TSTP Solution File: SEU695^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU695^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:50:49 EDT 2024
% Result : Theorem 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU695^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 16:47:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.38 % (715)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)
% 0.14/0.38 % (708)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (711)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (710)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)
% 0.14/0.38 % (709)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)
% 0.14/0.38 % (712)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)
% 0.14/0.38 % (715)Instruction limit reached!
% 0.14/0.38 % (715)------------------------------
% 0.14/0.38 % (715)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (715)Termination reason: Unknown
% 0.14/0.38 % (715)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (715)Memory used [KB]: 1023
% 0.14/0.38 % (713)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)
% 0.14/0.38 % (715)Time elapsed: 0.003 s
% 0.14/0.38 % (715)Instructions burned: 3 (million)
% 0.14/0.38 % (715)------------------------------
% 0.14/0.38 % (715)------------------------------
% 0.14/0.38 % (714)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (711)Instruction limit reached!
% 0.14/0.38 % (711)------------------------------
% 0.14/0.38 % (711)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (711)Termination reason: Unknown
% 0.14/0.38 % (711)Termination phase: Property scanning
% 0.14/0.38 % (712)Instruction limit reached!
% 0.14/0.38 % (712)------------------------------
% 0.14/0.38 % (712)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38
% 0.14/0.38 % (711)Memory used [KB]: 1023
% 0.14/0.38 % (711)Time elapsed: 0.003 s
% 0.14/0.38 % (711)Instructions burned: 2 (million)
% 0.14/0.38 % (711)------------------------------
% 0.14/0.38 % (711)------------------------------
% 0.14/0.38 % (712)Termination reason: Unknown
% 0.14/0.38 % (712)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (712)Memory used [KB]: 895
% 0.14/0.38 % (712)Time elapsed: 0.003 s
% 0.14/0.38 % (712)Instructions burned: 2 (million)
% 0.14/0.38 % (712)------------------------------
% 0.14/0.38 % (712)------------------------------
% 0.14/0.38 % (709)Instruction limit reached!
% 0.14/0.38 % (709)------------------------------
% 0.14/0.38 % (709)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (709)Termination reason: Unknown
% 0.14/0.38 % (709)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (709)Memory used [KB]: 1023
% 0.14/0.38 % (709)Time elapsed: 0.004 s
% 0.14/0.38 % (709)Instructions burned: 4 (million)
% 0.14/0.38 % (709)------------------------------
% 0.14/0.38 % (709)------------------------------
% 0.14/0.39 % (713)Refutation not found, incomplete strategy
% 0.14/0.39 % (713)------------------------------
% 0.14/0.39 % (713)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (713)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.39
% 0.14/0.39
% 0.14/0.39 % (713)Memory used [KB]: 5628
% 0.14/0.39 % (713)Time elapsed: 0.012 s
% 0.14/0.39 % (713)Instructions burned: 13 (million)
% 0.14/0.39 % (713)------------------------------
% 0.14/0.39 % (713)------------------------------
% 0.14/0.39 % (714)Instruction limit reached!
% 0.14/0.39 % (714)------------------------------
% 0.14/0.39 % (714)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (714)Termination reason: Unknown
% 0.14/0.39 % (714)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (714)Memory used [KB]: 5756
% 0.14/0.39 % (714)Time elapsed: 0.014 s
% 0.14/0.39 % (714)Instructions burned: 19 (million)
% 0.14/0.39 % (714)------------------------------
% 0.14/0.39 % (714)------------------------------
% 0.14/0.39 % (717)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)
% 0.14/0.39 % (716)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)
% 0.14/0.39 % (718)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)
% 0.14/0.39 % (719)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)
% 0.14/0.39 % (710)Instruction limit reached!
% 0.14/0.39 % (710)------------------------------
% 0.14/0.39 % (710)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (710)Termination reason: Unknown
% 0.14/0.39 % (710)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (710)Memory used [KB]: 5756
% 0.14/0.39 % (710)Time elapsed: 0.019 s
% 0.14/0.39 % (710)Instructions burned: 27 (million)
% 0.14/0.39 % (710)------------------------------
% 0.14/0.39 % (710)------------------------------
% 0.14/0.40 % (718)Instruction limit reached!
% 0.14/0.40 % (718)------------------------------
% 0.14/0.40 % (718)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (718)Termination reason: Unknown
% 0.14/0.40 % (718)Termination phase: Function definition elimination
% 0.14/0.40
% 0.14/0.40 % (718)Memory used [KB]: 1023
% 0.14/0.40 % (718)Time elapsed: 0.004 s
% 0.14/0.40 % (718)Instructions burned: 4 (million)
% 0.14/0.40 % (718)------------------------------
% 0.14/0.40 % (718)------------------------------
% 0.14/0.40 % (717)Instruction limit reached!
% 0.14/0.40 % (717)------------------------------
% 0.14/0.40 % (717)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (717)Termination reason: Unknown
% 0.14/0.40 % (717)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (717)Memory used [KB]: 5628
% 0.14/0.40 % (717)Time elapsed: 0.010 s
% 0.14/0.40 % (717)Instructions burned: 16 (million)
% 0.14/0.40 % (717)------------------------------
% 0.14/0.40 % (717)------------------------------
% 0.14/0.41 % (721)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.41 % (720)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.41 % (722)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)
% 0.14/0.41 % (720)Instruction limit reached!
