TSTP Solution File: SYO555^1 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SYO555^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n018.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 21:03:53 EDT 2024
% Result : Theorem 0.22s 0.46s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO555^1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.12 % Command : run_vampire %s %d THM
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Jun 23 06:21:54 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.36 This is a TH0_THM_EQU_NAR problem
% 0.12/0.36 Running higher-order theorem proving
% 0.12/0.36 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
% 0.22/0.38 % (6883)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)
% 0.22/0.38 % (6883)Instruction limit reached!
% 0.22/0.38 % (6883)------------------------------
% 0.22/0.38 % (6883)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (6883)Termination reason: Unknown
% 0.22/0.38 % (6883)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (6883)Memory used [KB]: 895
% 0.22/0.38 % (6883)Time elapsed: 0.003 s
% 0.22/0.38 % (6883)Instructions burned: 2 (million)
% 0.22/0.38 % (6883)------------------------------
% 0.22/0.38 % (6883)------------------------------
% 0.22/0.38 % (6885)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.39 % (6884)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)
% 0.22/0.39 % (6879)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.39 % (6882)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.39 % (6884)Refutation not found, incomplete strategy
% 0.22/0.39 % (6884)------------------------------
% 0.22/0.39 % (6884)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (6884)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.39
% 0.22/0.39
% 0.22/0.39 % (6884)Memory used [KB]: 5500
% 0.22/0.39 % (6884)Time elapsed: 0.004 s
% 0.22/0.39 % (6884)Instructions burned: 3 (million)
% 0.22/0.39 % (6884)------------------------------
% 0.22/0.39 % (6884)------------------------------
% 0.22/0.39 % (6886)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)
% 0.22/0.39 % (6882)Instruction limit reached!
% 0.22/0.39 % (6882)------------------------------
% 0.22/0.39 % (6882)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (6882)Termination reason: Unknown
% 0.22/0.39 % (6882)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (6882)Memory used [KB]: 5500
% 0.22/0.39 % (6882)Time elapsed: 0.004 s
% 0.22/0.39 % (6882)Instructions burned: 2 (million)
% 0.22/0.39 % (6882)------------------------------
% 0.22/0.39 % (6882)------------------------------
% 0.22/0.39 % (6881)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)
% 0.22/0.39 % (6886)Instruction limit reached!
% 0.22/0.39 % (6886)------------------------------
% 0.22/0.39 % (6886)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (6886)Termination reason: Unknown
% 0.22/0.39 % (6886)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (6886)Memory used [KB]: 5500
% 0.22/0.39 % (6886)Time elapsed: 0.004 s
% 0.22/0.39 % (6886)Instructions burned: 4 (million)
% 0.22/0.39 % (6886)------------------------------
% 0.22/0.39 % (6886)------------------------------
% 0.22/0.39 % (6880)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)
% 0.22/0.40 % (6885)Instruction limit reached!
% 0.22/0.40 % (6885)------------------------------
% 0.22/0.40 % (6885)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (6885)Termination reason: Unknown
% 0.22/0.40 % (6885)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (6885)Memory used [KB]: 5628
% 0.22/0.40 % (6885)Time elapsed: 0.013 s
% 0.22/0.40 % (6885)Instructions burned: 19 (million)
% 0.22/0.40 % (6885)------------------------------
% 0.22/0.40 % (6885)------------------------------
% 0.22/0.40 % (6880)Instruction limit reached!
% 0.22/0.40 % (6880)------------------------------
% 0.22/0.40 % (6880)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (6880)Termination reason: Unknown
% 0.22/0.40 % (6880)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (6880)Memory used [KB]: 5500
% 0.22/0.40 % (6880)Time elapsed: 0.006 s
% 0.22/0.40 % (6880)Instructions burned: 4 (million)
% 0.22/0.40 % (6880)------------------------------
% 0.22/0.40 % (6880)------------------------------
% 0.22/0.41 % (6888)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)
% 0.22/0.41 % (6889)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)
% 0.22/0.41 % (6887)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)
% 0.22/0.41 % (6888)Refutation not found, incomplete strategy
% 0.22/0.41 % (6888)------------------------------
% 0.22/0.41 % (6888)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.41 % (6888)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.41
% 0.22/0.41
% 0.22/0.41 % (6888)Memory used [KB]: 5500
% 0.22/0.41 % (6888)Time elapsed: 0.004 s
% 0.22/0.41 % (6888)Instructions burned: 2 (million)
% 0.22/0.41 % (6888)------------------------------
% 0.22/0.41 % (6888)------------------------------
% 0.22/0.41 % (6889)Refutation not found, incomplete strategy
% 0.22/0.41 % (6889)------------------------------
% 0.22/0.41 % (6889)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.41 % (6889)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.41
% 0.22/0.41
% 0.22/0.41 % (6889)Memory used [KB]: 5500
% 0.22/0.41 % (6889)Time elapsed: 0.003 s
% 0.22/0.41 % (6889)Instructions burned: 2 (million)
% 0.22/0.41 % (6889)------------------------------
% 0.22/0.41 % (6889)------------------------------
% 0.22/0.41 % (6881)Instruction limit reached!
