used [KB]: 1023
% 0.21/0.40 % (1581)Time elapsed: 0.006 s
% 0.21/0.40 % (1581)Instructions burned: 8 (million)
% 0.21/0.40 % (1581)------------------------------
% 0.21/0.40 % (1581)------------------------------
% 0.21/0.40 % (1583)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)
% 0.21/0.41 % (1583)Instruction limit reached!
% 0.21/0.41 % (1583)------------------------------
% 0.21/0.41 % (1583)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (1583)Termination reason: Unknown
% 0.21/0.41 % (1583)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (1583)Memory used [KB]: 1023
% 0.21/0.41 % (1583)Time elapsed: 0.004 s
% 0.21/0.41 % (1583)Instructions burned: 4 (million)
% 0.21/0.41 % (1583)------------------------------
% 0.21/0.41 % (1583)------------------------------
% 0.21/0.41 % (1577)Instruction limit reached!
% 0.21/0.41 % (1577)------------------------------
% 0.21/0.41 % (1577)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (1577)Termination reason: Unknown
% 0.21/0.41 % (1577)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (1577)Memory used [KB]: 5884
% 0.21/0.41 % (1577)Time elapsed: 0.023 s
% 0.21/0.41 % (1577)Instructions burned: 38 (million)
% 0.21/0.41 % (1577)------------------------------
% 0.21/0.41 % (1577)------------------------------
% 0.21/0.41 % (1582)Instruction limit reached!
% 0.21/0.41 % (1582)------------------------------
% 0.21/0.41 % (1582)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (1582)Termination reason: Unknown
% 0.21/0.41 % (1582)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (1582)Memory used [KB]: 5884
% 0.21/0.41 % (1582)Time elapsed: 0.035 s
% 0.21/0.41 % (1582)Instructions burned: 16 (million)
% 0.21/0.41 % (1582)------------------------------
% 0.21/0.41 % (1582)------------------------------
% 0.21/0.41 % (1584)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)
% 0.21/0.41 % (1585)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)
% 0.21/0.42 % (1584)Instruction limit reached!
% 0.21/0.42 % (1584)------------------------------
% 0.21/0.42 % (1584)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (1584)Termination reason: Unknown
% 0.21/0.42 % (1584)Termination phase: Function definition elimination
% 0.21/0.42
% 0.21/0.42 % (1584)Memory used [KB]: 1023
% 0.21/0.42 % (1584)Time elapsed: 0.004 s
% 0.21/0.42 % (1584)Instructions burned: 4 (million)
% 0.21/0.42 % (1584)------------------------------
% 0.21/0.42 % (1584)------------------------------
% 0.21/0.42 % (1585)Refutation not found, incomplete strategy
% 0.21/0.42 % (1585)------------------------------
% 0.21/0.42 % (1585)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (1586)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.42 % (1585)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 % (1585)Memory used [KB]: 5500
% 0.21/0.42 % (1585)Time elapsed: 0.005 s
% 0.21/0.42 % (1585)Instructions burned: 5 (million)
% 0.21/0.42 % (1585)------------------------------
% 0.21/0.42 % (1585)------------------------------
% 0.21/0.42 % (1586)Instruction limit reached!
% 0.21/0.42 % (1586)------------------------------
% 0.21/0.42 % (1586)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (1586)Termination reason: Unknown
% 0.21/0.42 % (1586)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (1586)Memory used [KB]: 1023
% 0.21/0.42 % (1586)Time elapsed: 0.003 s
% 0.21/0.42 % (1586)Instructions burned: 3 (million)
% 0.21/0.42 % (1586)------------------------------
% 0.21/0.42 % (1586)------------------------------
% 0.21/0.42 % (1587)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.42 % (1587)Instruction limit reached!
% 0.21/0.42 % (1587)------------------------------
% 0.21/0.42 % (1587)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (1587)Termination reason: Unknown
% 0.21/0.42 % (1587)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (1587)Memory used [KB]: 1023
% 0.21/0.42 % (1587)Time elapsed: 0.004 s
% 0.21/0.42 % (1587)Instructions burned: 4 (million)
% 0.21/0.42 % (1587)------------------------------
% 0.21/0.42 % (1587)------------------------------
% 0.21/0.42 % (1588)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.43 % (1589)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.43 % (1590)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.43 % (1590)Instruction limit reached!
