TSTP Solution File: SYO068^4.010 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SYO068^4.010 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n017.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 21:00:30 EDT 2024
% Result : Theorem 0.20s 0.46s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO068^4.010 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n017.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 : Sun Jun 23 10:37:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.34 This is a TH0_THM_EQU_NAR problem
% 0.20/0.35 Running higher-order theorem proving
% 0.20/0.35 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
% 0.20/0.37 % (11158)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.37 % (11159)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)
% 0.20/0.37 % (11160)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)
% 0.20/0.37 % (11161)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (11162)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)
% 0.20/0.37 % (11163)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)
% 0.20/0.37 % (11161)Instruction limit reached!
% 0.20/0.37 % (11161)------------------------------
% 0.20/0.37 % (11161)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (11161)Termination reason: Unknown
% 0.20/0.37 % (11161)Termination phase: Property scanning
% 0.20/0.37
% 0.20/0.37 % (11162)Instruction limit reached!
% 0.20/0.37 % (11162)------------------------------
% 0.20/0.37 % (11162)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (11162)Termination reason: Unknown
% 0.20/0.37 % (11162)Termination phase: Unused predicate definition removal
% 0.20/0.37
% 0.20/0.37 % (11162)Memory used [KB]: 1023
% 0.20/0.37 % (11162)Time elapsed: 0.004 s
% 0.20/0.37 % (11162)Instructions burned: 3 (million)
% 0.20/0.37 % (11162)------------------------------
% 0.20/0.37 % (11162)------------------------------
% 0.20/0.37 % (11161)Memory used [KB]: 1023
% 0.20/0.37 % (11161)Time elapsed: 0.004 s
% 0.20/0.37 % (11161)Instructions burned: 3 (million)
% 0.20/0.37 % (11161)------------------------------
% 0.20/0.37 % (11161)------------------------------
% 0.20/0.37 % (11159)Instruction limit reached!
% 0.20/0.37 % (11159)------------------------------
% 0.20/0.37 % (11159)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (11159)Termination reason: Unknown
% 0.20/0.37 % (11159)Termination phase: Function definition elimination
% 0.20/0.37
% 0.20/0.37 % (11159)Memory used [KB]: 1023
% 0.20/0.37 % (11159)Time elapsed: 0.005 s
% 0.20/0.37 % (11159)Instructions burned: 5 (million)
% 0.20/0.37 % (11159)------------------------------
% 0.20/0.37 % (11159)------------------------------
% 0.20/0.37 % (11163)Refutation not found, incomplete strategy
% 0.20/0.37 % (11163)------------------------------
% 0.20/0.37 % (11163)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (11163)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.37
% 0.20/0.37
% 0.20/0.37 % (11163)Memory used [KB]: 5500
% 0.20/0.37 % (11163)Time elapsed: 0.005 s
% 0.20/0.37 % (11163)Instructions burned: 5 (million)
% 0.20/0.37 % (11163)------------------------------
% 0.20/0.37 % (11163)------------------------------
% 0.20/0.38 % (11164)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.38 % (11160)Instruction limit reached!
% 0.20/0.38 % (11160)------------------------------
% 0.20/0.38 % (11160)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (11160)Termination reason: Unknown
% 0.20/0.38 % (11160)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (11160)Memory used [KB]: 5628
% 0.20/0.38 % (11160)Time elapsed: 0.017 s
% 0.20/0.38 % (11160)Instructions burned: 28 (million)
% 0.20/0.38 % (11160)------------------------------
% 0.20/0.38 % (11160)------------------------------
% 0.20/0.39 % (11167)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 % (11164)Instruction limit reached!
% 0.20/0.39 % (11164)------------------------------
% 0.20/0.39 % (11164)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (11164)Termination reason: Unknown
% 0.20/0.39 % (11164)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (11164)Memory used [KB]: 5628
% 0.20/0.39 % (11164)Time elapsed: 0.012 s
% 0.20/0.39 % (11164)Instructions burned: 18 (million)
% 0.20/0.39 % (11164)------------------------------
% 0.20/0.39 % (11164)------------------------------
% 0.20/0.39 % (11165)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 % (11166)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 % (11165)Instruction limit reached!
% 0.20/0.39 % (11165)------------------------------
% 0.20/0.39 % (11165)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (11165)Termination reason: Unknown
% 0.20/0.39 % (11165)Termination phase: Property scanning
% 0.20/0.39
% 0.20/0.39 % (11165)Memory used [KB]: 1023
% 0.20/0.39 % (11165)Time elapsed: 0.004 s
% 0.20/0.39 % (11165)Instructions burned: 3 (million)
% 0.20/0.39 % (11165)------------------------------
% 0.20/0.39 % (11165)------------------------------
% 0.20/0.39 % (11168)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)
% 0.20/0.39 % (11168)Instruction limit reached!
% 0.20/0.39 % (11168)------------------------------
% 0.20/0.39 % (11168)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (11168)Termination reason: Unknown
% 0.20/0.39 % (11168)Termination phase: Property scanning
% 0.20/0.39
% 0.20/0.39 % (11168)Memory used [KB]: 1023
% 0.20/0.39 % (11168)Time elapsed: 0.004 s
% 0.20/0.39 % (11168)Instructions burned: 4 (million)
% 0.20/0.39 % (11168)------------------------------
% 0.20/0.39 % (11168)------------------------------
% 0.20/0.39 % (11167)Instruction limit reached!
% 0.20/0.39 % (11167)------------------------------
% 0.20/0.39 % (11167)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (11167)Termination reason: Unknown
% 0.20/0.39 % (11167)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (11167)Memory used [KB]: 1151
% 0.20/0.39 % (11167)Time elapsed: 0.008 s
% 0.20/0.39 % (11167)Instructions burned: 15 (million)
% 0.20/0.39 % (11167)------------------------------
% 0.20/0.39 % (11167)------------------------------
% 0.20/0.40 % (11169)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 % (11170)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.40 % (11171)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.40 % (11170)Instruction limit reached!
% 0.20/0.40 % (11170)------------------------------
% 0.20/0.40 % (11170)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.40 % (11170)Termination reason: Unknown
% 0.20/0.41 % (11170)Termination phase: Property scanning
% 0.20/0.41
% 0.20/0.41 % (11170)Memory used [KB]: 1023
% 0.20/0.41 % (11170)Time elapsed: 0.006 s
% 0.20/0.41 % (11170)Instructions burned: 7 (million)
% 0.20/0.41 % (11170)------------------------------
% 0.20/0.41 % (11170)------------------------------
% 0.20/0.41 % (11166)Instruction limit reached!
% 0.20/0.41 % (11166)------------------------------
% 0.20/0.41 % (11166)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41 % (11166)Termination reason: Unknown
% 0.20/0.41 % (11166)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (11166)Memory used [KB]: 5756
% 0.20/0.41 % (11166)Time elapsed: 0.022 s
% 0.20/0.41 % (11166)Instructions burned: 37 (million)
% 0.20/0.41 % (11166)------------------------------
% 0.20/0.41 % (11166)------------------------------
% 0.20/0.41 % (11172)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)
% 0.20/0.41 % (11173)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)
% 0.20/0.41 % (11172)Instruction limit reached!
% 0.20/0.41 % (11172)------------------------------
% 0.20/0.41 % (11172)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41 % (11172)Termination reason: Unknown
% 0.20/0.41 % (11172)Termination phase: Property scanning
% 0.20/0.41
% 0.20/0.41 % (11172)Memory used [KB]: 1023
% 0.20/0.41 % (11172)Time elapsed: 0.004 s
% 0.20/0.41 % (11172)Instructions burned: 3 (million)
% 0.20/0.41 % (11172)------------------------------
% 0.20/0.41 % (11172)------------------------------
% 0.20/0.41 % (11173)Instruction limit reached!
% 0.20/0.41 % (11173)------------------------------
% 0.20/0.41 % (11173)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41 % (11173)Termination reason: Unknown
% 0.20/0.41 % (11173)Termination phase: Unused predicate definition removal
% 0.20/0.41
% 0.20/0.41 % (11173)Memory used [KB]: 1023
% 0.20/0.41 % (11173)Time elapsed: 0.004 s
% 0.20/0.41 % (11173)Instructions burned: 4 (million)
% 0.20/0.41 % (11173)------------------------------
% 0.20/0.41 % (11173)------------------------------
% 0.20/0.41 % (11171)Instruction limit reached!
% 0.20/0.41 % (11171)------------------------------
% 0.20/0.41 % (11171)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41 % (11171)Termination reason: Unknown
% 0.20/0.41 % (11171)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (11171)Memory used [KB]: 5628
% 0.20/0.41 % (11171)Time elapsed: 0.011 s
% 0.20/0.41 % (11171)Instructions burned: 17 (million)
% 0.20/0.41 % (11171)------------------------------
% 0.20/0.41 % (11171)------------------------------
% 0.20/0.42 % (11174)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)
% 0.20/0.42 % (11175)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)
% 0.20/0.42 % (11175)Instruction limit reached!
% 0.20/0.42 % (11175)------------------------------
% 0.20/0.42 % (11175)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.42 % (11175)Termination reason: Unknown
% 0.20/0.42 % (11175)Termination phase: Property scanning
% 0.20/0.42
% 0.20/0.42 % (11175)Memory used [KB]: 1023
% 0.20/0.42 % (11175)Time elapsed: 0.004 s
% 0.20/0.42 % (11175)Instructions burned: 4 (million)
% 0.20/0.42 % (11175)------------------------------
% 0.20/0.42 % (11175)------------------------------
% 0.20/0.42 % (11176)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.42 % (11174)Instruction limit reached!
% 0.20/0.42 % (11174)------------------------------
% 0.20/0.42 % (11174)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.42 % (11174)Termination reason: Unknown
% 0.20/0.42 % (11174)Termination phase: Property scanning
% 0.20/0.42
% 0.20/0.42 % (11174)Memory used [KB]: 1023
% 0.20/0.42 % (11174)Time elapsed: 0.006 s
% 0.20/0.42 % (11174)Instructions burned: 7 (million)
% 0.20/0.42 % (11174)------------------------------
% 0.20/0.42 % (11174)------------------------------
% 0.20/0.43 % (11177)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)
% 0.20/0.43 % (11176)Instruction limit reached!