% 0.22/0.41 % (6881)------------------------------
% 0.22/0.41 % (6881)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.41 % (6881)Termination reason: Unknown
% 0.22/0.41 % (6881)Termination phase: Saturation
% 0.22/0.41
% 0.22/0.41 % (6881)Memory used [KB]: 5628
% 0.22/0.41 % (6881)Time elapsed: 0.019 s
% 0.22/0.41 % (6881)Instructions burned: 28 (million)
% 0.22/0.41 % (6881)------------------------------
% 0.22/0.41 % (6881)------------------------------
% 0.22/0.41 % (6891)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.41 % (6890)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)
% 0.22/0.42 % (6891)Instruction limit reached!
% 0.22/0.42 % (6891)------------------------------
% 0.22/0.42 % (6891)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.42 % (6891)Termination reason: Unknown
% 0.22/0.42 % (6891)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (6891)Memory used [KB]: 1023
% 0.22/0.42 % (6891)Time elapsed: 0.006 s
% 0.22/0.42 % (6891)Instructions burned: 9 (million)
% 0.22/0.42 % (6891)------------------------------
% 0.22/0.42 % (6891)------------------------------
% 0.22/0.42 % (6894)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)
% 0.22/0.42 % (6893)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)
% 0.22/0.42 % (6894)Instruction limit reached!
% 0.22/0.42 % (6894)------------------------------
% 0.22/0.42 % (6894)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.42 % (6894)Termination reason: Unknown
% 0.22/0.42 % (6894)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (6894)Memory used [KB]: 1023
% 0.22/0.42 % (6894)Time elapsed: 0.003 s
% 0.22/0.42 % (6894)Instructions burned: 3 (million)
% 0.22/0.42 % (6894)------------------------------
% 0.22/0.42 % (6894)------------------------------
% 0.22/0.43 % (6892)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.43 % (6893)Instruction limit reached!
% 0.22/0.43 % (6893)------------------------------
% 0.22/0.43 % (6893)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.43 % (6893)Termination reason: Unknown
% 0.22/0.43 % (6893)Termination phase: Saturation
% 0.22/0.43
% 0.22/0.43 % (6893)Memory used [KB]: 5500
% 0.22/0.43 % (6893)Time elapsed: 0.004 s
% 0.22/0.43 % (6893)Instructions burned: 4 (million)
% 0.22/0.43 % (6893)------------------------------
% 0.22/0.43 % (6893)------------------------------
% 0.22/0.43 % (6887)Instruction limit reached!
% 0.22/0.43 % (6887)------------------------------
% 0.22/0.43 % (6887)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.43 % (6887)Termination reason: Unknown
% 0.22/0.43 % (6887)Termination phase: Saturation
% 0.22/0.43
% 0.22/0.43 % (6887)Memory used [KB]: 5884
% 0.22/0.43 % (6887)Time elapsed: 0.023 s
% 0.22/0.43 % (6887)Instructions burned: 38 (million)
% 0.22/0.43 % (6887)------------------------------
% 0.22/0.43 % (6887)------------------------------
% 0.22/0.44 % (6895)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)
% 0.22/0.44 % (6890)Refutation not found, incomplete strategy
% 0.22/0.44 % (6890)------------------------------
% 0.22/0.44 % (6890)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.44 % (6890)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.44
% 0.22/0.44
% 0.22/0.44 % (6890)Memory used [KB]: 5628
% 0.22/0.44 % (6890)Time elapsed: 0.025 s
% 0.22/0.44 % (6890)Instructions burned: 34 (million)
% 0.22/0.44 % (6890)------------------------------
% 0.22/0.44 % (6890)------------------------------
% 0.22/0.44 % (6892)Instruction limit reached!
% 0.22/0.44 % (6892)------------------------------
% 0.22/0.44 % (6892)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.44 % (6892)Termination reason: Unknown
% 0.22/0.44 % (6892)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (6892)Memory used [KB]: 5628
% 0.22/0.44 % (6892)Time elapsed: 0.014 s
% 0.22/0.44 % (6892)Instructions burned: 16 (million)
% 0.22/0.44 % (6892)------------------------------
% 0.22/0.44 % (6892)------------------------------
% 0.22/0.44 % (6896)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)
% 0.22/0.44 % (6895)Instruction limit reached!
% 0.22/0.44 % (6895)------------------------------
% 0.22/0.44 % (6895)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.44 % (6895)Termination reason: Unknown
% 0.22/0.44 % (6895)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (6895)Memory used [KB]: 5500
% 0.22/0.44 % (6895)Time elapsed: 0.006 s
% 0.22/0.44 % (6895)Instructions burned: 8 (million)
% 0.22/0.44 % (6895)------------------------------
% 0.22/0.44 % (6895)------------------------------
% 0.22/0.44 % (6897)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.44 % (6896)Instruction limit reached!