% 0.21/0.43 % (1590)------------------------------
% 0.21/0.43 % (1590)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (1590)Termination reason: Unknown
% 0.21/0.43 % (1590)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (1590)Memory used [KB]: 5500
% 0.21/0.43 % (1590)Time elapsed: 0.005 s
% 0.21/0.43 % (1590)Instructions burned: 6 (million)
% 0.21/0.43 % (1590)------------------------------
% 0.21/0.43 % (1590)------------------------------
% 0.21/0.43 % (1591)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.21/0.43 % (1592)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.21/0.44 % (1588)Instruction limit reached!
% 0.21/0.44 % (1588)------------------------------
% 0.21/0.44 % (1588)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (1588)Termination reason: Unknown
% 0.21/0.44 % (1588)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (1588)Memory used [KB]: 5628
% 0.21/0.44 % (1588)Time elapsed: 0.013 s
% 0.21/0.44 % (1588)Instructions burned: 18 (million)
% 0.21/0.44 % (1588)------------------------------
% 0.21/0.44 % (1588)------------------------------
% 0.21/0.44 % (1591)Refutation not found, incomplete strategy
% 0.21/0.44 % (1591)------------------------------
% 0.21/0.44 % (1591)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (1591)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.44
% 0.21/0.44
% 0.21/0.44 % (1591)Memory used [KB]: 5500
% 0.21/0.44 % (1591)Time elapsed: 0.006 s
% 0.21/0.44 % (1591)Instructions burned: 5 (million)
% 0.21/0.44 % (1591)------------------------------
% 0.21/0.44 % (1591)------------------------------
% 0.21/0.44 % (1593)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.44 % (1593)Instruction limit reached!
% 0.21/0.44 % (1593)------------------------------
% 0.21/0.44 % (1593)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (1593)Termination reason: Unknown
% 0.21/0.44 % (1593)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (1593)Memory used [KB]: 5500
% 0.21/0.44 % (1593)Time elapsed: 0.005 s
% 0.21/0.44 % (1593)Instructions burned: 6 (million)
% 0.21/0.44 % (1593)------------------------------
% 0.21/0.44 % (1593)------------------------------
% 0.21/0.45 % (1594)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.45 % (1592)Instruction limit reached!
% 0.21/0.45 % (1592)------------------------------
% 0.21/0.45 % (1592)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (1592)Termination reason: Unknown
% 0.21/0.45 % (1592)Termination phase: Saturation
% 0.21/0.45
% 0.21/0.45 % (1592)Memory used [KB]: 5628
% 0.21/0.45 % (1592)Time elapsed: 0.016 s
% 0.21/0.45 % (1592)Instructions burned: 21 (million)
% 0.21/0.45 % (1592)------------------------------
% 0.21/0.45 % (1592)------------------------------
% 0.21/0.45 % (1595)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.21/0.45 % (1594)Instruction limit reached!
% 0.21/0.45 % (1594)------------------------------
% 0.21/0.45 % (1594)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (1594)Termination reason: Unknown
% 0.21/0.45 % (1594)Termination phase: Saturation
% 0.21/0.45
% 0.21/0.45 % (1594)Memory used [KB]: 5500
% 0.21/0.45 % (1594)Time elapsed: 0.005 s
% 0.21/0.45 % (1594)Instructions burned: 6 (million)
% 0.21/0.45 % (1594)------------------------------
% 0.21/0.45 % (1594)------------------------------
% 0.21/0.45 % (1580)First to succeed.
% 0.21/0.45 % (1596)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.21/0.46 % (1580)Refutation found. Thanks to Tanya!
% 0.21/0.46 % SZS status Theorem for theBenchmark
% 0.21/0.46 % SZS output start Proof for theBenchmark
% 0.21/0.46 thf(func_def_0, type, in: $i > $i > $o).
% 0.21/0.46 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.21/0.46 thf(func_def_3, type, setunion: $i > $i).
% 0.21/0.46 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.46 thf(func_def_7, type, iskpair: $i > $o).
% 0.21/0.46 thf(func_def_8, type, singleton: $i > $o).
% 0.21/0.46 thf(func_def_9, type, ex1: $i > ($i > $o) > $o).
% 0.21/0.46 thf(func_def_27, type, ph1: !>[X0: $tType]:(X0)).
% 0.21/0.46 thf(f305,plain,(
% 0.21/0.46 $false),
% 0.21/0.46 inference(subsumption_resolution,[],[f294,f240])).