% 0.14/0.41 % (720)------------------------------
% 0.14/0.41 % (720)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (720)Termination reason: Unknown
% 0.14/0.41 % (720)Termination phase: Saturation
% 0.14/0.41
% 0.14/0.41 % (720)Memory used [KB]: 1023
% 0.14/0.41 % (720)Time elapsed: 0.006 s
% 0.14/0.41 % (720)Instructions burned: 7 (million)
% 0.14/0.41 % (720)------------------------------
% 0.14/0.41 % (720)------------------------------
% 0.14/0.41 % (722)Instruction limit reached!
% 0.14/0.41 % (722)------------------------------
% 0.14/0.41 % (722)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (722)Termination reason: Unknown
% 0.14/0.41 % (722)Termination phase: Function definition elimination
% 0.14/0.41
% 0.14/0.41 % (722)Memory used [KB]: 1023
% 0.14/0.41 % (722)Time elapsed: 0.004 s
% 0.14/0.41 % (722)Instructions burned: 4 (million)
% 0.14/0.41 % (722)------------------------------
% 0.14/0.41 % (722)------------------------------
% 0.14/0.41 % (723)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)
% 0.14/0.41 % (724)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)
% 0.14/0.41 % (716)Instruction limit reached!
% 0.14/0.41 % (716)------------------------------
% 0.14/0.41 % (716)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (716)Termination reason: Unknown
% 0.14/0.41 % (716)Termination phase: Saturation
% 0.14/0.41
% 0.14/0.42 % (716)Memory used [KB]: 5756
% 0.14/0.42 % (716)Time elapsed: 0.045 s
% 0.14/0.42 % (716)Instructions burned: 37 (million)
% 0.14/0.42 % (716)------------------------------
% 0.14/0.42 % (716)------------------------------
% 0.14/0.42 % (723)Instruction limit reached!
% 0.14/0.42 % (723)------------------------------
% 0.14/0.42 % (723)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (723)Termination reason: Unknown
% 0.14/0.42 % (723)Termination phase: Property scanning
% 0.14/0.42
% 0.14/0.42 % (723)Memory used [KB]: 1023
% 0.14/0.42 % (723)Time elapsed: 0.003 s
% 0.14/0.42 % (723)Instructions burned: 3 (million)
% 0.14/0.42 % (723)------------------------------
% 0.14/0.42 % (723)------------------------------
% 0.14/0.42 % (721)Instruction limit reached!
% 0.14/0.42 % (721)------------------------------
% 0.14/0.42 % (721)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (721)Termination reason: Unknown
% 0.14/0.42 % (721)Termination phase: Saturation
% 0.14/0.42
% 0.14/0.42 % (721)Memory used [KB]: 6012
% 0.14/0.42 % (721)Time elapsed: 0.013 s
% 0.14/0.42 % (721)Instructions burned: 16 (million)
% 0.14/0.42 % (721)------------------------------
% 0.14/0.42 % (721)------------------------------
% 0.14/0.42 % (724)Refutation not found, incomplete strategy
% 0.14/0.42 % (724)------------------------------
% 0.14/0.42 % (724)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (724)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.42
% 0.14/0.42
% 0.14/0.42 % (724)Memory used [KB]: 5500
% 0.14/0.42 % (724)Time elapsed: 0.005 s
% 0.14/0.42 % (724)Instructions burned: 5 (million)
% 0.14/0.42 % (724)------------------------------
% 0.14/0.42 % (724)------------------------------
% 0.14/0.42 % (725)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)
% 0.14/0.43 % (725)Instruction limit reached!
% 0.14/0.43 % (725)------------------------------
% 0.14/0.43 % (725)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.43 % (725)Termination reason: Unknown
% 0.14/0.43 % (725)Termination phase: Property scanning
% 0.14/0.43
% 0.14/0.43 % (725)Memory used [KB]: 1023
% 0.14/0.43 % (725)Time elapsed: 0.003 s
% 0.14/0.43 % (725)Instructions burned: 3 (million)
% 0.14/0.43 % (725)------------------------------
% 0.14/0.43 % (725)------------------------------
% 0.14/0.43 % (726)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.43 % (726)Instruction limit reached!
% 0.14/0.43 % (726)------------------------------
% 0.14/0.43 % (726)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.43 % (726)Termination reason: Unknown
% 0.14/0.43 % (726)Termination phase: Property scanning
% 0.14/0.43
% 0.14/0.43 % (726)Memory used [KB]: 1023
% 0.14/0.43 % (726)Time elapsed: 0.004 s
% 0.14/0.43 % (726)Instructions burned: 4 (million)
% 0.14/0.43 % (726)------------------------------
% 0.14/0.43 % (726)------------------------------
% 0.21/0.43 % (727)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.43 % (728)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.43 % (730)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.21/0.43 % (729)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.43 % (730)Refutation not found, incomplete strategy
% 0.21/0.43 % (730)------------------------------
% 0.21/0.43 % (730)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (730)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.43
% 0.21/0.43
% 0.21/0.43 % (730)Memory used [KB]: 5628
% 0.21/0.43 % (730)Time elapsed: 0.004 s
% 0.21/0.43 % (730)Instructions burned: 8 (million)
% 0.21/0.43 % (730)------------------------------
% 0.21/0.43 % (730)------------------------------
% 0.21/0.43 % (729)Instruction limit reached!