% 0.20/0.43 % (11176)------------------------------
% 0.20/0.43 % (11176)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43 % (11176)Termination reason: Unknown
% 0.20/0.43 % (11176)Termination phase: Function definition elimination
% 0.20/0.43
% 0.20/0.43 % (11176)Memory used [KB]: 1023
% 0.20/0.43 % (11176)Time elapsed: 0.005 s
% 0.20/0.43 % (11176)Instructions burned: 5 (million)
% 0.20/0.43 % (11176)------------------------------
% 0.20/0.43 % (11176)------------------------------
% 0.20/0.43 % (11178)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.20/0.43 % (11178)Refutation not found, incomplete strategy
% 0.20/0.43 % (11178)------------------------------
% 0.20/0.43 % (11178)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43 % (11178)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 % (11178)Memory used [KB]: 5500
% 0.20/0.43 % (11178)Time elapsed: 0.006 s
% 0.20/0.43 % (11178)Instructions burned: 5 (million)
% 0.20/0.43 % (11178)------------------------------
% 0.20/0.43 % (11178)------------------------------
% 0.20/0.44 % (11177)Instruction limit reached!
% 0.20/0.44 % (11177)------------------------------
% 0.20/0.44 % (11177)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.44 % (11177)Termination reason: Unknown
% 0.20/0.44 % (11177)Termination phase: Saturation
% 0.20/0.44
% 0.20/0.44 % (11177)Memory used [KB]: 5628
% 0.20/0.44 % (11177)Time elapsed: 0.035 s
% 0.20/0.44 % (11177)Instructions burned: 18 (million)
% 0.20/0.44 % (11177)------------------------------
% 0.20/0.44 % (11177)------------------------------
% 0.20/0.44 % (11179)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.44 % (11158)First to succeed.
% 0.20/0.44 % (11180)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)
% 0.20/0.44 % (11181)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)
% 0.20/0.44 % (11179)Instruction limit reached!
% 0.20/0.44 % (11179)------------------------------
% 0.20/0.44 % (11179)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.44 % (11179)Termination reason: Unknown
% 0.20/0.44 % (11179)Termination phase: Property scanning
% 0.20/0.44
% 0.20/0.44 % (11179)Memory used [KB]: 1023
% 0.20/0.44 % (11179)Time elapsed: 0.006 s
% 0.20/0.44 % (11179)Instructions burned: 8 (million)
% 0.20/0.44 % (11179)------------------------------
% 0.20/0.44 % (11179)------------------------------
% 0.20/0.44 % (11180)Refutation not found, incomplete strategy
% 0.20/0.44 % (11180)------------------------------
% 0.20/0.44 % (11180)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.44 % (11180)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 % (11180)Memory used [KB]: 5500
% 0.20/0.44 % (11180)Time elapsed: 0.006 s
% 0.20/0.44 % (11180)Instructions burned: 6 (million)
% 0.20/0.44 % (11180)------------------------------
% 0.20/0.44 % (11180)------------------------------
% 0.20/0.45 % (11182)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.20/0.45 % (11182)Instruction limit reached!
% 0.20/0.45 % (11182)------------------------------
% 0.20/0.45 % (11182)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.45 % (11182)Termination reason: Unknown
% 0.20/0.45 % (11182)Termination phase: Property scanning
% 0.20/0.45
% 0.20/0.45 % (11182)Memory used [KB]: 1023
% 0.20/0.45 % (11182)Time elapsed: 0.005 s
% 0.20/0.45 % (11182)Instructions burned: 6 (million)
% 0.20/0.45 % (11182)------------------------------
% 0.20/0.45 % (11182)------------------------------
% 0.20/0.45 % (11183)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)
% 0.20/0.46 % (11181)Instruction limit reached!
% 0.20/0.46 % (11181)------------------------------
% 0.20/0.46 % (11181)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.46 % (11181)Termination reason: Unknown
% 0.20/0.46 % (11181)Termination phase: Saturation
% 0.20/0.46
% 0.20/0.46 % (11181)Memory used [KB]: 5628
% 0.20/0.46 % (11181)Time elapsed: 0.014 s
% 0.20/0.46 % (11181)Instructions burned: 22 (million)
% 0.20/0.46 % (11181)------------------------------
% 0.20/0.46 % (11181)------------------------------
% 0.20/0.46 % (11158)Refutation found. Thanks to Tanya!
% 0.20/0.46 % SZS status Theorem for theBenchmark
% 0.20/0.46 % SZS output start Proof for theBenchmark
% 0.20/0.46 thf(func_def_0, type, irel: $i > $i > $o).
% 0.20/0.46 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 0.20/0.46 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.46 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.46 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.46 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 0.20/0.46 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 0.20/0.46 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 0.20/0.46 thf(func_def_9, type, itrue: $i > $o).
% 0.20/0.46 thf(func_def_10, type, ifalse: $i > $o).
% 0.20/0.46 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.46 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.46 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.46 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.46 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.46 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.46 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 0.20/0.46 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 0.20/0.46 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 0.20/0.46 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 0.20/0.46 thf(func_def_21, type, p0: $i > $o).
% 0.20/0.46 thf(func_def_22, type, p1: $i > $o).
% 0.20/0.46 thf(func_def_23, type, p10: $i > $o).
% 0.20/0.46 thf(func_def_24, type, p2: $i > $o).
% 0.20/0.46 thf(func_def_25, type, p3: $i > $o).
% 0.20/0.46 thf(func_def_26, type, p4: $i > $o).
% 0.20/0.46 thf(func_def_27, type, p5: $i > $o).
% 0.20/0.46 thf(func_def_28, type, p6: $i > $o).
% 0.20/0.46 thf(func_def_29, type, p7: $i > $o).
% 0.20/0.46 thf(func_def_30, type, p8: $i > $o).
% 0.20/0.46 thf(func_def_31, type, p9: $i > $o).
% 0.20/0.46 thf(func_def_45, type, sK1: $i > $i).
% 0.20/0.46 thf(func_def_46, type, sK2: $i > $i).
% 0.20/0.46 thf(func_def_47, type, sK3: $i > $i).
% 0.20/0.46 thf(func_def_48, type, sK4: $i > $i).
% 0.20/0.46 thf(func_def_49, type, sK5: $i > $i).
% 0.20/0.46 thf(func_def_50, type, sK6: $i > $i).
% 0.20/0.46 thf(func_def_51, type, sK7: $i > $i).
% 0.20/0.46 thf(func_def_52, type, sK8: $i > $i).
% 0.20/0.46 thf(func_def_53, type, sK9: $i > $i).
% 0.20/0.46 thf(func_def_54, type, sK10: $i > $i).
% 0.20/0.46 thf(func_def_55, type, sK11: $i > $i).
% 0.20/0.46 thf(func_def_56, type, sK12: $i > $i).
% 0.20/0.46 thf(func_def_57, type, sK13: $i > $i).
% 0.20/0.46 thf(func_def_58, type, sK14: $i > $i).
% 0.20/0.46 thf(func_def_59, type, sK15: $i > $i).
% 0.20/0.46 thf(func_def_61, type, sK17: $i > $i).
% 0.20/0.46 thf(func_def_62, type, sK18: $i > $i).
% 0.20/0.46 thf(func_def_63, type, sK19: $i > $i).
% 0.20/0.46 thf(func_def_64, type, sK20: $i > $i).
% 0.20/0.46 thf(func_def_65, type, sK21: $i > $i).
% 0.20/0.46 thf(func_def_66, type, sK22: $i > $i).
% 0.20/0.46 thf(func_def_67, type, sK23: $i > $i).
% 0.20/0.46 thf(func_def_68, type, sK24: $i > $i).
% 0.20/0.46 thf(func_def_69, type, sK25: $i > $i).
% 0.20/0.46 thf(func_def_70, type, sK26: $i > $i).
% 0.20/0.46 thf(func_def_71, type, sK27: $i > $i).
% 0.20/0.46 thf(func_def_72, type, sK28: $i > $i).
% 0.20/0.46 thf(func_def_73, type, sK29: $i > $i).
% 0.20/0.46 thf(func_def_74, type, sK30: $i > $i).
% 0.20/0.46 thf(func_def_75, type, sK31: $i > $i).
% 0.20/0.46 thf(f896,plain,(
% 0.20/0.46 $false),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f895])).
% 0.20/0.46 thf(f895,plain,(
% 0.20/0.46 ($false = $true)),
% 0.20/0.46 inference(superposition,[],[f309,f893])).
% 0.20/0.46 thf(f893,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p0 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f891])).
% 0.20/0.46 thf(f891,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p0 @ X0) = $true) | ($false = $true)) )),
% 0.20/0.46 inference(superposition,[],[f804,f808])).
% 0.20/0.46 thf(f808,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p1 @ (sK26 @ X0)) = $false) | ((p0 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f806])).
% 0.20/0.46 thf(f806,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ((p0 @ X0) = $true) | ((p1 @ (sK26 @ X0)) = $false)) )),
% 0.20/0.46 inference(superposition,[],[f672,f804])).
% 0.20/0.46 thf(f672,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p1 @ (sK28 @ X0)) = $false) | ((p0 @ X0) = $true) | ((p1 @ (sK26 @ X0)) = $false)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f667])).
% 0.20/0.46 thf(f667,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ((p1 @ (sK28 @ X0)) = $false) | ((p1 @ (sK26 @ X0)) = $false) | ((p0 @ X0) = $true)) )),
% 0.20/0.46 inference(superposition,[],[f126,f655])).
% 0.20/0.46 thf(f655,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p1 @ (sK28 @ X0)) = $false) | ($false = (p1 @ (sK26 @ X1))) | ((p0 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f647])).