% 0.21/0.46 thf(f240,plain,(
% 0.21/0.46 (sK5 != sK3)),
% 0.21/0.46 inference(equality_proxy_clausification,[],[f226])).
% 0.21/0.46 thf(f226,plain,(
% 0.21/0.46 ($false = (sK3 = sK5))),
% 0.21/0.46 inference(binary_proxy_clausification,[],[f200])).
% 0.21/0.46 thf(f200,plain,(
% 0.21/0.46 ($false = ((in @ (setadjoin @ sK5 @ emptyset) @ sK2) => (sK3 = sK5)))),
% 0.21/0.46 inference(binary_proxy_clausification,[],[f196])).
% 0.21/0.46 thf(f196,plain,(
% 0.21/0.46 ($false = ((in @ sK5 @ (setunion @ sK2)) => ((in @ (setadjoin @ sK5 @ emptyset) @ sK2) => (sK3 = sK5))))),
% 0.21/0.46 inference(beta_eta_normalization,[],[f194])).
% 0.21/0.46 thf(f194,plain,(
% 0.21/0.46 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (sK3 = Y0)))) @ sK5))),
% 0.21/0.46 inference(sigma_clausification,[],[f188])).
% 0.21/0.46 thf(f188,plain,(
% 0.21/0.46 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (sK3 = Y0))))) = $false)),
% 0.21/0.46 inference(not_proxy_clausification,[],[f160])).
% 0.21/0.46 thf(f160,plain,(
% 0.21/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (sK3 = Y0)))))))),
% 0.21/0.46 inference(boolean_simplification,[],[f159])).
% 0.21/0.46 thf(f159,plain,(
% 0.21/0.46 ($true = ($true => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (sK3 = Y0))))))))),
% 0.21/0.46 inference(backward_demodulation,[],[f138,f158])).
% 0.21/0.46 thf(f158,plain,(
% 0.21/0.46 ($true = (in @ (setadjoin @ sK3 @ emptyset) @ sK2))),
% 0.21/0.46 inference(superposition,[],[f47,f140])).
% 0.21/0.46 thf(f140,plain,(
% 0.21/0.46 ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2)),
% 0.21/0.46 inference(equality_proxy_clausification,[],[f124])).
% 0.21/0.46 thf(f124,plain,(
% 0.21/0.46 ($true = ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2))),
% 0.21/0.46 inference(binary_proxy_clausification,[],[f118])).
% 0.21/0.46 thf(f118,plain,(
% 0.21/0.46 (((in @ sK4 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ sK4 @ emptyset)) @ emptyset)) = sK2)) = $true)),
% 0.21/0.46 inference(beta_eta_normalization,[],[f117])).
% 0.21/0.46 thf(f117,plain,(
% 0.21/0.46 ($true = ((^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2))) @ sK4))),
% 0.21/0.46 inference(sigma_clausification,[],[f107])).
% 0.21/0.46 thf(f107,plain,(
% 0.21/0.46 ($true = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2)))))),
% 0.21/0.46 inference(binary_proxy_clausification,[],[f106])).
% 0.21/0.46 thf(f106,plain,(
% 0.21/0.46 ($true = ((in @ sK3 @ (setunion @ sK2)) & (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ sK3 @ emptyset) @ (setadjoin @ (setadjoin @ sK3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK2))))))),
% 0.21/0.46 inference(beta_eta_normalization,[],[f105])).
% 0.21/0.46 thf(f105,plain,(
% 0.21/0.46 (((^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2)))))) @ sK3) = $true)),
% 0.21/0.46 inference(sigma_clausification,[],[f100])).
% 0.21/0.46 thf(f100,plain,(
% 0.21/0.46 ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2))))))) = $true)),
% 0.21/0.46 inference(binary_proxy_clausification,[],[f98])).
% 0.21/0.46 thf(f98,plain,(
% 0.21/0.46 (((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) & (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ sK2)) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK2))))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ sK2)))) & (in @ Y0 @ (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ sK2)))))))) = $false)),
% 0.21/0.46 inference(beta_eta_normalization,[],[f97])).
% 0.21/0.46 thf(f97,plain,(
% 0.21/0.46 ($false = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0))))))))) @ sK2))),
% 0.21/0.46 inference(sigma_clausification,[],[f65])).