% 0.21/0.43 % (729)------------------------------
% 0.21/0.43 % (729)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (729)Termination reason: Unknown
% 0.21/0.43 % (729)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (729)Memory used [KB]: 5500
% 0.21/0.43 % (729)Time elapsed: 0.005 s
% 0.21/0.43 % (729)Instructions burned: 6 (million)
% 0.21/0.43 % (729)------------------------------
% 0.21/0.43 % (729)------------------------------
% 0.21/0.44 % (719)First to succeed.
% 0.21/0.44 % (734)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.21/0.44 % (727)Instruction limit reached!
% 0.21/0.44 % (727)------------------------------
% 0.21/0.44 % (727)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (727)Termination reason: Unknown
% 0.21/0.44 % (727)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (727)Memory used [KB]: 5628
% 0.21/0.44 % (727)Time elapsed: 0.013 s
% 0.21/0.44 % (727)Instructions burned: 19 (million)
% 0.21/0.44 % (727)------------------------------
% 0.21/0.44 % (727)------------------------------
% 0.21/0.44 % (737)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.44 % (737)Instruction limit reached!
% 0.21/0.44 % (737)------------------------------
% 0.21/0.44 % (737)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (737)Termination reason: Unknown
% 0.21/0.44 % (737)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (737)Memory used [KB]: 5500
% 0.21/0.44 % (737)Time elapsed: 0.003 s
% 0.21/0.44 % (737)Instructions burned: 7 (million)
% 0.21/0.44 % (737)------------------------------
% 0.21/0.44 % (737)------------------------------
% 0.21/0.44 % (719)Refutation found. Thanks to Tanya!
% 0.21/0.44 % SZS status Theorem for theBenchmark
% 0.21/0.44 % SZS output start Proof for theBenchmark
% 0.21/0.44 thf(func_def_0, type, in: $i > $i > $o).
% 0.21/0.44 thf(func_def_1, type, kpair: $i > $i > $i).
% 0.21/0.44 thf(func_def_2, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.21/0.44 thf(func_def_5, type, func: $i > $i > $i > $o).
% 0.21/0.44 thf(func_def_6, type, ap: $i > $i > $i > $i > $i).
% 0.21/0.44 thf(func_def_7, type, lam: $i > $i > ($i > $i) > $i).
% 0.21/0.44 thf(func_def_25, type, ph1: !>[X0: $tType]:(X0)).
% 0.21/0.44 thf(func_def_26, type, sK2: $i > $i).
% 0.21/0.44 thf(f173,plain,(
% 0.21/0.44 $false),
% 0.21/0.44 inference(trivial_inequality_removal,[],[f172])).
% 0.21/0.44 thf(f172,plain,(
% 0.21/0.44 ($false = $true)),
% 0.21/0.44 inference(boolean_simplification,[],[f171])).
% 0.21/0.44 thf(f171,plain,(
% 0.21/0.44 ($true = (~ $true))),
% 0.21/0.44 inference(boolean_simplification,[],[f170])).
% 0.21/0.44 thf(f170,plain,(
% 0.21/0.44 ($true = (~ ((sK2 @ sK5) = (sK2 @ sK5))))),
% 0.21/0.44 inference(boolean_simplification,[],[f169])).
% 0.21/0.44 thf(f169,plain,(
% 0.21/0.44 ($true = (((sK2 @ sK5) = (sK2 @ sK5)) => $false))),
% 0.21/0.44 inference(beta_eta_normalization,[],[f164])).
% 0.21/0.44 thf(f164,plain,(
% 0.21/0.44 ($true = (((^[Y0 : $i]: (= @ (sK2 @ Y0))) @ sK5 @ (sK2 @ sK5)) => $false))),
% 0.21/0.44 inference(superposition,[],[f114,f160])).
% 0.21/0.44 thf(f160,plain,(
% 0.21/0.44 ($false = (in @ (kpair @ sK5 @ (sK2 @ sK5)) @ (dpsetconstr @ sK3 @ sK4 @ (^[Y0 : $i]: (= @ (sK2 @ Y0))))))),
% 0.21/0.44 inference(not_proxy_clausification,[],[f157])).
% 0.21/0.44 thf(f157,plain,(
% 0.21/0.44 ($true = (~ (in @ (kpair @ sK5 @ (sK2 @ sK5)) @ (dpsetconstr @ sK3 @ sK4 @ (^[Y0 : $i]: (= @ (sK2 @ Y0)))))))),
% 0.21/0.44 inference(boolean_simplification,[],[f156])).
% 0.21/0.44 thf(f156,plain,(
% 0.21/0.44 ($true = ((in @ (kpair @ sK5 @ (sK2 @ sK5)) @ (dpsetconstr @ sK3 @ sK4 @ (^[Y0 : $i]: (= @ (sK2 @ Y0))))) => $false))),
% 0.21/0.44 inference(forward_demodulation,[],[f155,f85])).
% 0.21/0.44 thf(f85,plain,(
% 0.21/0.44 ($false = ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y0 : $i]: (= @ (sK2 @ Y0)))) @ sK5) = (sK2 @ sK5)))),
% 0.21/0.44 inference(binary_proxy_clausification,[],[f83])).
% 0.21/0.44 thf(f83,plain,(
% 0.21/0.44 ($false = ((in @ sK5 @ sK3) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y0 : $i]: (= @ (sK2 @ Y0)))) @ sK5) = (sK2 @ sK5))))),
% 0.21/0.44 inference(beta_eta_normalization,[],[f82])).