% 0.22/0.44 % (6896)------------------------------
% 0.22/0.44 % (6896)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.44 % (6896)Termination reason: Unknown
% 0.22/0.44 % (6896)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (6896)Memory used [KB]: 5500
% 0.22/0.44 % (6896)Time elapsed: 0.003 s
% 0.22/0.44 % (6896)Instructions burned: 3 (million)
% 0.22/0.44 % (6896)------------------------------
% 0.22/0.44 % (6896)------------------------------
% 0.22/0.44 % (6897)Instruction limit reached!
% 0.22/0.44 % (6897)------------------------------
% 0.22/0.44 % (6897)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.44 % (6897)Termination reason: Unknown
% 0.22/0.44 % (6897)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (6897)Memory used [KB]: 5500
% 0.22/0.44 % (6897)Time elapsed: 0.004 s
% 0.22/0.44 % (6897)Instructions burned: 4 (million)
% 0.22/0.44 % (6897)------------------------------
% 0.22/0.44 % (6897)------------------------------
% 0.22/0.44 % (6898)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)
% 0.22/0.45 % (6898)First to succeed.
% 0.22/0.45 % (6900)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.45 % (6899)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.45 % (6902)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)
% 0.22/0.46 % (6898)Refutation found. Thanks to Tanya!
% 0.22/0.46 % SZS status Theorem for theBenchmark
% 0.22/0.46 % SZS output start Proof for theBenchmark
% 0.22/0.46 thf(func_def_0, type, eps1: ($i > $o) > $i).
% 0.22/0.46 thf(func_def_2, type, if1: $o > $i > $i > $i).
% 0.22/0.46 thf(func_def_3, type, eps2: ($i > $o) > $i).
% 0.22/0.46 thf(func_def_4, type, if2: $o > $i > $i > $i).
% 0.22/0.46 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 0.22/0.46 thf(f213,plain,(
% 0.22/0.46 $false),
% 0.22/0.46 inference(avatar_sat_refutation,[],[f126,f139,f175,f190,f203,f212])).
% 0.22/0.46 thf(f212,plain,(
% 0.22/0.46 ~spl0_1),
% 0.22/0.46 inference(avatar_contradiction_clause,[],[f211])).
% 0.22/0.46 thf(f211,plain,(
% 0.22/0.46 $false | ~spl0_1),
% 0.22/0.46 inference(equality_resolution,[],[f121])).
% 0.22/0.46 thf(f121,plain,(
% 0.22/0.46 ( ! [X0 : $i] : ((sK3 != X0)) ) | ~spl0_1),
% 0.22/0.46 inference(avatar_component_clause,[],[f120])).
% 0.22/0.46 thf(f120,plain,(
% 0.22/0.46 spl0_1 <=> ! [X0] : (sK3 != X0)),
% 0.22/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.22/0.46 thf(f203,plain,(
% 0.22/0.46 ~spl0_10),
% 0.22/0.46 inference(avatar_contradiction_clause,[],[f202])).
% 0.22/0.46 thf(f202,plain,(
% 0.22/0.46 $false | ~spl0_10),
% 0.22/0.46 inference(equality_resolution,[],[f174])).
% 0.22/0.46 thf(f174,plain,(
% 0.22/0.46 ( ! [X0 : $i] : ((sK4 != X0)) ) | ~spl0_10),
% 0.22/0.46 inference(avatar_component_clause,[],[f173])).
% 0.22/0.46 thf(f173,plain,(
% 0.22/0.46 spl0_10 <=> ! [X0] : (sK4 != X0)),
% 0.22/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])).
% 0.22/0.46 thf(f190,plain,(
% 0.22/0.46 spl0_10 | spl0_9),
% 0.22/0.46 inference(avatar_split_clause,[],[f189,f169,f173])).
% 0.22/0.46 thf(f169,plain,(
% 0.22/0.46 spl0_9 <=> ((if1 @ $false @ sK3 @ sK4) = sK4)),
% 0.22/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 0.22/0.46 thf(f189,plain,(
% 0.22/0.46 ( ! [X0 : $i] : ((sK4 != X0)) ) | spl0_9),
% 0.22/0.46 inference(trivial_inequality_removal,[],[f187])).
% 0.22/0.46 thf(f187,plain,(
% 0.22/0.46 ( ! [X0 : $i] : ((sK4 != sK4) | (sK4 != X0) | ($true = $false)) ) | spl0_9),
% 0.22/0.46 inference(superposition,[],[f171,f69])).
% 0.22/0.46 thf(f69,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((if1 @ X0 @ X1 @ X2) = X2) | ($true = X0) | (X2 != X3)) )),
% 0.22/0.46 inference(equality_proxy_clausification,[],[f68])).
% 0.22/0.46 thf(f68,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($true = X0) | ((if1 @ X0 @ X1 @ X2) = X2) | ($false = (X2 = X3))) )),
% 0.22/0.46 inference(duplicate_literal_removal,[],[f67])).
