TSTP Solution File: NUM808^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM808^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n015.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 01:46:14 EDT 2024
% Result : Theorem 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM808^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.14/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 04:22:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.37 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/sandbox/benchmark/theBenchmark.p
% 0.14/0.39 % (15366)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 (3000ds/4Mi)
% 0.14/0.39 % (15365)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.14/0.39 % (15367)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 (3000ds/27Mi)
% 0.14/0.39 % (15368)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.14/0.39 % (15370)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 (3000ds/275Mi)
% 0.14/0.39 % (15371)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.14/0.39 % (15372)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.14/0.39 % (15369)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 (3000ds/2Mi)
% 0.14/0.39 % (15368)Instruction limit reached!
% 0.14/0.39 % (15368)------------------------------
% 0.14/0.39 % (15368)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (15368)Termination reason: Unknown
% 0.14/0.39 % (15369)Instruction limit reached!
% 0.14/0.39 % (15369)------------------------------
% 0.14/0.39 % (15369)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (15369)Termination reason: Unknown
% 0.14/0.39 % (15369)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (15369)Memory used [KB]: 895
% 0.14/0.39 % (15369)Time elapsed: 0.003 s
% 0.14/0.39 % (15369)Instructions burned: 2 (million)
% 0.14/0.39 % (15369)------------------------------
% 0.14/0.39 % (15369)------------------------------
% 0.14/0.39 % (15368)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (15368)Memory used [KB]: 5500
% 0.14/0.39 % (15368)Time elapsed: 0.004 s
% 0.14/0.39 % (15368)Instructions burned: 2 (million)
% 0.14/0.39 % (15368)------------------------------
% 0.14/0.39 % (15368)------------------------------
% 0.14/0.39 % (15372)Instruction limit reached!
% 0.14/0.39 % (15372)------------------------------
% 0.14/0.39 % (15372)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (15372)Termination reason: Unknown
% 0.14/0.39 % (15372)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (15372)Memory used [KB]: 5500
% 0.14/0.39 % (15372)Time elapsed: 0.005 s
% 0.14/0.39 % (15372)Instructions burned: 3 (million)
% 0.14/0.39 % (15372)------------------------------
% 0.14/0.39 % (15372)------------------------------
% 0.14/0.39 % (15366)Instruction limit reached!
% 0.14/0.39 % (15366)------------------------------
% 0.14/0.39 % (15366)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (15366)Termination reason: Unknown
% 0.14/0.39 % (15366)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (15366)Memory used [KB]: 5500
% 0.14/0.39 % (15366)Time elapsed: 0.006 s
% 0.14/0.39 % (15366)Instructions burned: 4 (million)
% 0.14/0.39 % (15366)------------------------------
% 0.14/0.39 % (15366)------------------------------
% 0.14/0.40 % (15371)Instruction limit reached!
% 0.14/0.40 % (15371)------------------------------
% 0.14/0.40 % (15371)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (15371)Termination reason: Unknown
% 0.14/0.40 % (15371)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (15371)Memory used [KB]: 5628
% 0.14/0.40 % (15371)Time elapsed: 0.015 s
% 0.14/0.40 % (15371)Instructions burned: 19 (million)
% 0.14/0.40 % (15371)------------------------------
% 0.14/0.40 % (15371)------------------------------
% 0.14/0.40 % (15370)Refutation not found, incomplete strategy
% 0.14/0.40 % (15370)------------------------------
% 0.14/0.40 % (15370)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (15370)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.40
% 0.14/0.40
% 0.14/0.40 % (15370)Memory used [KB]: 5628
% 0.14/0.40 % (15370)Time elapsed: 0.016 s
% 0.14/0.40 % (15370)Instructions burned: 19 (million)
% 0.14/0.40 % (15370)------------------------------
% 0.14/0.40 % (15370)------------------------------
% 0.14/0.40 % (15373)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)
% 0.14/0.40 % (15374)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)
% 0.14/0.40 % (15367)Instruction limit reached!