% 0.21/0.44 thf(f82,plain,(
% 0.21/0.44 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK3) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y1 : $i]: (= @ (sK2 @ Y1)))) @ Y0) = (sK2 @ Y0)))) @ sK5))),
% 0.21/0.44 inference(sigma_clausification,[],[f77])).
% 0.21/0.44 thf(f77,plain,(
% 0.21/0.44 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y1 : $i]: (= @ (sK2 @ Y1)))) @ Y0) = (sK2 @ Y0))))))),
% 0.21/0.44 inference(boolean_simplification,[],[f76])).
% 0.21/0.44 thf(f76,plain,(
% 0.21/0.44 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y1 : $i]: (= @ (sK2 @ Y1)))) @ Y0) = (sK2 @ Y0)))))))),
% 0.21/0.44 inference(backward_demodulation,[],[f72,f75])).
% 0.21/0.44 thf(f75,plain,(
% 0.21/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (sK2 @ Y0) @ sK4)))))),
% 0.21/0.44 inference(binary_proxy_clausification,[],[f72])).
% 0.21/0.44 thf(f72,plain,(
% 0.21/0.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (sK2 @ Y0) @ sK4)))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y1 : $i]: (= @ (sK2 @ Y1)))) @ Y0) = (sK2 @ Y0)))))))),
% 0.21/0.44 inference(beta_eta_normalization,[],[f71])).
% 0.21/0.44 thf(f71,plain,(
% 0.21/0.44 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (in @ (sK2 @ Y1) @ Y0)))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((ap @ sK3 @ Y0 @ (dpsetconstr @ sK3 @ Y0 @ (^[Y2 : $i]: (= @ (sK2 @ Y2)))) @ Y1) = (sK2 @ Y1))))))) @ sK4))),
% 0.21/0.44 inference(sigma_clausification,[],[f68])).
% 0.21/0.44 thf(f68,plain,(
% 0.21/0.44 ($false = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (in @ (sK2 @ Y1) @ Y0)))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((ap @ sK3 @ Y0 @ (dpsetconstr @ sK3 @ Y0 @ (^[Y2 : $i]: (= @ (sK2 @ Y2)))) @ Y1) = (sK2 @ Y1)))))))))),
% 0.21/0.44 inference(beta_eta_normalization,[],[f67])).
% 0.21/0.44 thf(f67,plain,(
% 0.21/0.44 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (sK2 @ Y2) @ Y1)))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (sK2 @ Y3)))) @ Y2) = (sK2 @ Y2))))))))) @ sK3) = $false)),
% 0.21/0.44 inference(sigma_clausification,[],[f64])).
% 0.21/0.44 thf(f64,plain,(
% 0.21/0.44 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (sK2 @ Y2) @ Y1)))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((ap @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: (= @ (sK2 @ Y3)))) @ Y2) = (sK2 @ Y2)))))))))))),
% 0.21/0.44 inference(beta_eta_normalization,[],[f63])).
% 0.21/0.44 thf(f63,plain,(
% 0.21/0.44 ($false = ((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y4 : $i]: (= @ (Y0 @ Y4)))) @ Y3) = (Y0 @ Y3))))))))))) @ sK2))),
% 0.21/0.44 inference(sigma_clausification,[],[f60])).
% 0.21/0.44 thf(f60,plain,(
% 0.21/0.44 ($false = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y4 : $i]: (= @ (Y0 @ Y4)))) @ Y3) = (Y0 @ Y3)))))))))))))),
% 0.21/0.44 inference(boolean_simplification,[],[f59])).
% 0.21/0.44 thf(f59,plain,(
% 0.21/0.44 ($false = ($true => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y4 : $i]: (= @ (Y0 @ Y4)))) @ Y3) = (Y0 @ Y3))))))))))))))),
% 0.21/0.44 inference(backward_demodulation,[],[f44,f58])).
% 0.21/0.44 thf(f58,plain,(
% 0.21/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))),
% 0.21/0.44 inference(binary_proxy_clausification,[],[f44])).
% 0.21/0.44 thf(f44,plain,(
% 0.21/0.44 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))) => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y4 : $i]: (= @ (Y0 @ Y4)))) @ Y3) = (Y0 @ Y3))))))))))))))),
% 0.21/0.44 inference(binary_proxy_clausification,[],[f29])).
% 0.21/0.44 thf(f29,plain,(
% 0.21/0.44 ($false = ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))) => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y4 : $i]: (= @ (Y0 @ Y4)))) @ Y3) = (Y0 @ Y3)))))))))))))))),
% 0.21/0.44 inference(binary_proxy_clausification,[],[f26])).
% 0.21/0.44 thf(f26,plain,(
% 0.21/0.44 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y3))))))))))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))) => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y4 : $i]: (= @ (Y0 @ Y4)))) @ Y3) = (Y0 @ Y3))))))))))))))))),
% 0.21/0.44 inference(not_proxy_clausification,[],[f25])).
% 0.21/0.44 thf(f25,plain,(
% 0.21/0.44 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y3))))))))))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))) => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y4 : $i]: (= @ (Y0 @ Y4)))) @ Y3) = (Y0 @ Y3)))))))))))))))) = $true)),
% 0.21/0.44 inference(beta_eta_normalization,[],[f24])).