% 0.20/0.46 thf(f647,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (($false = (p1 @ (sK26 @ X1))) | ($false = $true) | ((irel @ X1 @ X0) = $false) | ((p0 @ X0) = $true) | ((p1 @ (sK28 @ X0)) = $false)) )),
% 0.20/0.46 inference(superposition,[],[f430,f126])).
% 0.20/0.46 thf(f430,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((irel @ X1 @ X2) = $false) | ((p0 @ X3) = $true) | ((p1 @ (sK28 @ X2)) = $false) | ($false = (p1 @ (sK26 @ X1)))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f429])).
% 0.20/0.46 thf(f429,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (p1 @ (sK26 @ X1))) | ((irel @ X2 @ X3) = $false) | ($false = ((irel @ X2 @ (sK28 @ X2)) => (p1 @ (sK28 @ X2)))) | ((p0 @ X3) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f428])).
% 0.20/0.46 thf(f428,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p0 @ X3) = $true) | ($false = (p1 @ (sK26 @ X1))) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))) @ (sK28 @ X2)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f427])).
% 0.20/0.46 thf(f427,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((irel @ X2 @ X3) = $false) | ($false = (p1 @ (sK26 @ X1))) | ((p0 @ X3) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f426])).
% 0.20/0.46 thf(f426,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ X3) => (p0 @ X3)) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (p1 @ (sK26 @ X1))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))))) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f425])).
% 0.20/0.46 thf(f425,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0))) @ X3) = $true) | ($false = (p1 @ (sK26 @ X1))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))))) )),
% 0.20/0.46 inference(pi_clausification,[],[f424])).
% 0.20/0.46 thf(f424,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))) | ($false = (p1 @ (sK26 @ X1)))) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f423])).
% 0.20/0.46 thf(f423,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (($false = (p1 @ (sK26 @ X1))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0))))) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f422])).
% 0.20/0.46 thf(f422,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (p1 @ (sK26 @ X1))) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f410])).
% 0.20/0.46 thf(f410,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))))) = $true) | ($false = (p1 @ (sK26 @ X1)))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f409])).
% 0.20/0.46 thf(f409,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK26 @ X1)) => (p1 @ (sK26 @ X1))) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f408])).
% 0.20/0.46 thf(f408,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK26 @ X1)) => (p1 @ (sK26 @ X1))) = $false) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))))))) @ X2) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f407])).
% 0.20/0.46 thf(f407,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))))))) = $true) | (((irel @ X1 @ (sK26 @ X1)) => (p1 @ (sK26 @ X1))) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f406])).
% 0.20/0.46 thf(f406,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))) @ (sK26 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))))))) = $true)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f405])).
% 0.20/0.46 thf(f405,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))))))) = $true)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f404])).
% 0.20/0.46 thf(f404,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f403])).
% 0.20/0.46 thf(f403,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f402])).
% 0.20/0.46 thf(f402,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p0 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))))) @ X1) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f401])).
% 0.20/0.46 thf(f401,plain,(
% 0.20/0.46 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p0 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))))))) = $true)),
% 0.20/0.46 inference(beta_eta_normalization,[],[f154])).
% 0.20/0.46 thf(f154,plain,(
% 0.20/0.46 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p1) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p1) @ ((^[Y0 : $i > $o]: (Y0)) @ p0)))) = $true)),
% 0.20/0.46 inference(definition_unfolding,[],[f128,f107,f141,f129,f141,f129,f129])).
% 0.20/0.46 thf(f129,plain,(
% 0.20/0.46 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.20/0.46 inference(cnf_transformation,[],[f99])).
% 0.20/0.46 thf(f99,plain,(
% 0.20/0.46 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.20/0.46 inference(fool_elimination,[],[f98])).
% 0.20/0.46 thf(f98,plain,(
% 0.20/0.46 ((^[X0 : $i > $o] : (X0)) = iatom)),
% 0.20/0.46 inference(rectify,[],[f8])).
% 0.20/0.46 thf(f8,axiom,(
% 0.20/0.46 ((^[X5 : $i > $o] : (X5)) = iatom)),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iatom)).
% 0.20/0.46 thf(f141,plain,(
% 0.20/0.46 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 0.20/0.46 inference(definition_unfolding,[],[f103,f136,f110,f110])).
% 0.20/0.46 thf(f110,plain,(
% 0.20/0.46 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.20/0.46 inference(cnf_transformation,[],[f53])).
% 0.20/0.46 thf(f53,plain,(
% 0.20/0.46 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.20/0.46 inference(fool_elimination,[],[f52])).
% 0.20/0.46 thf(f52,plain,(
% 0.20/0.46 (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((irel @ X1 @ X2) => (X0 @ X2)))))),
% 0.20/0.46 inference(rectify,[],[f7])).
% 0.20/0.46 thf(f7,axiom,(
% 0.20/0.46 (mbox_s4 = (^[X5 : $i > $o, X0 : $i] : (! [X1] : ((irel @ X0 @ X1) => (X5 @ X1)))))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
% 0.20/0.46 thf(f136,plain,(
% 0.20/0.46 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.20/0.46 inference(definition_unfolding,[],[f132,f123,f109])).
% 0.20/0.46 thf(f109,plain,(
% 0.20/0.46 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.46 inference(cnf_transformation,[],[f89])).
% 0.20/0.46 thf(f89,plain,(
% 0.20/0.46 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.46 inference(fool_elimination,[],[f88])).
% 0.20/0.46 thf(f88,plain,(
% 0.20/0.46 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.20/0.46 inference(rectify,[],[f3])).
% 0.20/0.46 thf(f3,axiom,(
% 0.20/0.46 ((^[X0 : $i > $o, X3 : $i] : (~(X0 @ X3))) = mnot)),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.20/0.46 thf(f123,plain,(
% 0.20/0.46 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.46 inference(cnf_transformation,[],[f57])).
% 0.20/0.46 thf(f57,plain,(
% 0.20/0.46 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.46 inference(fool_elimination,[],[f56])).
% 0.20/0.46 thf(f56,plain,(
% 0.20/0.46 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.20/0.46 inference(rectify,[],[f4])).
% 0.20/0.46 thf(f4,axiom,(
% 0.20/0.46 ((^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X0 @ X3) | (X1 @ X3))) = mor)),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.20/0.46 thf(f132,plain,(
% 0.20/0.46 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.46 inference(cnf_transformation,[],[f55])).
% 0.20/0.46 thf(f55,plain,(
% 0.20/0.46 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.46 inference(fool_elimination,[],[f54])).
% 0.20/0.46 thf(f54,plain,(
% 0.20/0.46 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.20/0.46 inference(rectify,[],[f6])).
% 0.20/0.46 thf(f6,axiom,(
% 0.20/0.46 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.46 thf(f103,plain,(
% 0.20/0.46 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.20/0.46 inference(cnf_transformation,[],[f75])).
% 0.20/0.46 thf(f75,plain,(
% 0.20/0.46 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.20/0.46 inference(fool_elimination,[],[f74])).
% 0.20/0.46 thf(f74,plain,(
% 0.20/0.46 (iimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))))),
% 0.20/0.46 inference(rectify,[],[f14])).
% 0.20/0.46 thf(f14,axiom,(
% 0.20/0.46 (iimplies = (^[X5 : $i > $o, X7 : $i > $o] : (mimplies @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iimplies)).
% 0.20/0.46 thf(f107,plain,(
% 0.20/0.46 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.46 inference(cnf_transformation,[],[f91])).
% 0.20/0.46 thf(f91,plain,(
% 0.20/0.46 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.46 inference(fool_elimination,[],[f90])).
% 0.20/0.46 thf(f90,plain,(
% 0.20/0.46 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = ivalid)),
% 0.20/0.46 inference(rectify,[],[f18])).
% 0.20/0.46 thf(f18,axiom,(
% 0.20/0.46 ((^[X8 : $i > $o] : (! [X6] : (X8 @ X6))) = ivalid)),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ivalid)).
% 0.20/0.46 thf(f128,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0)))) = $true)),
% 0.20/0.46 inference(cnf_transformation,[],[f59])).
% 0.20/0.46 thf(f59,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0)))) = $true)),
% 0.20/0.46 inference(fool_elimination,[],[f58])).
% 0.20/0.46 thf(f58,plain,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0))))),
% 0.20/0.46 inference(rectify,[],[f23])).
% 0.20/0.46 thf(f23,axiom,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0))))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2)).
% 0.20/0.46 thf(f126,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((irel @ X0 @ X0) = $true)) )),
% 0.20/0.46 inference(cnf_transformation,[],[f73])).
% 0.20/0.46 thf(f73,plain,(
% 0.20/0.46 ! [X0] : ((irel @ X0 @ X0) = $true)),
% 0.20/0.46 inference(fool_elimination,[],[f72])).
% 0.20/0.46 thf(f72,plain,(
% 0.20/0.46 ! [X0] : (irel @ X0 @ X0)),
% 0.20/0.46 inference(rectify,[],[f1])).
% 0.20/0.46 thf(f1,axiom,(
% 0.20/0.46 ! [X0] : (irel @ X0 @ X0)),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom)).
% 0.20/0.46 thf(f804,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($true = (p1 @ X0))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f801])).
% 0.20/0.46 thf(f801,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ($true = (p1 @ X0))) )),
% 0.20/0.46 inference(superposition,[],[f800,f796])).
% 0.20/0.46 thf(f796,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p2 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f794])).
% 0.20/0.46 thf(f794,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ((p2 @ X0) = $true)) )),
% 0.20/0.46 inference(superposition,[],[f788,f792])).
% 0.20/0.46 thf(f792,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p3 @ (sK23 @ X0)) = $false) | ((p2 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f790])).
% 0.20/0.46 thf(f790,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ((p2 @ X0) = $true) | ((p3 @ (sK23 @ X0)) = $false)) )),
% 0.20/0.46 inference(superposition,[],[f663,f788])).
% 0.20/0.46 thf(f663,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p3 @ (sK25 @ X0)) = $false) | ((p3 @ (sK23 @ X0)) = $false) | ((p2 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f659])).