% 0.21/0.46 thf(f65,plain,(
% 0.21/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))))),
% 0.21/0.46 inference(binary_proxy_clausification,[],[f48])).
% 0.21/0.46 thf(f48,plain,(
% 0.21/0.46 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0))))))))))))),
% 0.21/0.46 inference(binary_proxy_clausification,[],[f38])).
% 0.21/0.46 thf(f38,plain,(
% 0.21/0.46 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))))))),
% 0.21/0.46 inference(binary_proxy_clausification,[],[f35])).
% 0.21/0.46 thf(f35,plain,(
% 0.21/0.46 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0))))))))))))))),
% 0.21/0.46 inference(not_proxy_clausification,[],[f34])).
% 0.21/0.46 thf(f34,plain,(
% 0.21/0.46 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))) => (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & (in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))))))))),
% 0.21/0.46 inference(beta_eta_normalization,[],[f33])).
% 0.21/0.46 thf(f33,plain,(
% 0.21/0.46 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (((setadjoin @ Y6 @ emptyset) = Y5) & (in @ Y6 @ Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))) => (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y1)) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = Y1)))))))) @ Y0) => ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = Y1) & (in @ Y2 @ Y1))))) @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))))))),
% 0.21/0.46 inference(definition_unfolding,[],[f26,f30,f32,f25,f24,f27])).
% 0.21/0.46 thf(f27,plain,(
% 0.21/0.46 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 0.21/0.46 inference(cnf_transformation,[],[f19])).
% 0.21/0.46 thf(f19,plain,(
% 0.21/0.46 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 0.21/0.46 inference(fool_elimination,[],[f18])).
% 0.21/0.46 thf(f18,plain,(
% 0.21/0.46 ((^[X0 : $i] : (? [X1] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 0.21/0.46 inference(rectify,[],[f3])).
% 0.21/0.46 thf(f3,axiom,(
% 0.21/0.46 ((^[X2 : $i] : (? [X0] : ((in @ X0 @ X2) & ((setadjoin @ X0 @ emptyset) = X2)))) = singleton)),
% 0.21/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)).
% 0.21/0.46 thf(f24,plain,(
% 0.21/0.46 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))))))))),
% 0.21/0.46 inference(cnf_transformation,[],[f11])).
% 0.21/0.46 thf(f11,plain,(
% 0.21/0.46 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))))))))),
% 0.21/0.46 inference(fool_elimination,[],[f10])).
% 0.21/0.46 thf(f10,plain,(
% 0.21/0.46 ((^[X0 : $i] : (? [X1] : (? [X2] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0) & (in @ X2 @ (setunion @ X0))) & (in @ X1 @ (setunion @ X0))))) = iskpair)),
% 0.21/0.46 inference(rectify,[],[f2])).
% 0.21/0.46 thf(f2,axiom,(
% 0.21/0.46 ((^[X2 : $i] : (? [X0] : (? [X1] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = X2) & (in @ X1 @ (setunion @ X2))) & (in @ X0 @ (setunion @ X2))))) = iskpair)),
% 0.21/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iskpair)).
% 0.21/0.46 thf(f25,plain,(
% 0.21/0.46 (setukpairinjL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))),
% 0.21/0.46 inference(cnf_transformation,[],[f21])).
% 0.21/0.46 thf(f21,plain,(
% 0.21/0.46 (setukpairinjL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))),
% 0.21/0.46 inference(fool_elimination,[],[f20])).
% 0.21/0.46 thf(f20,plain,(
% 0.21/0.46 (setukpairinjL1 = ! [X0,X1,X2] : ((in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) => (X1 = X2)))),
% 0.21/0.46 inference(rectify,[],[f6])).
% 0.21/0.46 thf(f6,axiom,(
% 0.21/0.46 (setukpairinjL1 = ! [X1,X4,X0] : ((in @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X0 = X4)))),
% 0.21/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1)).
% 0.21/0.46 thf(f32,plain,(
% 0.21/0.46 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (((setadjoin @ Y6 @ emptyset) = Y5) & (in @ Y6 @ Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 0.21/0.46 inference(definition_unfolding,[],[f29,f31])).
% 0.21/0.46 thf(f31,plain,(
% 0.21/0.46 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.21/0.46 inference(definition_unfolding,[],[f28,f27])).
% 0.21/0.46 thf(f28,plain,(
% 0.21/0.46 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.21/0.46 inference(cnf_transformation,[],[f13])).