% 0.22/0.46 thf(f67,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($false = (X2 = X3)) | ($true = X0) | ($true = X0) | ((if1 @ X0 @ X1 @ X2) = X2)) )),
% 0.22/0.46 inference(not_proxy_clausification,[],[f66])).
% 0.22/0.46 thf(f66,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((~ X0) = $false) | ($true = X0) | ($false = (X2 = X3)) | ((if1 @ X0 @ X1 @ X2) = X2)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f65])).
% 0.22/0.46 thf(f65,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($false = ((X2 = X3) & (~ X0))) | ($true = X0) | ((if1 @ X0 @ X1 @ X2) = X2)) )),
% 0.22/0.46 inference(equality_proxy_clausification,[],[f64])).
% 0.22/0.46 thf(f64,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($true = X0) | ((X2 = (if1 @ X0 @ X1 @ X2)) = $true) | ($false = ((X2 = X3) & (~ X0)))) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f62])).
% 0.22/0.46 thf(f62,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($true = X0) | (((X2 = (if1 @ X0 @ X1 @ X2)) & (~ X0)) = $true) | ($false = ((X2 = X3) & (~ X0)))) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f42])).
% 0.22/0.46 thf(f42,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($true = (X0 & (X1 = (if1 @ X0 @ X1 @ X2)))) | ($false = ((X2 = X3) & (~ X0))) | (((X2 = (if1 @ X0 @ X1 @ X2)) & (~ X0)) = $true)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f41])).
% 0.22/0.46 thf(f41,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((X0 & (X1 = X3)) | ((X2 = X3) & (~ X0))) != $true) | ($true = (X0 & (X1 = (if1 @ X0 @ X1 @ X2)))) | (((X2 = (if1 @ X0 @ X1 @ X2)) & (~ X0)) = $true)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f40])).
% 0.22/0.46 thf(f40,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($true = ((X0 & (X1 = (if1 @ X0 @ X1 @ X2))) | ((X2 = (if1 @ X0 @ X1 @ X2)) & (~ X0)))) | (((X0 & (X1 = X3)) | ((X2 = X3) & (~ X0))) != $true)) )),
% 0.22/0.46 inference(beta_eta_normalization,[],[f39])).
% 0.22/0.46 thf(f39,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((X2 = Y0) & (~ X0)))) @ (if1 @ X0 @ X1 @ X2)) = $true) | ($true != ((^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((X2 = Y0) & (~ X0)))) @ X3))) )),
% 0.22/0.46 inference(superposition,[],[f20,f36])).
% 0.22/0.46 thf(f36,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X1 : $o] : (((eps1 @ (^[Y0 : $i]: ((X1 & (X2 = Y0)) | ((X3 = Y0) & (~ X1))))) = (if1 @ X1 @ X2 @ X3))) )),
% 0.22/0.46 inference(beta_eta_normalization,[],[f35])).
% 0.22/0.46 thf(f35,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X1 : $o] : ((((^[Y0 : $i]: (eps1 @ (^[Y1 : $i]: ((X1 & (X2 = Y1)) | ((Y0 = Y1) & (~ X1)))))) @ X3) = (if1 @ X1 @ X2 @ X3))) )),
% 0.22/0.46 inference(argument_congruence,[],[f32])).
% 0.22/0.46 thf(f32,plain,(
% 0.22/0.46 ( ! [X2 : $i,X1 : $o] : (((if1 @ X1 @ X2) = (^[Y0 : $i]: (eps1 @ (^[Y1 : $i]: ((X1 & (X2 = Y1)) | ((Y0 = Y1) & (~ X1)))))))) )),
% 0.22/0.46 inference(beta_eta_normalization,[],[f31])).
% 0.22/0.46 thf(f31,plain,(
% 0.22/0.46 ( ! [X2 : $i,X1 : $o] : (((if1 @ X1 @ X2) = ((^[Y0 : $i]: ((^[Y1 : $i]: (eps1 @ (^[Y2 : $i]: ((X1 & (Y0 = Y2)) | ((Y1 = Y2) & (~ X1)))))))) @ X2))) )),
% 0.22/0.46 inference(argument_congruence,[],[f26])).
% 0.22/0.46 thf(f26,plain,(
% 0.22/0.46 ( ! [X1 : $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: (eps1 @ (^[Y2 : $i]: ((X1 & (Y0 = Y2)) | ((Y1 = Y2) & (~ X1)))))))) = (if1 @ X1))) )),
% 0.22/0.46 inference(beta_eta_normalization,[],[f25])).
% 0.22/0.46 thf(f25,plain,(
% 0.22/0.46 ( ! [X1 : $o] : ((((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps1 @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((Y2 = Y3) & (~ Y0)))))))))) @ X1) = (if1 @ X1))) )),
% 0.22/0.46 inference(argument_congruence,[],[f19])).
% 0.22/0.46 thf(f19,plain,(
% 0.22/0.46 (if1 = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps1 @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((Y2 = Y3) & (~ Y0)))))))))))),
% 0.22/0.46 inference(cnf_transformation,[],[f9])).