% 0.20/0.46 thf(f659,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ((p2 @ X0) = $true) | ((p3 @ (sK23 @ X0)) = $false) | ((p3 @ (sK25 @ X0)) = $false)) )),
% 0.20/0.46 inference(superposition,[],[f126,f612])).
% 0.20/0.46 thf(f612,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p2 @ X0) = $true) | ((p3 @ (sK23 @ X1)) = $false) | ((p3 @ (sK25 @ X0)) = $false)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f607])).
% 0.20/0.46 thf(f607,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((p2 @ X0) = $true) | ($false = $true) | ((p3 @ (sK25 @ X0)) = $false) | ((p3 @ (sK23 @ X1)) = $false) | ((irel @ X1 @ X0) = $false)) )),
% 0.20/0.46 inference(superposition,[],[f126,f400])).
% 0.20/0.46 thf(f400,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p3 @ (sK25 @ X2)) = $false) | ((p3 @ (sK23 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((p2 @ X3) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f399])).
% 0.20/0.46 thf(f399,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p3 @ (sK23 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ X3) => (p2 @ X3)) = $true) | ((p3 @ (sK25 @ X2)) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f398])).
% 0.20/0.46 thf(f398,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))) @ X3) = $true) | ((p3 @ (sK25 @ X2)) = $false) | ((p3 @ (sK23 @ X1)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(pi_clausification,[],[f393])).
% 0.20/0.46 thf(f393,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((p3 @ (sK23 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false) | ((p3 @ (sK25 @ X2)) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f392])).
% 0.20/0.46 thf(f392,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X2 @ (sK25 @ X2)) => (p3 @ (sK25 @ X2))) = $false) | ((irel @ X1 @ X2) = $false) | ((p3 @ (sK23 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f391])).
% 0.20/0.46 thf(f391,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))) @ (sK25 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((p3 @ (sK23 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f390])).
% 0.20/0.46 thf(f390,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((p3 @ (sK23 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f389])).
% 0.20/0.46 thf(f389,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))))) | ((irel @ X1 @ X2) = $false) | ((p3 @ (sK23 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f388])).
% 0.20/0.46 thf(f388,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((p3 @ (sK23 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))))))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f387])).
% 0.20/0.46 thf(f387,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((p3 @ (sK23 @ X1)) = $false) | ($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))))))) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f386])).
% 0.20/0.46 thf(f386,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))))))) @ X2) = $true) | ((p3 @ (sK23 @ X1)) = $false)) )),
% 0.20/0.46 inference(pi_clausification,[],[f372])).
% 0.20/0.46 thf(f372,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((p3 @ (sK23 @ X1)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f371])).
% 0.20/0.46 thf(f371,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((irel @ X1 @ (sK23 @ X1)) => (p3 @ (sK23 @ X1))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))))) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f370])).
% 0.20/0.46 thf(f370,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0))) @ (sK23 @ X1))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))))) )),
% 0.20/0.46 inference(sigma_clausification,[],[f369])).
% 0.20/0.46 thf(f369,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0)))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))))) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f368])).
% 0.20/0.46 thf(f368,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0))))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f367])).
% 0.20/0.46 thf(f367,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0)))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f366])).
% 0.20/0.46 thf(f366,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p3 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))) @ X1) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f365])).
% 0.20/0.46 thf(f365,plain,(
% 0.20/0.46 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p3 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))))))) = $true)),
% 0.20/0.46 inference(beta_eta_normalization,[],[f151])).
% 0.20/0.46 thf(f151,plain,(
% 0.20/0.46 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p3) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p3) @ ((^[Y0 : $i > $o]: (Y0)) @ p2)))) = $true)),
% 0.20/0.46 inference(definition_unfolding,[],[f121,f107,f141,f129,f141,f129,f129])).
% 0.20/0.46 thf(f121,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2)))) = $true)),
% 0.20/0.46 inference(cnf_transformation,[],[f43])).
% 0.20/0.46 thf(f43,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2)))) = $true)),
% 0.20/0.46 inference(fool_elimination,[],[f42])).
% 0.20/0.46 thf(f42,plain,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2))))),
% 0.20/0.46 inference(rectify,[],[f25])).
% 0.20/0.46 thf(f25,axiom,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2))))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4)).
% 0.20/0.46 thf(f788,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p3 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f786])).
% 0.20/0.46 thf(f786,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ((p3 @ X0) = $true)) )),
% 0.20/0.46 inference(superposition,[],[f780,f784])).
% 0.20/0.46 thf(f784,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p4 @ (sK4 @ X0)) = $false) | ((p3 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f781])).
% 0.20/0.46 thf(f781,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p4 @ (sK4 @ X0)) = $false) | ((p3 @ X0) = $true) | ($false = $true)) )),
% 0.20/0.46 inference(superposition,[],[f780,f505])).
% 0.20/0.46 thf(f505,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p4 @ (sK6 @ X0)) = $false) | ((p3 @ X0) = $true) | ((p4 @ (sK4 @ X0)) = $false)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f501])).
% 0.20/0.46 thf(f501,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p3 @ X0) = $true) | ((p4 @ (sK6 @ X0)) = $false) | ((p4 @ (sK4 @ X0)) = $false) | ($false = $true)) )),
% 0.20/0.46 inference(superposition,[],[f126,f498])).
% 0.20/0.46 thf(f498,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p4 @ (sK4 @ X1)) = $false) | ((p4 @ (sK6 @ X0)) = $false) | ((p3 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f491])).
% 0.20/0.46 thf(f491,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((p4 @ (sK4 @ X1)) = $false) | ((p3 @ X0) = $true) | ((irel @ X1 @ X0) = $false) | ((p4 @ (sK6 @ X0)) = $false) | ($false = $true)) )),
% 0.20/0.46 inference(superposition,[],[f126,f213])).
% 0.20/0.46 thf(f213,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p4 @ (sK4 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (p4 @ (sK6 @ X2))) | ((p3 @ X3) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f212])).
% 0.20/0.46 thf(f212,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p4 @ (sK4 @ X1)) = $false) | (((irel @ X2 @ (sK6 @ X2)) => (p4 @ (sK6 @ X2))) = $false) | ((irel @ X2 @ X3) = $false) | ((p3 @ X3) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f211])).
% 0.20/0.46 thf(f211,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((irel @ X2 @ X3) => (p3 @ X3))) | ((p4 @ (sK4 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK6 @ X2)) => (p4 @ (sK6 @ X2))) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f210])).
% 0.20/0.46 thf(f210,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))) @ (sK6 @ X2)) = $false) | ($true = ((irel @ X2 @ X3) => (p3 @ X3))) | ((irel @ X1 @ X2) = $false) | ((p4 @ (sK4 @ X1)) = $false)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f209])).
% 0.20/0.46 thf(f209,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p3 @ X3))) | ((p4 @ (sK4 @ X1)) = $false)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f208])).
% 0.20/0.46 thf(f208,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p4 @ (sK4 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) = $true) | ($true = ((irel @ X2 @ X3) => (p3 @ X3)))) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f207])).
% 0.20/0.46 thf(f207,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))) @ X3) = $true) | ((p4 @ (sK4 @ X1)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f206])).
% 0.20/0.46 thf(f206,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) = $true) | ((irel @ X1 @ X2) = $false) | ((p4 @ (sK4 @ X1)) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f205])).
% 0.20/0.46 thf(f205,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((p4 @ (sK4 @ X1)) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))))) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f192])).
% 0.20/0.46 thf(f192,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((p4 @ (sK4 @ X1)) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f191])).
% 0.20/0.46 thf(f191,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK4 @ X1)) => (p4 @ (sK4 @ X1))) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f190])).
% 0.20/0.46 thf(f190,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK4 @ X1)) => (p4 @ (sK4 @ X1))) = $false) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))))))) @ X2) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f189])).
% 0.20/0.46 thf(f189,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))))) = $true) | (((irel @ X1 @ (sK4 @ X1)) => (p4 @ (sK4 @ X1))) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f188])).
% 0.20/0.46 thf(f188,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))) @ (sK4 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))))) = $true)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f187])).
% 0.20/0.46 thf(f187,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))))) = $true)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f186])).
% 0.20/0.46 thf(f186,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f185])).
% 0.20/0.46 thf(f185,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f184])).
% 0.20/0.46 thf(f184,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p3 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))) @ X1))) )),
% 0.20/0.46 inference(pi_clausification,[],[f183])).
% 0.20/0.46 thf(f183,plain,(
% 0.20/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p3 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))))))))),
% 0.20/0.46 inference(beta_eta_normalization,[],[f147])).
% 0.20/0.46 thf(f147,plain,(
% 0.20/0.46 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p4) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p4) @ ((^[Y0 : $i > $o]: (Y0)) @ p3)))) = $true)),
% 0.20/0.46 inference(definition_unfolding,[],[f112,f107,f141,f129,f141,f129,f129])).
% 0.20/0.46 thf(f112,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3)))) = $true)),
% 0.20/0.46 inference(cnf_transformation,[],[f45])).
% 0.20/0.46 thf(f45,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3)))) = $true)),
% 0.20/0.46 inference(fool_elimination,[],[f44])).
% 0.20/0.46 thf(f44,plain,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3))))),
% 0.20/0.46 inference(rectify,[],[f26])).
% 0.20/0.46 thf(f26,axiom,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3))))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5)).
% 0.20/0.46 thf(f780,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p4 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f778])).
% 0.20/0.46 thf(f778,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p4 @ X0) = $true) | ($false = $true)) )),
% 0.20/0.46 inference(superposition,[],[f646,f694])).
% 0.20/0.46 thf(f694,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p5 @ (sK29 @ X0)) = $false) | ((p4 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f691])).
% 0.20/0.46 thf(f691,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p5 @ (sK29 @ X0)) = $false) | ((p4 @ X0) = $true) | ($false = $true)) )),
% 0.20/0.46 inference(superposition,[],[f690,f646])).