% 0.21/0.44 thf(f24,plain,(
% 0.21/0.44 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6))))))))))))))))))) => ((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))) => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y2 @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i > $i]: (dpsetconstr @ Y4 @ Y5 @ (^[Y7 : $i]: ((^[Y8 : $i]: ((Y6 @ Y7) = Y8)))))))))) @ Y1 @ Y2 @ (^[Y4 : $i]: (Y0 @ Y4))) @ Y3) = (Y0 @ Y3)))))))))))))))))),
% 0.21/0.44 inference(definition_unfolding,[],[f18,f19,f23,f22,f21])).
% 0.21/0.44 thf(f21,plain,(
% 0.21/0.44 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 0.21/0.44 inference(cnf_transformation,[],[f9])).
% 0.21/0.44 thf(f9,plain,(
% 0.21/0.44 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 0.21/0.44 inference(fool_elimination,[],[f8])).
% 0.21/0.44 thf(f8,plain,(
% 0.21/0.44 ((^[X0 : $i, X1 : $i, X2 : $i > $i] : (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : (((X2 @ X3) = X4))))) = lam)),
% 0.21/0.44 inference(rectify,[],[f2])).
% 0.21/0.44 thf(f2,axiom,(
% 0.21/0.44 ((^[X0 : $i, X1 : $i, X7 : $i > $i] : (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : (((X7 @ X3) = X4))))) = lam)),
% 0.21/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam)).
% 0.21/0.44 thf(f22,plain,(
% 0.21/0.44 (funcGraphProp2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))),
% 0.21/0.44 inference(cnf_transformation,[],[f15])).
% 0.21/0.44 thf(f15,plain,(
% 0.21/0.44 (funcGraphProp2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4))))))))))))))))),
% 0.21/0.44 inference(fool_elimination,[],[f14])).
% 0.21/0.44 thf(f14,plain,(
% 0.21/0.44 (! [X0,X1,X2] : ((func @ X1 @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => ! [X4] : ((in @ X4 @ X2) => ((in @ (kpair @ X3 @ X4) @ X0) => ((ap @ X1 @ X2 @ X0 @ X3) = X4))))) = funcGraphProp2)),
% 0.21/0.44 inference(rectify,[],[f4])).
% 0.21/0.44 thf(f4,axiom,(
% 0.21/0.44 (! [X7,X0,X1] : ((func @ X0 @ X1 @ X7) => ! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X7) => ((ap @ X0 @ X1 @ X7 @ X3) = X4))))) = funcGraphProp2)),
% 0.21/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2)).
% 0.21/0.44 thf(f23,plain,(
% 0.21/0.44 (lamp = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))),
% 0.21/0.44 inference(definition_unfolding,[],[f20,f21])).
% 0.21/0.44 thf(f20,plain,(
% 0.21/0.44 (lamp = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (lam @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))),
% 0.21/0.44 inference(cnf_transformation,[],[f11])).
% 0.21/0.44 thf(f11,plain,(
% 0.21/0.44 (lamp = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (lam @ Y1 @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3))))))))))))),
% 0.21/0.44 inference(fool_elimination,[],[f10])).
% 0.21/0.44 thf(f10,plain,(
% 0.21/0.44 (lamp = ! [X0,X1,X2 : $i > $i] : (! [X3] : ((in @ X3 @ X1) => (in @ (X2 @ X3) @ X0)) => (func @ X1 @ X0 @ (lam @ X1 @ X0 @ (^[X4 : $i] : (X2 @ X4))))))),
% 0.21/0.44 inference(rectify,[],[f3])).
% 0.21/0.44 thf(f3,axiom,(
% 0.21/0.44 (lamp = ! [X1,X0,X7 : $i > $i] : (! [X3] : ((in @ X3 @ X0) => (in @ (X7 @ X3) @ X1)) => (func @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X3 : $i] : (X7 @ X3))))))),
% 0.21/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamp)).
% 0.21/0.44 thf(f19,plain,(
% 0.21/0.44 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6))))))))))))))))))))),
% 0.21/0.44 inference(cnf_transformation,[],[f17])).
% 0.21/0.44 thf(f17,plain,(
% 0.21/0.44 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6))))))))))))))))))))),
% 0.21/0.45 inference(fool_elimination,[],[f16])).
% 0.21/0.45 thf(f16,plain,(
% 0.21/0.45 (! [X0 : $i > $i > $o,X1,X2,X3] : ((in @ X3 @ X2) => ! [X4] : ((in @ X4 @ X1) => ((X0 @ X3 @ X4) => (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X2 @ X1 @ (^[X5 : $i, X6 : $i] : (X0 @ X5 @ X6))))))) = dpsetconstrI)),
% 0.21/0.45 inference(rectify,[],[f1])).
% 0.21/0.45 thf(f1,axiom,(
% 0.21/0.45 (! [X2 : $i > $i > $o,X1,X0,X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X1) => ((X2 @ X3 @ X4) => (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : (X2 @ X5 @ X6))))))) = dpsetconstrI)),
% 0.21/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI)).
% 0.21/0.45 thf(f18,plain,(
% 0.21/0.45 ($true = (~ (dpsetconstrI => (lamp => (funcGraphProp2 => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y2 @ (lam @ Y1 @ Y2 @ (^[Y4 : $i]: (Y0 @ Y4))) @ Y3) = (Y0 @ Y3)))))))))))))))))),
% 0.21/0.45 inference(cnf_transformation,[],[f13])).