% 0.22/0.46 thf(f9,plain,(
% 0.22/0.46 (if1 = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps1 @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((Y2 = Y3) & (~ Y0)))))))))))),
% 0.22/0.46 inference(fool_elimination,[],[f8])).
% 0.22/0.46 thf(f8,plain,(
% 0.22/0.46 (if1 = (^[X0 : $o, X1 : $i, X2 : $i] : (eps1 @ (^[X3 : $i] : ((~X0 & (X2 = X3)) | ((X1 = X3) & X0))))))),
% 0.22/0.46 inference(rectify,[],[f2])).
% 0.22/0.46 thf(f2,axiom,(
% 0.22/0.46 (if1 = (^[X2 : $o, X1 : $i, X3 : $i] : (eps1 @ (^[X4 : $i] : ((~X2 & (X3 = X4)) | ((X1 = X4) & X2))))))),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',if1d)).
% 0.22/0.46 thf(f20,plain,(
% 0.22/0.46 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ (eps1 @ X0)) = $true) | ((X0 @ X1) != $true)) )),
% 0.22/0.46 inference(cnf_transformation,[],[f17])).
% 0.22/0.46 thf(f17,plain,(
% 0.22/0.46 ! [X0 : $i > $o] : (((X0 @ (eps1 @ X0)) = $true) | ! [X1] : ((X0 @ X1) != $true))),
% 0.22/0.46 inference(ennf_transformation,[],[f15])).
% 0.22/0.46 thf(f15,plain,(
% 0.22/0.46 ! [X0 : $i > $o] : (? [X1] : ((X0 @ X1) = $true) => ((X0 @ (eps1 @ X0)) = $true))),
% 0.22/0.46 inference(fool_elimination,[],[f14])).
% 0.22/0.46 thf(f14,plain,(
% 0.22/0.46 ! [X0 : $i > $o] : (? [X1] : (X0 @ X1) => (X0 @ (eps1 @ X0)))),
% 0.22/0.46 inference(rectify,[],[f1])).
% 0.22/0.46 thf(f1,axiom,(
% 0.22/0.46 ! [X0 : $i > $o] : (? [X1] : (X0 @ X1) => (X0 @ (eps1 @ X0)))),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceax1)).
% 0.22/0.46 thf(f171,plain,(
% 0.22/0.46 ((if1 @ $false @ sK3 @ sK4) != sK4) | spl0_9),
% 0.22/0.46 inference(avatar_component_clause,[],[f169])).
% 0.22/0.46 thf(f175,plain,(
% 0.22/0.46 ~spl0_9 | spl0_10 | spl0_4),
% 0.22/0.46 inference(avatar_split_clause,[],[f167,f136,f173,f169])).
% 0.22/0.46 thf(f136,plain,(
% 0.22/0.46 spl0_4 <=> ((if2 @ $false @ sK3 @ sK4) = (if1 @ $false @ sK3 @ sK4))),
% 0.22/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.22/0.46 thf(f167,plain,(
% 0.22/0.46 ( ! [X0 : $i] : ((sK4 != X0) | ((if1 @ $false @ sK3 @ sK4) != sK4)) ) | spl0_4),
% 0.22/0.46 inference(trivial_inequality_removal,[],[f165])).
% 0.22/0.46 thf(f165,plain,(
% 0.22/0.46 ( ! [X0 : $i] : (($true = $false) | ((if1 @ $false @ sK3 @ sK4) != sK4) | (sK4 != X0)) ) | spl0_4),
% 0.22/0.46 inference(superposition,[],[f138,f109])).
% 0.22/0.46 thf(f109,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((if2 @ X0 @ X1 @ X2) = X2) | ($true = X0) | (X2 != X3)) )),
% 0.22/0.46 inference(equality_proxy_clausification,[],[f106])).
% 0.22/0.46 thf(f106,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((X2 != X3) | ($true = X0) | ((X2 = (if2 @ X0 @ X1 @ X2)) = $true)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f105])).
% 0.22/0.46 thf(f105,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((X2 != X3) | (((~ X0) & (X2 = (if2 @ X0 @ X1 @ X2))) = $true) | ($true = X0)) )),
% 0.22/0.46 inference(duplicate_literal_removal,[],[f104])).
% 0.22/0.46 thf(f104,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($true = X0) | (((~ X0) & (X2 = (if2 @ X0 @ X1 @ X2))) = $true) | ($true = X0) | (X2 != X3)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f102])).
% 0.22/0.46 thf(f102,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((X2 != X3) | ($true = X0) | ((X0 & (X1 = (if2 @ X0 @ X1 @ X2))) = $true) | (((~ X0) & (X2 = (if2 @ X0 @ X1 @ X2))) = $true)) )),
% 0.22/0.46 inference(not_proxy_clausification,[],[f101])).