% 0.14/0.40 % (15367)------------------------------
% 0.14/0.40 % (15367)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (15367)Termination reason: Unknown
% 0.14/0.40 % (15367)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (15367)Memory used [KB]: 5628
% 0.14/0.40 % (15367)Time elapsed: 0.020 s
% 0.14/0.40 % (15367)Instructions burned: 27 (million)
% 0.14/0.40 % (15367)------------------------------
% 0.14/0.40 % (15367)------------------------------
% 0.14/0.40 % (15375)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)
% 0.14/0.40 % (15376)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)
% 0.14/0.41 % (15375)Instruction limit reached!
% 0.14/0.41 % (15375)------------------------------
% 0.14/0.41 % (15375)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (15375)Termination reason: Unknown
% 0.14/0.41 % (15375)Termination phase: Saturation
% 0.14/0.41
% 0.14/0.41 % (15375)Memory used [KB]: 5500
% 0.14/0.41 % (15375)Time elapsed: 0.025 s
% 0.14/0.41 % (15375)Instructions burned: 3 (million)
% 0.14/0.41 % (15375)------------------------------
% 0.14/0.41 % (15375)------------------------------
% 0.14/0.41 % (15374)Instruction limit reached!
% 0.14/0.41 % (15374)------------------------------
% 0.14/0.41 % (15374)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (15374)Termination reason: Unknown
% 0.14/0.41 % (15374)Termination phase: Saturation
% 0.14/0.41
% 0.14/0.41 % (15374)Memory used [KB]: 5628
% 0.14/0.41 % (15374)Time elapsed: 0.034 s
% 0.14/0.41 % (15374)Instructions burned: 15 (million)
% 0.14/0.41 % (15374)------------------------------
% 0.14/0.41 % (15374)------------------------------
% 0.14/0.41 % (15377)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 % (15378)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.42 % (15377)Instruction limit reached!
% 0.14/0.42 % (15377)------------------------------
% 0.14/0.42 % (15377)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (15377)Termination reason: Unknown
% 0.14/0.42 % (15377)Termination phase: Saturation
% 0.14/0.42
% 0.14/0.42 % (15377)Memory used [KB]: 1023
% 0.14/0.42 % (15377)Time elapsed: 0.028 s
% 0.14/0.42 % (15377)Instructions burned: 7 (million)
% 0.14/0.42 % (15377)------------------------------
% 0.14/0.42 % (15377)------------------------------
% 0.14/0.42 % (15379)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)
% 0.14/0.42 % (15380)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)
% 0.14/0.42 % (15379)Instruction limit reached!
% 0.14/0.42 % (15379)------------------------------
% 0.14/0.42 % (15379)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (15379)Termination reason: Unknown
% 0.14/0.42 % (15379)Termination phase: Saturation
% 0.14/0.42
% 0.14/0.42 % (15379)Memory used [KB]: 5500
% 0.14/0.42 % (15379)Time elapsed: 0.005 s
% 0.14/0.42 % (15379)Instructions burned: 4 (million)
% 0.14/0.42 % (15379)------------------------------
% 0.14/0.42 % (15379)------------------------------
% 0.14/0.42 % (15380)Instruction limit reached!
% 0.14/0.42 % (15380)------------------------------
% 0.14/0.42 % (15380)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (15380)Termination reason: Unknown
% 0.14/0.42 % (15380)Termination phase: Saturation
% 0.14/0.42
% 0.14/0.42 % (15380)Memory used [KB]: 1023
% 0.14/0.42 % (15380)Time elapsed: 0.004 s
% 0.14/0.42 % (15380)Instructions burned: 3 (million)
% 0.14/0.42 % (15380)------------------------------
% 0.14/0.42 % (15380)------------------------------
% 0.14/0.42 % (15373)Instruction limit reached!