% 0.20/0.46 thf(f690,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p5 @ (sK31 @ X0)) = $false) | ((p5 @ (sK29 @ X0)) = $false) | ((p4 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f683])).
% 0.20/0.46 thf(f683,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p5 @ (sK29 @ X0)) = $false) | ($false = $true) | ((p5 @ (sK31 @ X0)) = $false) | ((p4 @ X0) = $true)) )),
% 0.20/0.46 inference(superposition,[],[f682,f126])).
% 0.20/0.46 thf(f682,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p5 @ (sK29 @ X1)) = $false) | ((p5 @ (sK31 @ X0)) = $false) | ((p4 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f673])).
% 0.20/0.46 thf(f673,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((p5 @ (sK31 @ X0)) = $false) | ((p5 @ (sK29 @ X1)) = $false) | ((p4 @ X0) = $true) | ((irel @ X1 @ X0) = $false) | ($false = $true)) )),
% 0.20/0.46 inference(superposition,[],[f461,f126])).
% 0.20/0.46 thf(f461,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p4 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ((p5 @ (sK29 @ X1)) = $false) | ($false = (p5 @ (sK31 @ X2)))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f460])).
% 0.20/0.46 thf(f460,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p5 @ (sK29 @ X1)) = $false) | ((p4 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK31 @ X2)) => (p5 @ (sK31 @ X2))) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f459])).
% 0.20/0.46 thf(f459,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p4 @ X3) = $true) | ((p5 @ (sK29 @ X1)) = $false) | ((irel @ X2 @ X3) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))) @ (sK31 @ X2)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f458])).
% 0.20/0.46 thf(f458,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p4 @ X3) = $true) | ((irel @ X2 @ X3) = $false) | ((p5 @ (sK29 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f457])).
% 0.20/0.46 thf(f457,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ X3) => (p4 @ X3)) = $true) | ((p5 @ (sK29 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) = $false)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f456])).
% 0.20/0.46 thf(f456,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))))) | ((p5 @ (sK29 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ X3) => (p4 @ X3)) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f455])).
% 0.20/0.46 thf(f455,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p5 @ (sK29 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))) @ X3) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))) )),
% 0.20/0.46 inference(pi_clausification,[],[f454])).
% 0.20/0.46 thf(f454,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) = $true) | ((p5 @ (sK29 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f442])).
% 0.20/0.46 thf(f442,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))))) = $true) | ((irel @ X1 @ X2) = $false) | ((p5 @ (sK29 @ X1)) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f441])).
% 0.20/0.46 thf(f441,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK29 @ X1)) => (p5 @ (sK29 @ X1))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f440])).
% 0.20/0.46 thf(f440,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))) = $true) | (((irel @ X1 @ (sK29 @ X1)) => (p5 @ (sK29 @ X1))) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f439])).
% 0.20/0.46 thf(f439,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))) = $true) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))) @ (sK29 @ X1)) = $false)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f438])).
% 0.20/0.46 thf(f438,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))))) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))) = $true)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f437])).
% 0.20/0.46 thf(f437,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))))) = $true) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f436])).
% 0.20/0.46 thf(f436,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))))))) @ X2) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))))) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f435])).
% 0.20/0.46 thf(f435,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1))))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f434])).
% 0.20/0.46 thf(f434,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f433])).
% 0.20/0.46 thf(f433,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p4 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p5 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1))))))) @ X1) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f432])).
% 0.20/0.46 thf(f432,plain,(
% 0.20/0.46 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p4 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p5 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))))))) = $true)),
% 0.20/0.46 inference(beta_eta_normalization,[],[f156])).
% 0.20/0.46 thf(f156,plain,(
% 0.20/0.46 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p5) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p5) @ ((^[Y0 : $i > $o]: (Y0)) @ p4)))) = $true)),
% 0.20/0.46 inference(definition_unfolding,[],[f134,f107,f141,f129,f141,f129,f129])).
% 0.20/0.46 thf(f134,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4)))) = $true)),
% 0.20/0.46 inference(cnf_transformation,[],[f39])).
% 0.20/0.46 thf(f39,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4)))) = $true)),
% 0.20/0.46 inference(fool_elimination,[],[f38])).
% 0.20/0.46 thf(f38,plain,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4))))),
% 0.20/0.46 inference(rectify,[],[f27])).
% 0.20/0.46 thf(f27,axiom,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4))))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6)).
% 0.20/0.46 thf(f646,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($true = (p5 @ X0))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f643])).
% 0.20/0.46 thf(f643,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ($true = (p5 @ X0))) )),
% 0.20/0.46 inference(superposition,[],[f642,f638])).
% 0.20/0.46 thf(f638,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p6 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f636])).
% 0.20/0.46 thf(f636,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ((p6 @ X0) = $true)) )),
% 0.20/0.46 inference(superposition,[],[f630,f634])).
% 0.20/0.46 thf(f634,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p7 @ (sK7 @ X0)) = $false) | ((p6 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f632])).
% 0.20/0.46 thf(f632,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ((p6 @ X0) = $true) | ((p7 @ (sK7 @ X0)) = $false)) )),
% 0.20/0.46 inference(superposition,[],[f523,f630])).
% 0.20/0.46 thf(f523,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p7 @ (sK9 @ X0)) = $false) | ((p6 @ X0) = $true) | ((p7 @ (sK7 @ X0)) = $false)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f519])).
% 0.20/0.46 thf(f519,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p6 @ X0) = $true) | ((p7 @ (sK7 @ X0)) = $false) | ($false = $true) | ((p7 @ (sK9 @ X0)) = $false)) )),
% 0.20/0.46 inference(superposition,[],[f126,f516])).
% 0.20/0.46 thf(f516,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p6 @ X0) = $true) | ($false = (p7 @ (sK7 @ X1))) | ((p7 @ (sK9 @ X0)) = $false)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f507])).
% 0.20/0.46 thf(f507,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((p6 @ X0) = $true) | ($false = (p7 @ (sK7 @ X1))) | ($false = $true) | ((p7 @ (sK9 @ X0)) = $false) | ((irel @ X1 @ X0) = $false)) )),
% 0.20/0.46 inference(superposition,[],[f245,f126])).
% 0.20/0.46 thf(f245,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (p7 @ (sK7 @ X1))) | ((p6 @ X3) = $true) | ((p7 @ (sK9 @ X2)) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f244])).
% 0.20/0.46 thf(f244,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ (sK9 @ X2)) => (p7 @ (sK9 @ X2))) = $false) | ($false = (p7 @ (sK7 @ X1))) | ((p6 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ((irel @ X2 @ X3) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f243])).
% 0.20/0.46 thf(f243,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p7 @ (sK7 @ X1))) | (((irel @ X2 @ X3) => (p6 @ X3)) = $true) | ((irel @ X1 @ X2) = $false) | (((irel @ X2 @ (sK9 @ X2)) => (p7 @ (sK9 @ X2))) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f242])).
% 0.20/0.46 thf(f242,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p7 @ (sK7 @ X1))) | (((irel @ X2 @ (sK9 @ X2)) => (p7 @ (sK9 @ X2))) = $false) | ((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))) @ X3) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f241])).
% 0.20/0.46 thf(f241,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) = $true) | (((irel @ X2 @ (sK9 @ X2)) => (p7 @ (sK9 @ X2))) = $false) | ($false = (p7 @ (sK7 @ X1)))) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f240])).
% 0.20/0.46 thf(f240,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (($false = (p7 @ (sK7 @ X1))) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))) @ (sK9 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) = $true)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f239])).
% 0.20/0.46 thf(f239,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))))) | ($false = (p7 @ (sK7 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) = $true)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f238])).
% 0.20/0.46 thf(f238,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))))) = $true) | ($false = (p7 @ (sK7 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f237])).
% 0.20/0.46 thf(f237,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (p7 @ (sK7 @ X1))) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f224])).
% 0.20/0.46 thf(f224,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (($false = (p7 @ (sK7 @ X1))) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f223])).
% 0.20/0.46 thf(f223,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK7 @ X1)) => (p7 @ (sK7 @ X1))) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f222])).
% 0.20/0.46 thf(f222,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))))))) = $true) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0))) @ (sK7 @ X1)) = $false)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f221])).
% 0.20/0.46 thf(f221,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f220])).
% 0.20/0.46 thf(f220,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))) = $false) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))))))) @ X2) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f219])).
% 0.20/0.46 thf(f219,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1))))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))) = $false)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f218])).
% 0.20/0.46 thf(f218,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1))))))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f217])).
% 0.20/0.46 thf(f217,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p7 @ Y0)))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f216])).
% 0.20/0.46 thf(f216,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p6 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p7 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1))))))) @ X1) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f215])).
% 0.20/0.46 thf(f215,plain,(
% 0.20/0.46 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p6 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p7 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))))))) = $true)),
% 0.20/0.46 inference(beta_eta_normalization,[],[f153])).
% 0.20/0.46 thf(f153,plain,(
% 0.20/0.46 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p7) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p7) @ ((^[Y0 : $i > $o]: (Y0)) @ p6)))) = $true)),
% 0.20/0.46 inference(definition_unfolding,[],[f125,f107,f141,f129,f141,f129,f129])).
% 0.20/0.46 thf(f125,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6)))) = $true)),
% 0.20/0.46 inference(cnf_transformation,[],[f85])).
% 0.20/0.46 thf(f85,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6)))) = $true)),
% 0.20/0.46 inference(fool_elimination,[],[f84])).
% 0.20/0.46 thf(f84,plain,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6))))),
% 0.20/0.46 inference(rectify,[],[f29])).
% 0.20/0.46 thf(f29,axiom,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6))))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8)).
% 0.20/0.46 thf(f630,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($true = (p7 @ X0))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f627])).
% 0.20/0.46 thf(f627,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ($true = (p7 @ X0))) )),
% 0.20/0.46 inference(superposition,[],[f626,f622])).
% 0.20/0.46 thf(f622,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($true = (p8 @ X0))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f620])).