% 0.22/0.46 thf(f101,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((~ X0) = $false) | (X2 != X3) | (((~ X0) & (X2 = (if2 @ X0 @ X1 @ X2))) = $true) | ((X0 & (X1 = (if2 @ X0 @ X1 @ X2))) = $true)) )),
% 0.22/0.46 inference(equality_proxy_clausification,[],[f100])).
% 0.22/0.46 thf(f100,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($false = (X2 = X3)) | (((~ X0) & (X2 = (if2 @ X0 @ X1 @ X2))) = $true) | ((~ X0) = $false) | ((X0 & (X1 = (if2 @ X0 @ X1 @ X2))) = $true)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f99])).
% 0.22/0.46 thf(f99,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((~ X0) & (X2 = X3)) = $false) | (((~ X0) & (X2 = (if2 @ X0 @ X1 @ X2))) = $true) | ((X0 & (X1 = (if2 @ X0 @ X1 @ X2))) = $true)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f84])).
% 0.22/0.46 thf(f84,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((X0 & (X1 = (if2 @ X0 @ X1 @ X2))) | ((~ X0) & (X2 = (if2 @ X0 @ X1 @ X2)))) = $true) | (((~ X0) & (X2 = X3)) = $false)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f83])).
% 0.22/0.46 thf(f83,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((X0 & (X1 = X3)) | ((~ X0) & (X2 = X3))) != $true) | (((X0 & (X1 = (if2 @ X0 @ X1 @ X2))) | ((~ X0) & (X2 = (if2 @ X0 @ X1 @ X2)))) = $true)) )),
% 0.22/0.46 inference(beta_eta_normalization,[],[f82])).
% 0.22/0.46 thf(f82,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X2 = Y0)))) @ (if2 @ X0 @ X1 @ X2)) = $true) | (((^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X2 = Y0)))) @ X3) != $true)) )),
% 0.22/0.46 inference(superposition,[],[f21,f38])).
% 0.22/0.46 thf(f38,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X1 : $o] : (((if2 @ X1 @ X2 @ X3) = (eps2 @ (^[Y0 : $i]: ((X1 & (X2 = Y0)) | ((~ X1) & (X3 = Y0))))))) )),
% 0.22/0.46 inference(beta_eta_normalization,[],[f37])).
% 0.22/0.46 thf(f37,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X1 : $o] : (((if2 @ X1 @ X2 @ X3) = ((^[Y0 : $i]: (eps2 @ (^[Y1 : $i]: ((X1 & (X2 = Y1)) | ((~ X1) & (Y0 = Y1)))))) @ X3))) )),
% 0.22/0.46 inference(argument_congruence,[],[f34])).
% 0.22/0.46 thf(f34,plain,(
% 0.22/0.46 ( ! [X2 : $i,X1 : $o] : (((if2 @ X1 @ X2) = (^[Y0 : $i]: (eps2 @ (^[Y1 : $i]: ((X1 & (X2 = Y1)) | ((~ X1) & (Y0 = Y1)))))))) )),
% 0.22/0.46 inference(beta_eta_normalization,[],[f33])).
% 0.22/0.46 thf(f33,plain,(
% 0.22/0.46 ( ! [X2 : $i,X1 : $o] : (((if2 @ X1 @ X2) = ((^[Y0 : $i]: ((^[Y1 : $i]: (eps2 @ (^[Y2 : $i]: ((X1 & (Y0 = Y2)) | ((~ X1) & (Y1 = Y2)))))))) @ X2))) )),
% 0.22/0.46 inference(argument_congruence,[],[f29])).
% 0.22/0.46 thf(f29,plain,(
% 0.22/0.46 ( ! [X1 : $o] : (((if2 @ X1) = (^[Y0 : $i]: ((^[Y1 : $i]: (eps2 @ (^[Y2 : $i]: ((X1 & (Y0 = Y2)) | ((~ X1) & (Y1 = Y2)))))))))) )),
% 0.22/0.46 inference(beta_eta_normalization,[],[f28])).
% 0.22/0.46 thf(f28,plain,(
% 0.22/0.46 ( ! [X1 : $o] : ((((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps2 @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))) @ X1) = (if2 @ X1))) )),
% 0.22/0.46 inference(argument_congruence,[],[f22])).
% 0.22/0.46 thf(f22,plain,(
% 0.22/0.46 (if2 = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps2 @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))))),
% 0.22/0.46 inference(cnf_transformation,[],[f11])).
% 0.22/0.46 thf(f11,plain,(
% 0.22/0.46 (if2 = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps2 @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))))),
% 0.22/0.46 inference(fool_elimination,[],[f10])).
% 0.22/0.46 thf(f10,plain,(
% 0.22/0.46 ((^[X0 : $o, X1 : $i, X2 : $i] : (eps2 @ (^[X3 : $i] : (((X2 = X3) & ~X0) | ((X1 = X3) & X0))))) = if2)),
% 0.22/0.46 inference(rectify,[],[f4])).