% 0.21/0.45 thf(f13,plain,(
% 0.21/0.45 ($true = (~ (dpsetconstrI => (lamp => (funcGraphProp2 => (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ap @ Y1 @ Y2 @ (lam @ Y1 @ Y2 @ (^[Y4 : $i]: (Y0 @ Y4))) @ Y3) = (Y0 @ Y3)))))))))))))))))),
% 0.21/0.45 inference(fool_elimination,[],[f12])).
% 0.21/0.45 thf(f12,plain,(
% 0.21/0.45 ~(dpsetconstrI => (lamp => (funcGraphProp2 => ! [X0,X1,X2 : $i > $i] : (! [X3] : ((in @ X3 @ X1) => (in @ (X2 @ X3) @ X0)) => ! [X4] : ((in @ X4 @ X1) => ((ap @ X1 @ X0 @ (lam @ X1 @ X0 @ (^[X5 : $i] : (X2 @ X5))) @ X4) = (X2 @ X4)))))))),
% 0.21/0.45 inference(rectify,[],[f6])).
% 0.21/0.45 thf(f6,negated_conjecture,(
% 0.21/0.45 ~(dpsetconstrI => (lamp => (funcGraphProp2 => ! [X1,X0,X7 : $i > $i] : (! [X3] : ((in @ X3 @ X0) => (in @ (X7 @ X3) @ X1)) => ! [X3] : ((in @ X3 @ X0) => ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : (X7 @ X4))) @ X3) = (X7 @ X3)))))))),
% 0.21/0.45 inference(negated_conjecture,[],[f5])).
% 0.21/0.45 thf(f5,conjecture,(
% 0.21/0.45 dpsetconstrI => (lamp => (funcGraphProp2 => ! [X1,X0,X7 : $i > $i] : (! [X3] : ((in @ X3 @ X0) => (in @ (X7 @ X3) @ X1)) => ! [X3] : ((in @ X3 @ X0) => ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : (X7 @ X4))) @ X3) = (X7 @ X3))))))),
% 0.21/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta1)).
% 0.21/0.45 thf(f155,plain,(
% 0.21/0.45 (((in @ (kpair @ sK5 @ (sK2 @ sK5)) @ (dpsetconstr @ sK3 @ sK4 @ (^[Y0 : $i]: (= @ (sK2 @ Y0))))) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y0 : $i]: (= @ (sK2 @ Y0)))) @ sK5) = (sK2 @ sK5))) = $true)),
% 0.21/0.45 inference(boolean_simplification,[],[f153])).
% 0.21/0.45 thf(f153,plain,(
% 0.21/0.45 ($true = ($true => ((in @ (kpair @ sK5 @ (sK2 @ sK5)) @ (dpsetconstr @ sK3 @ sK4 @ (^[Y0 : $i]: (= @ (sK2 @ Y0))))) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y0 : $i]: (= @ (sK2 @ Y0)))) @ sK5) = (sK2 @ sK5)))))),
% 0.21/0.45 inference(superposition,[],[f150,f94])).
% 0.21/0.45 thf(f94,plain,(
% 0.21/0.45 ($true = (in @ (sK2 @ sK5) @ sK4))),
% 0.21/0.45 inference(boolean_simplification,[],[f91])).
% 0.21/0.45 thf(f91,plain,(
% 0.21/0.45 (($true => (in @ (sK2 @ sK5) @ sK4)) = $true)),
% 0.21/0.45 inference(superposition,[],[f81,f86])).
% 0.21/0.45 thf(f86,plain,(
% 0.21/0.45 ($true = (in @ sK5 @ sK3))),
% 0.21/0.45 inference(binary_proxy_clausification,[],[f83])).
% 0.21/0.45 thf(f81,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK3) => (in @ (sK2 @ X1) @ sK4)))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f78])).
% 0.21/0.45 thf(f78,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK3) => (in @ (sK2 @ Y0) @ sK4))) @ X1))) )),
% 0.21/0.45 inference(pi_clausification,[],[f75])).
% 0.21/0.45 thf(f150,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK4) => ((in @ (kpair @ sK5 @ X1) @ (dpsetconstr @ sK3 @ sK4 @ (^[Y0 : $i]: (= @ (sK2 @ Y0))))) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y0 : $i]: (= @ (sK2 @ Y0)))) @ sK5) = X1))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f147])).
% 0.21/0.45 thf(f147,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ sK4 @ (^[Y1 : $i]: (= @ (sK2 @ Y1))))) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y1 : $i]: (= @ (sK2 @ Y1)))) @ sK5) = Y0)))) @ X1))) )),
% 0.21/0.45 inference(pi_clausification,[],[f143])).
% 0.21/0.45 thf(f143,plain,(
% 0.21/0.45 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ sK4 @ (^[Y1 : $i]: (= @ (sK2 @ Y1))))) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y1 : $i]: (= @ (sK2 @ Y1)))) @ sK5) = Y0))))) = $true)),
% 0.21/0.45 inference(boolean_simplification,[],[f142])).
% 0.21/0.45 thf(f142,plain,(
% 0.21/0.45 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ sK4 @ (^[Y1 : $i]: (= @ (sK2 @ Y1))))) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y1 : $i]: (= @ (sK2 @ Y1)))) @ sK5) = Y0)))))))),
% 0.21/0.45 inference(superposition,[],[f136,f86])).