% 0.20/0.46 thf(f620,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($true = (p8 @ X0)) | ($false = $true)) )),
% 0.20/0.46 inference(superposition,[],[f488,f618])).
% 0.20/0.46 thf(f618,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p9 @ (sK20 @ X0)) = $false) | ($true = (p8 @ X0))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f615])).
% 0.20/0.46 thf(f615,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ($true = (p8 @ X0)) | ((p9 @ (sK20 @ X0)) = $false)) )),
% 0.20/0.46 inference(superposition,[],[f602,f488])).
% 0.20/0.46 thf(f602,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = (p9 @ (sK22 @ X0))) | ((p9 @ (sK20 @ X0)) = $false) | ($true = (p8 @ X0))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f599])).
% 0.20/0.46 thf(f599,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ($true = (p8 @ X0)) | ((p9 @ (sK20 @ X0)) = $false) | ($false = (p9 @ (sK22 @ X0)))) )),
% 0.20/0.46 inference(superposition,[],[f126,f596])).
% 0.20/0.46 thf(f596,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($false = (p9 @ (sK20 @ X1))) | ($true = (p8 @ X0)) | ($false = (p9 @ (sK22 @ X0)))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f587])).
% 0.20/0.46 thf(f587,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ((irel @ X1 @ X0) = $false) | ($false = (p9 @ (sK20 @ X1))) | ($true = (p8 @ X0)) | ($false = (p9 @ (sK22 @ X0)))) )),
% 0.20/0.46 inference(superposition,[],[f361,f126])).
% 0.20/0.46 thf(f361,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p8 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ((p9 @ (sK22 @ X2)) = $false) | ($false = (p9 @ (sK20 @ X1)))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f360])).
% 0.20/0.46 thf(f360,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ($false = ((irel @ X2 @ (sK22 @ X2)) => (p9 @ (sK22 @ X2)))) | ($false = (p9 @ (sK20 @ X1))) | ((irel @ X1 @ X2) = $false) | ((p8 @ X3) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f359])).
% 0.20/0.46 thf(f359,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p9 @ (sK20 @ X1))) | ((irel @ X1 @ X2) = $false) | ((irel @ X2 @ X3) = $false) | ((p8 @ X3) = $true) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))) @ (sK22 @ X2)) = $false)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f353])).
% 0.20/0.46 thf(f353,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p8 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) = $false) | ($false = (p9 @ (sK20 @ X1)))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f352])).
% 0.20/0.46 thf(f352,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X1 @ (sK20 @ X1)) => (p9 @ (sK20 @ X1))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) = $false) | ((p8 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ((irel @ X2 @ X3) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f351])).
% 0.20/0.46 thf(f351,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ X3) => (p8 @ X3)) = $true) | (((irel @ X1 @ (sK20 @ X1)) => (p9 @ (sK20 @ X1))) = $false) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f350])).
% 0.20/0.46 thf(f350,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X1 @ (sK20 @ X1)) => (p9 @ (sK20 @ X1))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))) @ X3) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(pi_clausification,[],[f349])).
% 0.20/0.46 thf(f349,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) = $true) | (((irel @ X1 @ (sK20 @ X1)) => (p9 @ (sK20 @ X1))) = $false) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f348])).
% 0.20/0.46 thf(f348,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0))) @ (sK20 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) = $false)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f347])).
% 0.20/0.46 thf(f347,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) = $true)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f346])).
% 0.20/0.46 thf(f346,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))))) = $true) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f345])).
% 0.20/0.46 thf(f345,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f344])).
% 0.20/0.46 thf(f344,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f343])).
% 0.20/0.46 thf(f343,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))))))) @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))) = $false)) )),
% 0.20/0.46 inference(pi_clausification,[],[f342])).
% 0.20/0.46 thf(f342,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1))))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))) = $false)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f341])).
% 0.20/0.46 thf(f341,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1))))))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f340])).
% 0.20/0.46 thf(f340,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p9 @ Y0)))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f339])).
% 0.20/0.46 thf(f339,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p8 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p9 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1))))))) @ X1) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f338])).
% 0.20/0.46 thf(f338,plain,(
% 0.20/0.46 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p8 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p9 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))))))) = $true)),
% 0.20/0.46 inference(beta_eta_normalization,[],[f145])).
% 0.20/0.46 thf(f145,plain,(
% 0.20/0.46 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p9) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p9) @ ((^[Y0 : $i > $o]: (Y0)) @ p8)))) = $true)),
% 0.20/0.46 inference(definition_unfolding,[],[f104,f107,f141,f129,f141,f129,f129])).
% 0.20/0.46 thf(f104,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8)))) = $true)),
% 0.20/0.46 inference(cnf_transformation,[],[f97])).
% 0.20/0.46 thf(f97,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8)))) = $true)),
% 0.20/0.46 inference(fool_elimination,[],[f96])).
% 0.20/0.46 thf(f96,plain,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8))))),
% 0.20/0.46 inference(rectify,[],[f31])).
% 0.20/0.46 thf(f31,axiom,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8))))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10)).
% 0.20/0.46 thf(f488,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p9 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f485])).
% 0.20/0.46 thf(f485,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ((p9 @ X0) = $true)) )),
% 0.20/0.46 inference(superposition,[],[f484,f364])).
% 0.20/0.46 thf(f364,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((p10 @ X1) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f363])).
% 0.20/0.46 thf(f363,plain,(
% 0.20/0.46 ((!! @ $i @ p10) = $true)),
% 0.20/0.46 inference(beta_eta_normalization,[],[f148])).
% 0.20/0.46 thf(f148,plain,(
% 0.20/0.46 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ p10)) = $true)),
% 0.20/0.46 inference(definition_unfolding,[],[f114,f107,f129])).
% 0.20/0.46 thf(f114,plain,(
% 0.20/0.46 ((ivalid @ (iatom @ p10)) = $true)),
% 0.20/0.46 inference(cnf_transformation,[],[f51])).
% 0.20/0.46 thf(f51,plain,(
% 0.20/0.46 ((ivalid @ (iatom @ p10)) = $true)),
% 0.20/0.46 inference(fool_elimination,[],[f50])).
% 0.20/0.46 thf(f50,plain,(
% 0.20/0.46 (ivalid @ (iatom @ p10))),
% 0.20/0.46 inference(rectify,[],[f22])).
% 0.20/0.46 thf(f22,axiom,(
% 0.20/0.46 (ivalid @ (iatom @ p10))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1)).
% 0.20/0.46 thf(f484,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p10 @ (sK1 @ X0)) = $false) | ((p9 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f482])).
% 0.20/0.46 thf(f482,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p9 @ X0) = $true) | ((p10 @ (sK1 @ X0)) = $false) | ($false = $true)) )),
% 0.20/0.46 inference(superposition,[],[f364,f480])).
% 0.20/0.46 thf(f480,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = (p10 @ (sK3 @ X0))) | ((p9 @ X0) = $true) | ((p10 @ (sK1 @ X0)) = $false)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f473])).
% 0.20/0.46 thf(f473,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ((p9 @ X0) = $true) | ((p10 @ (sK1 @ X0)) = $false) | ($false = (p10 @ (sK3 @ X0)))) )),
% 0.20/0.46 inference(superposition,[],[f472,f126])).
% 0.20/0.46 thf(f472,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($false = (p10 @ (sK3 @ X0))) | ((p10 @ (sK1 @ X1)) = $false) | ((p9 @ X0) = $true)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f465])).
% 0.20/0.46 thf(f465,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p10 @ (sK1 @ X1)) = $false) | ((p9 @ X0) = $true) | ($false = $true) | ($false = (p10 @ (sK3 @ X0)))) )),
% 0.20/0.46 inference(superposition,[],[f126,f181])).
% 0.20/0.46 thf(f181,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((irel @ X1 @ X2) = $false) | ($false = (p10 @ (sK3 @ X2))) | ((p10 @ (sK1 @ X1)) = $false) | ((p9 @ X3) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f180])).
% 0.20/0.46 thf(f180,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p10 @ (sK1 @ X1)) = $false) | (((irel @ X2 @ (sK3 @ X2)) => (p10 @ (sK3 @ X2))) = $false) | ((irel @ X1 @ X2) = $false) | ((p9 @ X3) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f179])).
% 0.20/0.46 thf(f179,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p9 @ X3) = $true) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))) @ (sK3 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((p10 @ (sK1 @ X1)) = $false)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f178])).
% 0.20/0.46 thf(f178,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p9 @ X3) = $true) | ((p10 @ (sK1 @ X1)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))) | ((irel @ X2 @ X3) = $false)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f171])).
% 0.20/0.46 thf(f171,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p9 @ X3) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0)))))) | ((irel @ X2 @ X3) = $false) | ((irel @ X1 @ X2) = $false) | ((p10 @ (sK1 @ X1)) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f170])).
% 0.20/0.46 thf(f170,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ($false = ((irel @ X1 @ (sK1 @ X1)) => (p10 @ (sK1 @ X1)))) | ((p9 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f169])).
% 0.20/0.46 thf(f169,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ X3) => (p9 @ X3)) = $true) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0)))))) | ($false = ((irel @ X1 @ (sK1 @ X1)) => (p10 @ (sK1 @ X1))))) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f168])).
% 0.20/0.46 thf(f168,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((irel @ X1 @ (sK1 @ X1)) => (p10 @ (sK1 @ X1)))) | ((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0))) @ X3) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))) )),
% 0.20/0.46 inference(pi_clausification,[],[f167])).
% 0.20/0.46 thf(f167,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false) | ($false = ((irel @ X1 @ (sK1 @ X1)) => (p10 @ (sK1 @ X1)))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f166])).
% 0.20/0.46 thf(f166,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))) | ($false = ((irel @ X1 @ (sK1 @ X1)) => (p10 @ (sK1 @ X1))))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f165])).
% 0.20/0.46 thf(f165,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))) = $true) | ($false = ((irel @ X1 @ (sK1 @ X1)) => (p10 @ (sK1 @ X1))))) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f164])).