% 0.21/0.46 thf(f13,plain,(
% 0.21/0.46 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.21/0.46 inference(fool_elimination,[],[f12])).
% 0.21/0.46 thf(f12,plain,(
% 0.21/0.46 ((^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))) = ex1)),
% 0.21/0.46 inference(rectify,[],[f4])).
% 0.21/0.46 thf(f4,axiom,(
% 0.21/0.46 ((^[X2 : $i, X3 : $i > $o] : (singleton @ (dsetconstr @ X2 @ (^[X0 : $i] : (X3 @ X0))))) = ex1)),
% 0.21/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1)).
% 0.21/0.46 thf(f29,plain,(
% 0.21/0.46 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => (ex1 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 0.21/0.46 inference(cnf_transformation,[],[f17])).
% 0.21/0.46 thf(f17,plain,(
% 0.21/0.46 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => (ex1 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 0.21/0.46 inference(fool_elimination,[],[f16])).
% 0.21/0.46 thf(f16,plain,(
% 0.21/0.46 (ex1I = ! [X0,X1 : $i > $o,X2] : ((in @ X0 @ X2) => ((X1 @ X0) => (! [X3] : ((in @ X3 @ X2) => ((X1 @ X3) => (X0 = X3))) => (ex1 @ X2 @ (^[X4 : $i] : (X1 @ X4)))))))),
% 0.21/0.46 inference(rectify,[],[f5])).
% 0.21/0.46 thf(f5,axiom,(
% 0.21/0.46 (ex1I = ! [X0,X3 : $i > $o,X2] : ((in @ X0 @ X2) => ((X3 @ X0) => (! [X1] : ((in @ X1 @ X2) => ((X3 @ X1) => (X0 = X1))) => (ex1 @ X2 @ (^[X1 : $i] : (X3 @ X1)))))))),
% 0.21/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I)).
% 0.21/0.46 thf(f30,plain,(
% 0.21/0.46 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 0.21/0.46 inference(cnf_transformation,[],[f23])).
% 0.21/0.46 thf(f23,plain,(
% 0.21/0.46 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 0.21/0.46 inference(fool_elimination,[],[f22])).
% 0.21/0.46 thf(f22,plain,(
% 0.21/0.46 (! [X0,X1] : (in @ X1 @ (setadjoin @ X1 @ X0)) = setadjoinIL)),
% 0.21/0.46 inference(rectify,[],[f1])).
% 0.21/0.46 thf(f1,axiom,(
% 0.21/0.46 (! [X1,X0] : (in @ X0 @ (setadjoin @ X0 @ X1)) = setadjoinIL)),
% 0.21/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL)).
% 0.21/0.46 thf(f26,plain,(
% 0.21/0.46 ($true = (~ (setadjoinIL => (ex1I => (setukpairinjL1 => (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))))))),
% 0.21/0.46 inference(cnf_transformation,[],[f15])).
% 0.21/0.46 thf(f15,plain,(
% 0.21/0.46 ($true = (~ (setadjoinIL => (ex1I => (setukpairinjL1 => (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))))))),
% 0.21/0.46 inference(fool_elimination,[],[f14])).
% 0.21/0.46 thf(f14,plain,(
% 0.21/0.46 ~(setadjoinIL => (ex1I => (setukpairinjL1 => ! [X0] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (in @ (setadjoin @ X1 @ emptyset) @ X0))))))))),
% 0.21/0.46 inference(rectify,[],[f8])).
% 0.21/0.46 thf(f8,negated_conjecture,(
% 0.21/0.46 ~(setadjoinIL => (ex1I => (setukpairinjL1 => ! [X5] : ((iskpair @ X5) => (singleton @ (dsetconstr @ (setunion @ X5) @ (^[X0 : $i] : (in @ (setadjoin @ X0 @ emptyset) @ X5))))))))),
% 0.21/0.46 inference(negated_conjecture,[],[f7])).
% 0.21/0.46 thf(f7,conjecture,(
% 0.21/0.46 setadjoinIL => (ex1I => (setukpairinjL1 => ! [X5] : ((iskpair @ X5) => (singleton @ (dsetconstr @ (setunion @ X5) @ (^[X0 : $i] : (in @ (setadjoin @ X0 @ emptyset) @ X5)))))))),
% 0.21/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton)).