% 0.21/0.45 thf(f136,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) => ((in @ (kpair @ X1 @ Y0) @ (dpsetconstr @ sK3 @ sK4 @ (^[Y1 : $i]: (= @ (sK2 @ Y1))))) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y1 : $i]: (= @ (sK2 @ Y1)))) @ X1) = Y0)))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f134])).
% 0.21/0.45 thf(f134,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ (dpsetconstr @ sK3 @ sK4 @ (^[Y2 : $i]: (= @ (sK2 @ Y2))))) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y2 : $i]: (= @ (sK2 @ Y2)))) @ Y0) = Y1))))))) @ X1))) )),
% 0.21/0.45 inference(pi_clausification,[],[f102])).
% 0.21/0.45 thf(f102,plain,(
% 0.21/0.45 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ (dpsetconstr @ sK3 @ sK4 @ (^[Y2 : $i]: (= @ (sK2 @ Y2))))) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y2 : $i]: (= @ (sK2 @ Y2)))) @ Y0) = Y1)))))))))),
% 0.21/0.45 inference(boolean_simplification,[],[f101])).
% 0.21/0.45 thf(f101,plain,(
% 0.21/0.45 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) => ((in @ (kpair @ Y0 @ Y1) @ (dpsetconstr @ sK3 @ sK4 @ (^[Y2 : $i]: (= @ (sK2 @ Y2))))) => ((ap @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y2 : $i]: (= @ (sK2 @ Y2)))) @ Y0) = Y1))))))))))),
% 0.21/0.45 inference(superposition,[],[f70,f80])).
% 0.21/0.45 thf(f80,plain,(
% 0.21/0.45 ($true = (func @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y0 : $i]: (= @ (sK2 @ Y0))))))),
% 0.21/0.45 inference(boolean_simplification,[],[f79])).
% 0.21/0.45 thf(f79,plain,(
% 0.21/0.45 ($true = ($true => (func @ sK3 @ sK4 @ (dpsetconstr @ sK3 @ sK4 @ (^[Y0 : $i]: (= @ (sK2 @ Y0)))))))),
% 0.21/0.45 inference(superposition,[],[f55,f75])).
% 0.21/0.45 thf(f55,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i > $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (X1 @ Y0) @ X3)))) => (func @ X2 @ X3 @ (dpsetconstr @ X2 @ X3 @ (^[Y0 : $i]: (= @ (X1 @ Y0)))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f54])).
% 0.21/0.45 thf(f54,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i > $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (X1 @ Y1) @ Y0)))) => (func @ X2 @ Y0 @ (dpsetconstr @ X2 @ Y0 @ (^[Y1 : $i]: (= @ (X1 @ Y1))))))) @ X3) = $true)) )),
% 0.21/0.45 inference(pi_clausification,[],[f53])).
% 0.21/0.45 thf(f53,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i > $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (X1 @ Y1) @ Y0)))) => (func @ X2 @ Y0 @ (dpsetconstr @ X2 @ Y0 @ (^[Y1 : $i]: (= @ (X1 @ Y1)))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f52])).
% 0.21/0.45 thf(f52,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i > $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (X1 @ Y2) @ Y1)))) => (func @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y2 : $i]: (= @ (X1 @ Y2))))))))) @ X2))) )),
% 0.21/0.45 inference(pi_clausification,[],[f51])).
% 0.21/0.45 thf(f51,plain,(
% 0.21/0.45 ( ! [X1 : $i > $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (X1 @ Y2) @ Y1)))) => (func @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y2 : $i]: (= @ (X1 @ Y2)))))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f50])).
% 0.21/0.45 thf(f50,plain,(
% 0.21/0.45 ( ! [X1 : $i > $i] : (($true = ((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3))))))))))) @ X1))) )),
% 0.21/0.45 inference(pi_clausification,[],[f45])).
% 0.21/0.45 thf(f45,plain,(
% 0.21/0.45 ($true = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (Y0 @ Y3) @ Y2)))) => (func @ Y1 @ Y2 @ (dpsetconstr @ Y1 @ Y2 @ (^[Y3 : $i]: (= @ (Y0 @ Y3)))))))))))))),
% 0.21/0.45 inference(binary_proxy_clausification,[],[f29])).
% 0.21/0.45 thf(f70,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((func @ X2 @ X1 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ (kpair @ Y0 @ Y1) @ X3) => ((ap @ X2 @ X1 @ X3 @ Y0) = Y1))))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f69])).
% 0.21/0.45 thf(f69,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((func @ X2 @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => ((ap @ X2 @ X1 @ Y0 @ Y1) = Y2)))))))))) @ X3))) )),
% 0.21/0.45 inference(pi_clausification,[],[f66])).
% 0.21/0.45 thf(f66,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((func @ X2 @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ (kpair @ Y1 @ Y2) @ Y0) => ((ap @ X2 @ X1 @ Y0 @ Y1) = Y2))))))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f65])).
% 0.21/0.45 thf(f65,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ Y0 @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => ((ap @ Y0 @ X1 @ Y1 @ Y2) = Y3)))))))))))) @ X2))) )),
% 0.21/0.45 inference(pi_clausification,[],[f62])).
% 0.21/0.45 thf(f62,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((func @ Y0 @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => ((in @ (kpair @ Y2 @ Y3) @ Y1) => ((ap @ Y0 @ X1 @ Y1 @ Y2) = Y3))))))))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f61])).