% 0.20/0.46 thf(f164,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0))) @ (sK1 @ X1)) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))) = $true)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f163])).
% 0.20/0.46 thf(f163,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0)))) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))) = $true)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f162])).
% 0.20/0.46 thf(f162,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0))))) = $true) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p9 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p10 @ Y0))))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f161])).
% 0.20/0.46 thf(f161,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1)))))))) @ X2) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0))))) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f160])).
% 0.20/0.46 thf(f160,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1))))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f159])).
% 0.20/0.46 thf(f159,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p9 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p10 @ Y0)))))))) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f158])).
% 0.20/0.46 thf(f158,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p9 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p10 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1))))))) @ X1) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f157])).
% 0.20/0.46 thf(f157,plain,(
% 0.20/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p9 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p10 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p10 @ Y1)))))))))),
% 0.20/0.46 inference(beta_eta_normalization,[],[f152])).
% 0.20/0.46 thf(f152,plain,(
% 0.20/0.46 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p10) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p10) @ ((^[Y0 : $i > $o]: (Y0)) @ p9)))) = $true)),
% 0.20/0.46 inference(definition_unfolding,[],[f124,f107,f141,f129,f141,f129,f129])).
% 0.20/0.46 thf(f124,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9)))) = $true)),
% 0.20/0.46 inference(cnf_transformation,[],[f71])).
% 0.20/0.46 thf(f71,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9)))) = $true)),
% 0.20/0.46 inference(fool_elimination,[],[f70])).
% 0.20/0.46 thf(f70,plain,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9))))),
% 0.20/0.46 inference(rectify,[],[f32])).
% 0.20/0.46 thf(f32,axiom,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9))))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11)).
% 0.20/0.46 thf(f626,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p8 @ (sK13 @ X0)) = $false) | ($true = (p7 @ X0))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f624])).
% 0.20/0.46 thf(f624,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p8 @ (sK13 @ X0)) = $false) | ($true = (p7 @ X0)) | ($false = $true)) )),
% 0.20/0.46 inference(superposition,[],[f568,f622])).
% 0.20/0.46 thf(f568,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p8 @ (sK15 @ X0)) = $false) | ((p8 @ (sK13 @ X0)) = $false) | ($true = (p7 @ X0))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f563])).
% 0.20/0.46 thf(f563,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($true = (p7 @ X0)) | ((p8 @ (sK15 @ X0)) = $false) | ($false = $true) | ((p8 @ (sK13 @ X0)) = $false)) )),
% 0.20/0.46 inference(superposition,[],[f126,f552])).
% 0.20/0.46 thf(f552,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($false = (p8 @ (sK13 @ X1))) | ((p8 @ (sK15 @ X0)) = $false) | ($true = (p7 @ X0))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f545])).
% 0.20/0.46 thf(f545,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (($true = (p7 @ X0)) | ((irel @ X1 @ X0) = $false) | ($false = (p8 @ (sK13 @ X1))) | ((p8 @ (sK15 @ X0)) = $false) | ($false = $true)) )),
% 0.20/0.46 inference(superposition,[],[f126,f306])).
% 0.20/0.46 thf(f306,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p8 @ (sK15 @ X2)) = $false) | ($false = (p8 @ (sK13 @ X1))) | ((irel @ X1 @ X2) = $false) | ((p7 @ X3) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f305])).
% 0.20/0.46 thf(f305,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = ((irel @ X2 @ (sK15 @ X2)) => (p8 @ (sK15 @ X2)))) | ((p7 @ X3) = $true) | ($false = (p8 @ (sK13 @ X1))) | ((irel @ X2 @ X3) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f304])).
% 0.20/0.46 thf(f304,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((irel @ X2 @ X3) = $false) | ($false = (p8 @ (sK13 @ X1))) | ($false = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))) @ (sK15 @ X2))) | ((p7 @ X3) = $true)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f303])).
% 0.20/0.46 thf(f303,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((irel @ X1 @ X2) = $false) | ((p7 @ X3) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) = $false) | ($false = (p8 @ (sK13 @ X1)))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f302])).
% 0.20/0.46 thf(f302,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((irel @ X2 @ X3) => (p7 @ X3))) | ((irel @ X1 @ X2) = $false) | ($false = (p8 @ (sK13 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))) = $false)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f301])).
% 0.20/0.46 thf(f301,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))) = $true) | ($false = (p8 @ (sK13 @ X1))) | ((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p7 @ X3)))) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f300])).
% 0.20/0.46 thf(f300,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p8 @ (sK13 @ X1))) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))) @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f299])).
% 0.20/0.46 thf(f299,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))) = $true) | ($false = (p8 @ (sK13 @ X1)))) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f288])).
% 0.20/0.46 thf(f288,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))))) = $true) | ($false = (p8 @ (sK13 @ X1))) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f287])).
% 0.20/0.46 thf(f287,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ X1 @ (sK13 @ X1)) => (p8 @ (sK13 @ X1)))) | ((irel @ X1 @ X2) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f286])).
% 0.20/0.46 thf(f286,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0))) @ (sK13 @ X1))) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))))) = $true)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f285])).
% 0.20/0.46 thf(f285,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))))) = $true)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f284])).
% 0.20/0.46 thf(f284,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0)))))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f283])).
% 0.20/0.46 thf(f283,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p7 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p8 @ Y0))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f282])).
% 0.20/0.46 thf(f282,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0))))) = $true) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))))))) @ X2) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f281])).
% 0.20/0.46 thf(f281,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1))))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f280])).
% 0.20/0.46 thf(f280,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p7 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p8 @ Y0)))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f279])).
% 0.20/0.46 thf(f279,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p7 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p8 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1))))))) @ X1) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f278])).
% 0.20/0.46 thf(f278,plain,(
% 0.20/0.46 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p7 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p8 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p8 @ Y1)))))))) = $true)),
% 0.20/0.46 inference(beta_eta_normalization,[],[f150])).
% 0.20/0.46 thf(f150,plain,(
% 0.20/0.46 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p8) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p8) @ ((^[Y0 : $i > $o]: (Y0)) @ p7)))))),
% 0.20/0.46 inference(definition_unfolding,[],[f119,f107,f141,f129,f141,f129,f129])).
% 0.20/0.46 thf(f119,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7)))) = $true)),
% 0.20/0.46 inference(cnf_transformation,[],[f65])).
% 0.20/0.46 thf(f65,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7)))) = $true)),
% 0.20/0.46 inference(fool_elimination,[],[f64])).
% 0.20/0.46 thf(f64,plain,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7))))),
% 0.20/0.46 inference(rectify,[],[f30])).
% 0.20/0.46 thf(f30,axiom,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7))))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9)).
% 0.20/0.46 thf(f642,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p6 @ (sK10 @ X0)) = $false) | ($true = (p5 @ X0))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f640])).
% 0.20/0.46 thf(f640,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($true = (p5 @ X0)) | ((p6 @ (sK10 @ X0)) = $false) | ($false = $true)) )),
% 0.20/0.46 inference(superposition,[],[f541,f638])).
% 0.20/0.46 thf(f541,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p6 @ (sK12 @ X0)) = $false) | ((p6 @ (sK10 @ X0)) = $false) | ($true = (p5 @ X0))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f537])).
% 0.20/0.46 thf(f537,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p6 @ (sK12 @ X0)) = $false) | ((p6 @ (sK10 @ X0)) = $false) | ($false = $true) | ($true = (p5 @ X0))) )),
% 0.20/0.46 inference(superposition,[],[f126,f532])).
% 0.20/0.46 thf(f532,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p5 @ X0)) | ((p6 @ (sK12 @ X0)) = $false) | ((p6 @ (sK10 @ X1)) = $false)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f527])).
% 0.20/0.46 thf(f527,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((p6 @ (sK10 @ X1)) = $false) | ((irel @ X1 @ X0) = $false) | ($true = (p5 @ X0)) | ($false = $true) | ((p6 @ (sK12 @ X0)) = $false)) )),
% 0.20/0.46 inference(superposition,[],[f126,f276])).
% 0.20/0.46 thf(f276,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p6 @ (sK10 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((p5 @ X3) = $true) | ((p6 @ (sK12 @ X2)) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f275])).
% 0.20/0.46 thf(f275,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | (((irel @ X2 @ (sK12 @ X2)) => (p6 @ (sK12 @ X2))) = $false) | ((p6 @ (sK10 @ X1)) = $false) | ((p5 @ X3) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f274])).
% 0.20/0.46 thf(f274,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p6 @ (sK10 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($false = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))) @ (sK12 @ X2))) | ((p5 @ X3) = $true) | ((irel @ X2 @ X3) = $false)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f273])).
% 0.20/0.46 thf(f273,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))) = $false) | ((p6 @ (sK10 @ X1)) = $false) | ((p5 @ X3) = $true) | ((irel @ X2 @ X3) = $false)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f272])).
% 0.20/0.46 thf(f272,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p5 @ X3) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))))) = $true) | ((irel @ X2 @ X3) = $false) | ((irel @ X1 @ X2) = $false) | ((p6 @ (sK10 @ X1)) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f271])).
% 0.20/0.46 thf(f271,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p6 @ (sK10 @ X1)) = $false) | (((irel @ X2 @ X3) => (p5 @ X3)) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f270])).
% 0.20/0.46 thf(f270,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p6 @ (sK10 @ X1)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))))) = $true) | ((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))) @ X3) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f269])).
% 0.20/0.46 thf(f269,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) = $true) | ((p6 @ (sK10 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f268])).
% 0.20/0.46 thf(f268,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0)))))) = $true) | ((p6 @ (sK10 @ X1)) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f256])).
% 0.20/0.46 thf(f256,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))))))) = $true) | ((p6 @ (sK10 @ X1)) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f255])).
% 0.20/0.46 thf(f255,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK10 @ X1)) => (p6 @ (sK10 @ X1))) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p6 @ Y0))))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f254])).
% 0.20/0.46 thf(f254,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK10 @ X1)) => (p6 @ (sK10 @ X1))) = $false) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))))))) @ X2) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f253])).