% 0.21/0.46 thf(f47,plain,(
% 0.21/0.46 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X1 @ X2)))) )),
% 0.21/0.46 inference(beta_eta_normalization,[],[f46])).
% 0.21/0.46 thf(f46,plain,(
% 0.21/0.46 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (in @ X1 @ (setadjoin @ X1 @ Y0))) @ X2))) )),
% 0.21/0.46 inference(pi_clausification,[],[f45])).
% 0.21/0.46 thf(f45,plain,(
% 0.21/0.46 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ X1 @ (setadjoin @ X1 @ Y0)))))) )),
% 0.21/0.46 inference(beta_eta_normalization,[],[f44])).
% 0.21/0.46 thf(f44,plain,(
% 0.21/0.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1))))) @ X1))) )),
% 0.21/0.46 inference(pi_clausification,[],[f39])).
% 0.21/0.46 thf(f39,plain,(
% 0.21/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 0.21/0.46 inference(binary_proxy_clausification,[],[f35])).
% 0.21/0.46 thf(f138,plain,(
% 0.21/0.46 ($true = ((in @ (setadjoin @ sK3 @ emptyset) @ sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (sK3 = Y0))))))))),
% 0.21/0.46 inference(boolean_simplification,[],[f136])).
% 0.21/0.46 thf(f136,plain,(
% 0.21/0.46 ($true = ($true => ((in @ (setadjoin @ sK3 @ emptyset) @ sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (sK3 = Y0)))))))))),
% 0.21/0.46 inference(superposition,[],[f122,f110])).
% 0.21/0.46 thf(f110,plain,(
% 0.21/0.46 ($true = (in @ sK3 @ (setunion @ sK2)))),
% 0.21/0.46 inference(boolean_simplification,[],[f109])).
% 0.21/0.46 thf(f109,plain,(
% 0.21/0.46 (((in @ sK3 @ (setunion @ sK2)) & $true) = $true)),
% 0.21/0.46 inference(backward_demodulation,[],[f106,f107])).
% 0.21/0.46 thf(f122,plain,(
% 0.21/0.46 ( ! [X0 : $i] : (($true = ((in @ X0 @ (setunion @ sK2)) => ((in @ (setadjoin @ X0 @ emptyset) @ sK2) => (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (X0 = Y0)))))))))) )),
% 0.21/0.46 inference(boolean_simplification,[],[f121])).
% 0.21/0.46 thf(f121,plain,(
% 0.21/0.46 ( ! [X0 : $i] : ((((in @ X0 @ (setunion @ sK2)) => ((in @ (setadjoin @ X0 @ emptyset) @ sK2) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => ((in @ (setadjoin @ Y0 @ emptyset) @ sK2) => (X0 = Y0))))) => $false))) = $true)) )),
% 0.21/0.46 inference(beta_eta_normalization,[],[f120])).
% 0.21/0.46 thf(f120,plain,(
% 0.21/0.46 ( ! [X0 : $i] : (($true = ((in @ X0 @ (setunion @ sK2)) => (((^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ sK2)) @ X0) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ sK2)) => (((^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ sK2)) @ Y0) => (X0 = Y0))))) => $false))))) )),
% 0.21/0.46 inference(superposition,[],[f59,f99])).
% 0.21/0.46 thf(f99,plain,(
% 0.21/0.46 ($false = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ sK2)))) & (in @ Y0 @ (dsetconstr @ (setunion @ sK2) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ sK2))))))))),
% 0.21/0.46 inference(binary_proxy_clausification,[],[f98])).
% 0.21/0.46 thf(f59,plain,(
% 0.21/0.46 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ X1) => ((X2 @ X3) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => (X3 = Y0))))) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y0 @ (dsetconstr @ X1 @ X2)))))))))) )),
% 0.21/0.46 inference(beta_eta_normalization,[],[f58])).
% 0.21/0.46 thf(f58,plain,(
% 0.21/0.46 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((X2 @ Y1) => (Y0 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y1 @ (dsetconstr @ X1 @ X2))))))))) @ X3))) )),
% 0.21/0.46 inference(pi_clausification,[],[f57])).
% 0.21/0.46 thf(f57,plain,(
% 0.21/0.46 ( ! [X2 : $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((X2 @ Y1) => (Y0 = Y1))))) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X1 @ X2)) & (in @ Y1 @ (dsetconstr @ X1 @ X2)))))))))) = $true)) )),
% 0.21/0.46 inference(beta_eta_normalization,[],[f56])).