% 0.22/0.46 thf(f4,axiom,(
% 0.22/0.46 ((^[X2 : $o, X1 : $i, X3 : $i] : (eps2 @ (^[X4 : $i] : (((X3 = X4) & ~X2) | ((X1 = X4) & X2))))) = if2)),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',if2d)).
% 0.22/0.46 thf(f21,plain,(
% 0.22/0.46 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ (eps2 @ X0)) = $true) | ((X0 @ X1) != $true)) )),
% 0.22/0.46 inference(cnf_transformation,[],[f18])).
% 0.22/0.46 thf(f18,plain,(
% 0.22/0.46 ! [X0 : $i > $o] : (((X0 @ (eps2 @ X0)) = $true) | ! [X1] : ((X0 @ X1) != $true))),
% 0.22/0.46 inference(ennf_transformation,[],[f13])).
% 0.22/0.46 thf(f13,plain,(
% 0.22/0.46 ! [X0 : $i > $o] : (? [X1] : ((X0 @ X1) = $true) => ((X0 @ (eps2 @ X0)) = $true))),
% 0.22/0.46 inference(fool_elimination,[],[f12])).
% 0.22/0.46 thf(f12,plain,(
% 0.22/0.46 ! [X0 : $i > $o] : (? [X1] : (X0 @ X1) => (X0 @ (eps2 @ X0)))),
% 0.22/0.46 inference(rectify,[],[f3])).
% 0.22/0.46 thf(f3,axiom,(
% 0.22/0.46 ! [X0 : $i > $o] : (? [X1] : (X0 @ X1) => (X0 @ (eps2 @ X0)))),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceax2)).
% 0.22/0.46 thf(f138,plain,(
% 0.22/0.46 ((if2 @ $false @ sK3 @ sK4) != (if1 @ $false @ sK3 @ sK4)) | spl0_4),
% 0.22/0.46 inference(avatar_component_clause,[],[f136])).
% 0.22/0.46 thf(f139,plain,(
% 0.22/0.46 ~spl0_4 | ~spl0_2),
% 0.22/0.46 inference(avatar_split_clause,[],[f127,f123,f136])).
% 0.22/0.46 thf(f123,plain,(
% 0.22/0.46 spl0_2 <=> (sK2 = $false)),
% 0.22/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.22/0.46 thf(f127,plain,(
% 0.22/0.46 ((if2 @ $false @ sK3 @ sK4) != (if1 @ $false @ sK3 @ sK4)) | ~spl0_2),
% 0.22/0.46 inference(backward_demodulation,[],[f30,f125])).
% 0.22/0.46 thf(f125,plain,(
% 0.22/0.46 (sK2 = $false) | ~spl0_2),
% 0.22/0.46 inference(avatar_component_clause,[],[f123])).
% 0.22/0.46 thf(f30,plain,(
% 0.22/0.46 ((if1 @ sK2 @ sK3 @ sK4) != (if2 @ sK2 @ sK3 @ sK4))),
% 0.22/0.46 inference(negative_extensionality,[],[f27])).
% 0.22/0.46 thf(f27,plain,(
% 0.22/0.46 ((if1 @ sK2 @ sK3) != (if2 @ sK2 @ sK3))),
% 0.22/0.46 inference(negative_extensionality,[],[f24])).
% 0.22/0.46 thf(f24,plain,(
% 0.22/0.46 ((if1 @ sK2) != (if2 @ sK2))),
% 0.22/0.46 inference(negative_extensionality,[],[f23])).
% 0.22/0.46 thf(f23,plain,(
% 0.22/0.46 (if1 != if2)),
% 0.22/0.46 inference(cnf_transformation,[],[f16])).
% 0.22/0.46 thf(f16,plain,(
% 0.22/0.46 (if1 != if2)),
% 0.22/0.46 inference(flattening,[],[f6])).
% 0.22/0.46 thf(f6,negated_conjecture,(
% 0.22/0.46 ~(if1 = if2)),
% 0.22/0.46 inference(negated_conjecture,[],[f5])).
% 0.22/0.46 thf(f5,conjecture,(
% 0.22/0.46 (if1 = if2)),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.22/0.46 thf(f126,plain,(
% 0.22/0.46 spl0_1 | spl0_2),
% 0.22/0.46 inference(avatar_split_clause,[],[f118,f123,f120])).
% 0.22/0.46 thf(f118,plain,(
% 0.22/0.46 ( ! [X0 : $i] : ((sK3 != X0) | (sK2 = $false)) )),
% 0.22/0.46 inference(subsumption_resolution,[],[f117,f60])).
% 0.22/0.46 thf(f60,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((if1 @ X0 @ X1 @ X2) = X1) | ($false = X0) | (X1 != X3)) )),
% 0.22/0.46 inference(duplicate_literal_removal,[],[f59])).
% 0.22/0.46 thf(f59,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($false = X0) | (X1 != X3) | ((if1 @ X0 @ X1 @ X2) = X1) | ($false = X0)) )),
% 0.22/0.46 inference(not_proxy_clausification,[],[f58])).