% 0.21/0.45 thf(f61,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y2) => ((ap @ Y1 @ Y0 @ Y2 @ Y3) = Y4)))))))))))))) @ X1))) )),
% 0.21/0.45 inference(pi_clausification,[],[f58])).
% 0.21/0.45 thf(f114,plain,(
% 0.21/0.45 ( ! [X0 : $i > $i > $o] : (($true = ((X0 @ sK5 @ (sK2 @ sK5)) => (in @ (kpair @ sK5 @ (sK2 @ sK5)) @ (dpsetconstr @ sK3 @ sK4 @ X0))))) )),
% 0.21/0.45 inference(boolean_simplification,[],[f111])).
% 0.21/0.45 thf(f111,plain,(
% 0.21/0.45 ( ! [X0 : $i > $i > $o] : (($true = ($true => ((X0 @ sK5 @ (sK2 @ sK5)) => (in @ (kpair @ sK5 @ (sK2 @ sK5)) @ (dpsetconstr @ sK3 @ sK4 @ X0)))))) )),
% 0.21/0.45 inference(superposition,[],[f107,f94])).
% 0.21/0.45 thf(f107,plain,(
% 0.21/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i > $i > $o] : (($true = ((in @ X2 @ X0) => ((X1 @ sK5 @ X2) => (in @ (kpair @ sK5 @ X2) @ (dpsetconstr @ sK3 @ X0 @ X1)))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f104])).
% 0.21/0.45 thf(f104,plain,(
% 0.21/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X0) => ((X1 @ sK5 @ Y0) => (in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ X0 @ X1))))) @ X2))) )),
% 0.21/0.45 inference(pi_clausification,[],[f93])).
% 0.21/0.45 thf(f93,plain,(
% 0.21/0.45 ( ! [X0 : $i,X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X0) => ((X1 @ sK5 @ Y0) => (in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ X0 @ X1)))))))) )),
% 0.21/0.45 inference(boolean_simplification,[],[f92])).
% 0.21/0.45 thf(f92,plain,(
% 0.21/0.45 ( ! [X0 : $i,X1 : $i > $i > $o] : ((($true => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X0) => ((X1 @ sK5 @ Y0) => (in @ (kpair @ sK5 @ Y0) @ (dpsetconstr @ sK3 @ X0 @ X1))))))) = $true)) )),
% 0.21/0.45 inference(superposition,[],[f42,f86])).
% 0.21/0.45 thf(f42,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = ((in @ X1 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => ((X4 @ X1 @ Y0) => (in @ (kpair @ X1 @ Y0) @ (dpsetconstr @ X2 @ X3 @ X4))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f41])).
% 0.21/0.45 thf(f41,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: ((in @ X1 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => ((Y0 @ X1 @ Y1) => (in @ (kpair @ X1 @ Y1) @ (dpsetconstr @ X2 @ X3 @ Y0)))))))) @ X4))) )),
% 0.21/0.45 inference(pi_clausification,[],[f40])).
% 0.21/0.45 thf(f40,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((in @ X1 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => ((Y0 @ X1 @ Y1) => (in @ (kpair @ X1 @ Y1) @ (dpsetconstr @ X2 @ X3 @ Y0))))))))) = $true)) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f39])).
% 0.21/0.45 thf(f39,plain,(
% 0.21/0.45 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((in @ X1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ X1 @ Y2) => (in @ (kpair @ X1 @ Y2) @ (dpsetconstr @ X2 @ Y0 @ Y1)))))))))) @ X3))) )),
% 0.21/0.45 inference(pi_clausification,[],[f38])).
% 0.21/0.45 thf(f38,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((in @ X1 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ X1 @ Y2) => (in @ (kpair @ X1 @ Y2) @ (dpsetconstr @ X2 @ Y0 @ Y1))))))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f37])).
% 0.21/0.45 thf(f37,plain,(
% 0.21/0.45 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ X1 @ Y3) => (in @ (kpair @ X1 @ Y3) @ (dpsetconstr @ Y0 @ Y1 @ Y2)))))))))))) @ X2))) )),
% 0.21/0.45 inference(pi_clausification,[],[f36])).
% 0.21/0.45 thf(f36,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ X1 @ Y3) => (in @ (kpair @ X1 @ Y3) @ (dpsetconstr @ Y0 @ Y1 @ Y2))))))))))))))) )),
% 0.21/0.45 inference(beta_eta_normalization,[],[f35])).
% 0.21/0.45 thf(f35,plain,(
% 0.21/0.45 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y3)))))))))))))) @ X1))) )),
% 0.21/0.45 inference(pi_clausification,[],[f30])).
% 0.21/0.45 thf(f30,plain,(
% 0.21/0.45 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y3))))))))))))))) = $true)),
% 0.21/0.45 inference(binary_proxy_clausification,[],[f26])).
% 0.21/0.45 % SZS output end Proof for theBenchmark
% 0.21/0.45 % (719)------------------------------
% 0.21/0.45 % (719)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (719)Termination reason: Refutation
% 0.21/0.45
% 0.21/0.45 % (719)Memory used [KB]: 6012
% 0.21/0.45 % (719)Time elapsed: 0.073 s
% 0.21/0.45 % (719)Instructions burned: 70 (million)
% 0.21/0.45 % (719)------------------------------
% 0.21/0.45 % (719)------------------------------
% 0.21/0.45 % (707)Success in time 0.076 s
% 0.21/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------