% 0.21/0.46 thf(f56,plain,(
% 0.21/0.46 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y0 @ Y2) => (Y1 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X1 @ Y0)) & (in @ Y2 @ (dsetconstr @ X1 @ Y0))))))))))) @ X2))) )),
% 0.21/0.46 inference(pi_clausification,[],[f55])).
% 0.21/0.46 thf(f55,plain,(
% 0.21/0.46 ( ! [X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((Y0 @ Y2) => (Y1 = Y2))))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X1 @ Y0)) & (in @ Y2 @ (dsetconstr @ X1 @ Y0)))))))))))) = $true)) )),
% 0.21/0.46 inference(beta_eta_normalization,[],[f54])).
% 0.21/0.46 thf(f54,plain,(
% 0.21/0.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y1))))))))))))) @ X1))) )),
% 0.21/0.46 inference(pi_clausification,[],[f49])).
% 0.21/0.46 thf(f49,plain,(
% 0.21/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ Y1)) & (in @ Y3 @ (dsetconstr @ Y0 @ Y1)))))))))))))))),
% 0.21/0.46 inference(binary_proxy_clausification,[],[f38])).
% 0.21/0.46 thf(f294,plain,(
% 0.21/0.46 (sK5 = sK3)),
% 0.21/0.46 inference(equality_proxy_clausification,[],[f285])).
% 0.21/0.46 thf(f285,plain,(
% 0.21/0.46 ((sK5 = sK3) = $true)),
% 0.21/0.46 inference(boolean_simplification,[],[f277])).
% 0.21/0.46 thf(f277,plain,(
% 0.21/0.46 ($true = ($true => (sK5 = sK3)))),
% 0.21/0.46 inference(superposition,[],[f155,f227])).
% 0.21/0.46 thf(f227,plain,(
% 0.21/0.46 ($true = (in @ (setadjoin @ sK5 @ emptyset) @ sK2))),
% 0.21/0.46 inference(binary_proxy_clausification,[],[f200])).
% 0.21/0.46 thf(f155,plain,(
% 0.21/0.46 ( ! [X0 : $i] : (($true = ((in @ (setadjoin @ X0 @ emptyset) @ sK2) => (X0 = sK3)))) )),
% 0.21/0.46 inference(superposition,[],[f76,f140])).
% 0.21/0.46 thf(f76,plain,(
% 0.21/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) => (X2 = X1)))) )),
% 0.21/0.46 inference(beta_eta_normalization,[],[f75])).
% 0.21/0.46 thf(f75,plain,(
% 0.21/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (X2 = X1))) @ X3) = $true)) )),
% 0.21/0.46 inference(pi_clausification,[],[f74])).
% 0.21/0.46 thf(f74,plain,(
% 0.21/0.46 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (X2 = X1)))))) )),
% 0.21/0.46 inference(beta_eta_normalization,[],[f73])).
% 0.21/0.46 thf(f73,plain,(
% 0.21/0.46 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y0 = X1))))) @ X2))) )),
% 0.21/0.46 inference(pi_clausification,[],[f72])).
% 0.21/0.46 thf(f72,plain,(
% 0.21/0.46 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y0 = X1)))))))) )),
% 0.21/0.46 inference(beta_eta_normalization,[],[f71])).
% 0.21/0.46 thf(f71,plain,(
% 0.21/0.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0))))))) @ X1))) )),
% 0.21/0.46 inference(pi_clausification,[],[f66])).
% 0.21/0.46 thf(f66,plain,(
% 0.21/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))),
% 0.21/0.46 inference(binary_proxy_clausification,[],[f48])).
% 0.21/0.46 % SZS output end Proof for theBenchmark
% 0.21/0.46 % (1580)------------------------------
% 0.21/0.46 % (1580)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (1580)Termination reason: Refutation
% 0.21/0.46
% 0.21/0.46 % (1580)Memory used [KB]: 6140
% 0.21/0.46 % (1580)Time elapsed: 0.058 s
% 0.21/0.46 % (1580)Instructions burned: 105 (million)
% 0.21/0.46 % (1580)------------------------------
% 0.21/0.46 % (1580)------------------------------
% 0.21/0.46 % (1568)Success in time 0.093 s
% 0.21/0.46 % Vampire---4.8 exiting
%------------------------------------------------------------------------------