% 0.22/0.46 thf(f58,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((X1 != X3) | ($false = X0) | ((if1 @ X0 @ X1 @ X2) = X1) | ((~ X0) = $true)) )),
% 0.22/0.46 inference(equality_proxy_clausification,[],[f56])).
% 0.22/0.46 thf(f56,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($true = (X1 = (if1 @ X0 @ X1 @ X2))) | ($false = X0) | ((~ X0) = $true) | (X1 != X3)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f55])).
% 0.22/0.46 thf(f55,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($true = (X0 & (X1 = (if1 @ X0 @ X1 @ X2)))) | ((~ X0) = $true) | ($false = X0) | (X1 != X3)) )),
% 0.22/0.46 inference(equality_proxy_clausification,[],[f54])).
% 0.22/0.46 thf(f54,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((X1 = X3) = $false) | ((~ X0) = $true) | ($false = X0) | ($true = (X0 & (X1 = (if1 @ X0 @ X1 @ X2))))) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f44])).
% 0.22/0.46 thf(f44,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((X0 & (X1 = X3)) = $false) | ($true = (X0 & (X1 = (if1 @ X0 @ X1 @ X2)))) | ((~ X0) = $true)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f43])).
% 0.22/0.46 thf(f43,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((X2 = (if1 @ X0 @ X1 @ X2)) & (~ X0)) = $true) | ($true = (X0 & (X1 = (if1 @ X0 @ X1 @ X2)))) | ((X0 & (X1 = X3)) = $false)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f41])).
% 0.22/0.46 thf(f117,plain,(
% 0.22/0.46 ( ! [X0 : $i] : (((if1 @ sK2 @ sK3 @ sK4) != sK3) | (sK3 != X0) | (sK2 = $false)) )),
% 0.22/0.46 inference(superposition,[],[f30,f96])).
% 0.22/0.46 thf(f96,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((if2 @ X0 @ X1 @ X2) = X1) | ($false = X0) | (X1 != X3)) )),
% 0.22/0.46 inference(equality_proxy_clausification,[],[f95])).
% 0.22/0.46 thf(f95,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((if2 @ X0 @ X1 @ X2) = X1) | ((X1 = X3) = $false) | ($false = X0)) )),
% 0.22/0.46 inference(duplicate_literal_removal,[],[f94])).
% 0.22/0.46 thf(f94,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((X1 = X3) = $false) | ($false = X0) | ($false = X0) | ((if2 @ X0 @ X1 @ X2) = X1)) )),
% 0.22/0.46 inference(not_proxy_clausification,[],[f93])).
% 0.22/0.46 thf(f93,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((~ X0) = $true) | ((if2 @ X0 @ X1 @ X2) = X1) | ($false = X0) | ((X1 = X3) = $false)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f91])).
% 0.22/0.46 thf(f91,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((if2 @ X0 @ X1 @ X2) = X1) | (((~ X0) & (X2 = (if2 @ X0 @ X1 @ X2))) = $true) | ($false = X0) | ((X1 = X3) = $false)) )),
% 0.22/0.46 inference(equality_proxy_clausification,[],[f90])).
% 0.22/0.46 thf(f90,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (($false = X0) | ($true = (X1 = (if2 @ X0 @ X1 @ X2))) | ((X1 = X3) = $false) | (((~ X0) & (X2 = (if2 @ X0 @ X1 @ X2))) = $true)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f87])).
% 0.22/0.46 thf(f87,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((X0 & (X1 = X3)) = $false) | ($true = (X1 = (if2 @ X0 @ X1 @ X2))) | (((~ X0) & (X2 = (if2 @ X0 @ X1 @ X2))) = $true)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f86])).
% 0.22/0.46 thf(f86,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : (((X0 & (X1 = (if2 @ X0 @ X1 @ X2))) = $true) | (((~ X0) & (X2 = (if2 @ X0 @ X1 @ X2))) = $true) | ((X0 & (X1 = X3)) = $false)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f85])).
% 0.22/0.46 thf(f85,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X0 : $o,X1 : $i] : ((((X0 & (X1 = (if2 @ X0 @ X1 @ X2))) | ((~ X0) & (X2 = (if2 @ X0 @ X1 @ X2)))) = $true) | ((X0 & (X1 = X3)) = $false)) )),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f83])).
% 0.22/0.46 % SZS output end Proof for theBenchmark
% 0.22/0.46 % (6898)------------------------------
% 0.22/0.46 % (6898)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.46 % (6898)Termination reason: Refutation
% 0.22/0.46
% 0.22/0.46 % (6898)Memory used [KB]: 5628
% 0.22/0.46 % (6898)Time elapsed: 0.013 s
% 0.22/0.46 % (6898)Instructions burned: 15 (million)
% 0.22/0.46 % (6898)------------------------------
% 0.22/0.46 % (6898)------------------------------
% 0.22/0.46 % (6878)Success in time 0.086 s
%------------------------------------------------------------------------------