% 0.20/0.46 thf(f253,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1))))))))) = $true) | (((irel @ X1 @ (sK10 @ X1)) => (p6 @ (sK10 @ X1))) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f252])).
% 0.20/0.46 thf(f252,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1))))))))) = $true) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0))) @ (sK10 @ X1)) = $false)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f251])).
% 0.20/0.46 thf(f251,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1))))))))) = $true)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f250])).
% 0.20/0.46 thf(f250,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1))))))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f249])).
% 0.20/0.46 thf(f249,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p6 @ Y0)))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f248])).
% 0.20/0.46 thf(f248,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p5 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p6 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1))))))) @ X1) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f247])).
% 0.20/0.46 thf(f247,plain,(
% 0.20/0.46 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p5 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p6 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p6 @ Y1)))))))) = $true)),
% 0.20/0.46 inference(beta_eta_normalization,[],[f149])).
% 0.20/0.46 thf(f149,plain,(
% 0.20/0.46 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p6) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p6) @ ((^[Y0 : $i > $o]: (Y0)) @ p5)))) = $true)),
% 0.20/0.46 inference(definition_unfolding,[],[f116,f107,f141,f129,f141,f129,f129])).
% 0.20/0.46 thf(f116,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5)))) = $true)),
% 0.20/0.46 inference(cnf_transformation,[],[f77])).
% 0.20/0.46 thf(f77,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5)))) = $true)),
% 0.20/0.46 inference(fool_elimination,[],[f76])).
% 0.20/0.46 thf(f76,plain,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5))))),
% 0.20/0.46 inference(rectify,[],[f28])).
% 0.20/0.46 thf(f28,axiom,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5))))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7)).
% 0.20/0.46 thf(f800,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p2 @ (sK17 @ X0)) = $false) | ($true = (p1 @ X0))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f798])).
% 0.20/0.46 thf(f798,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($true = (p1 @ X0)) | ((p2 @ (sK17 @ X0)) = $false) | ($false = $true)) )),
% 0.20/0.46 inference(superposition,[],[f585,f796])).
% 0.20/0.46 thf(f585,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (((p2 @ (sK19 @ X0)) = $false) | ($true = (p1 @ X0)) | ((p2 @ (sK17 @ X0)) = $false)) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f579])).
% 0.20/0.46 thf(f579,plain,(
% 0.20/0.46 ( ! [X0 : $i] : (($false = $true) | ($true = (p1 @ X0)) | ((p2 @ (sK19 @ X0)) = $false) | ((p2 @ (sK17 @ X0)) = $false)) )),
% 0.20/0.46 inference(superposition,[],[f577,f126])).
% 0.20/0.46 thf(f577,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($true = (p1 @ X0)) | ((p2 @ (sK19 @ X0)) = $false) | ($false = (p2 @ (sK17 @ X1)))) )),
% 0.20/0.46 inference(trivial_inequality_removal,[],[f569])).
% 0.20/0.46 thf(f569,plain,(
% 0.20/0.46 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ((p2 @ (sK19 @ X0)) = $false) | ($true = (p1 @ X0)) | ((irel @ X1 @ X0) = $false) | ($false = (p2 @ (sK17 @ X1)))) )),
% 0.20/0.46 inference(superposition,[],[f336,f126])).
% 0.20/0.46 thf(f336,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ($false = (p2 @ (sK17 @ X1))) | ((p1 @ X3) = $true) | ((p2 @ (sK19 @ X2)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f335])).
% 0.20/0.46 thf(f335,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p2 @ (sK17 @ X1))) | ((irel @ X1 @ X2) = $false) | ((p1 @ X3) = $true) | (((irel @ X2 @ (sK19 @ X2)) => (p2 @ (sK19 @ X2))) = $false) | ((irel @ X2 @ X3) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f334])).
% 0.20/0.46 thf(f334,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))) @ (sK19 @ X2))) | ($false = (p2 @ (sK17 @ X1))) | ((p1 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ((irel @ X2 @ X3) = $false)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f333])).
% 0.20/0.46 thf(f333,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $false) | ($false = (p2 @ (sK17 @ X1))) | ((irel @ X1 @ X2) = $false) | ((irel @ X2 @ X3) = $false) | ((p1 @ X3) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f332])).
% 0.20/0.46 thf(f332,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((irel @ X2 @ X3) => (p1 @ X3))) | ((irel @ X1 @ X2) = $false) | ($false = (p2 @ (sK17 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f331])).
% 0.20/0.46 thf(f331,plain,(
% 0.20/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))) @ X3) = $true) | ($false = (p2 @ (sK17 @ X1))) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(pi_clausification,[],[f322])).
% 0.20/0.46 thf(f322,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $false) | ($false = (p2 @ (sK17 @ X1))) | ((irel @ X1 @ X2) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f321])).
% 0.20/0.46 thf(f321,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK17 @ X1)) => (p2 @ (sK17 @ X1))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $false) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $true)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f320])).
% 0.20/0.46 thf(f320,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))) = $true) | (((irel @ X1 @ (sK17 @ X1)) => (p2 @ (sK17 @ X1))) = $false) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f319])).
% 0.20/0.46 thf(f319,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))))) = $true) | ((irel @ X1 @ X2) = $false) | (((irel @ X1 @ (sK17 @ X1)) => (p2 @ (sK17 @ X1))) = $false)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f318])).
% 0.20/0.46 thf(f318,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) = $true) | (((irel @ X1 @ (sK17 @ X1)) => (p2 @ (sK17 @ X1))) = $false)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f317])).
% 0.20/0.46 thf(f317,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) = $true) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0))) @ (sK17 @ X1)) = $false)) )),
% 0.20/0.46 inference(sigma_clausification,[],[f316])).
% 0.20/0.46 thf(f316,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) = $true)) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f315])).
% 0.20/0.46 thf(f315,plain,(
% 0.20/0.46 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))))))) @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))) = $false)) )),
% 0.20/0.46 inference(pi_clausification,[],[f314])).
% 0.20/0.46 thf(f314,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1))))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))) = $false)) )),
% 0.20/0.46 inference(not_proxy_clausification,[],[f313])).
% 0.20/0.46 thf(f313,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1))))))))) = $true)) )),
% 0.20/0.46 inference(binary_proxy_clausification,[],[f312])).
% 0.20/0.46 thf(f312,plain,(
% 0.20/0.46 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))))))) )),
% 0.20/0.46 inference(beta_eta_normalization,[],[f311])).
% 0.20/0.46 thf(f311,plain,(
% 0.20/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p2 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1))))))) @ X1) = $true)) )),
% 0.20/0.46 inference(pi_clausification,[],[f310])).
% 0.20/0.46 thf(f310,plain,(
% 0.20/0.46 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p2 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))))))) = $true)),
% 0.20/0.46 inference(beta_eta_normalization,[],[f155])).
% 0.20/0.46 thf(f155,plain,(
% 0.20/0.46 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p2) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p2) @ ((^[Y0 : $i > $o]: (Y0)) @ p1)))) = $true)),
% 0.20/0.46 inference(definition_unfolding,[],[f133,f107,f141,f129,f141,f129,f129])).
% 0.20/0.46 thf(f133,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1)))) = $true)),
% 0.20/0.46 inference(cnf_transformation,[],[f47])).
% 0.20/0.46 thf(f47,plain,(
% 0.20/0.46 ((ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1)))) = $true)),
% 0.20/0.46 inference(fool_elimination,[],[f46])).
% 0.20/0.46 thf(f46,plain,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1))))),
% 0.20/0.46 inference(rectify,[],[f24])).
% 0.20/0.46 thf(f24,axiom,(
% 0.20/0.46 (ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1))))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3)).
% 0.20/0.46 thf(f309,plain,(
% 0.20/0.46 ($false = (p0 @ sK16))),
% 0.20/0.46 inference(sigma_clausification,[],[f308])).
% 0.20/0.46 thf(f308,plain,(
% 0.20/0.46 ((!! @ $i @ p0) != $true)),
% 0.20/0.46 inference(beta_eta_normalization,[],[f146])).
% 0.20/0.46 thf(f146,plain,(
% 0.20/0.46 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ p0)))),
% 0.20/0.46 inference(definition_unfolding,[],[f111,f107,f129])).
% 0.20/0.46 thf(f111,plain,(
% 0.20/0.46 ((ivalid @ (iatom @ p0)) != $true)),
% 0.20/0.46 inference(cnf_transformation,[],[f100])).
% 0.20/0.46 thf(f100,plain,(
% 0.20/0.46 ((ivalid @ (iatom @ p0)) != $true)),
% 0.20/0.46 inference(flattening,[],[f61])).
% 0.20/0.46 thf(f61,plain,(
% 0.20/0.46 ~((ivalid @ (iatom @ p0)) = $true)),
% 0.20/0.46 inference(fool_elimination,[],[f60])).
% 0.20/0.46 thf(f60,plain,(
% 0.20/0.46 ~(ivalid @ (iatom @ p0))),
% 0.20/0.46 inference(rectify,[],[f34])).
% 0.20/0.46 thf(f34,negated_conjecture,(
% 0.20/0.46 ~(ivalid @ (iatom @ p0))),
% 0.20/0.46 inference(negated_conjecture,[],[f33])).
% 0.20/0.46 thf(f33,conjecture,(
% 0.20/0.46 (ivalid @ (iatom @ p0))),
% 0.20/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.20/0.46 % SZS output end Proof for theBenchmark
% 0.20/0.46 % (11158)------------------------------
% 0.20/0.46 % (11158)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.46 % (11158)Termination reason: Refutation
% 0.20/0.46
% 0.20/0.46 % (11158)Memory used [KB]: 6140
% 0.20/0.46 % (11158)Time elapsed: 0.089 s
% 0.20/0.46 % (11158)Instructions burned: 122 (million)
% 0.20/0.46 % (11158)------------------------------
% 0.20/0.46 % (11158)------------------------------
% 0.20/0.46 % (11157)Success in time 0.107 s
%------------------------------------------------------------------------------