% 0.14/0.42 % (15373)------------------------------
% 0.14/0.42 % (15373)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (15373)Termination reason: Unknown
% 0.14/0.42 % (15373)Termination phase: Saturation
% 0.14/0.42
% 0.14/0.42 % (15373)Memory used [KB]: 5756
% 0.14/0.42 % (15373)Time elapsed: 0.046 s
% 0.14/0.42 % (15373)Instructions burned: 37 (million)
% 0.14/0.42 % (15373)------------------------------
% 0.14/0.42 % (15373)------------------------------
% 0.14/0.43 % (15378)Instruction limit reached!
% 0.14/0.43 % (15378)------------------------------
% 0.14/0.43 % (15378)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.43 % (15378)Termination reason: Unknown
% 0.14/0.43 % (15378)Termination phase: Saturation
% 0.14/0.43
% 0.14/0.43 % (15378)Memory used [KB]: 5756
% 0.14/0.43 % (15378)Time elapsed: 0.039 s
% 0.14/0.43 % (15378)Instructions burned: 16 (million)
% 0.14/0.43 % (15378)------------------------------
% 0.14/0.43 % (15378)------------------------------
% 0.14/0.43 % (15381)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)
% 0.14/0.43 % (15381)Refutation not found, incomplete strategy
% 0.14/0.43 % (15381)------------------------------
% 0.14/0.43 % (15381)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.43 % (15381)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.43
% 0.14/0.43
% 0.14/0.43 % (15381)Memory used [KB]: 5500
% 0.14/0.43 % (15381)Time elapsed: 0.004 s
% 0.14/0.43 % (15381)Instructions burned: 2 (million)
% 0.14/0.43 % (15381)------------------------------
% 0.14/0.43 % (15381)------------------------------
% 0.14/0.43 % (15382)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 % (15382)Instruction limit reached!
% 0.14/0.43 % (15382)------------------------------
% 0.14/0.43 % (15382)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.43 % (15382)Termination reason: Unknown
% 0.14/0.43 % (15382)Termination phase: Saturation
% 0.14/0.43
% 0.14/0.43 % (15382)Memory used [KB]: 5500
% 0.14/0.43 % (15382)Time elapsed: 0.004 s
% 0.14/0.43 % (15382)Instructions burned: 3 (million)
% 0.14/0.43 % (15382)------------------------------
% 0.14/0.43 % (15382)------------------------------
% 0.14/0.44 % (15383)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.44 % (15384)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)
% 0.22/0.44 % (15383)Instruction limit reached!
% 0.22/0.44 % (15383)------------------------------
% 0.22/0.44 % (15383)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (15383)Termination reason: Unknown
% 0.22/0.44 % (15383)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (15383)Memory used [KB]: 5500
% 0.22/0.44 % (15383)Time elapsed: 0.005 s
% 0.22/0.44 % (15383)Instructions burned: 5 (million)
% 0.22/0.44 % (15383)------------------------------
% 0.22/0.44 % (15383)------------------------------
% 0.22/0.44 % (15385)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.44 % (15384)Refutation not found, incomplete strategy
% 0.22/0.44 % (15384)------------------------------
% 0.22/0.44 % (15384)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (15384)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.44
% 0.22/0.44
% 0.22/0.44 % (15384)Memory used [KB]: 5500
% 0.22/0.44 % (15384)Time elapsed: 0.006 s
% 0.22/0.44 % (15384)Instructions burned: 4 (million)
% 0.22/0.44 % (15384)------------------------------
% 0.22/0.44 % (15384)------------------------------
% 0.22/0.44 % (15386)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.44 % (15365)First to succeed.
% 0.22/0.45 % (15387)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)
% 0.22/0.45 % (15365)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Theorem for theBenchmark
% 0.22/0.45 % SZS output start Proof for theBenchmark
% 0.22/0.45 thf(func_def_1, type, cS: $i > $i).
% 0.22/0.45 thf(func_def_2, type, r: $i > $i > $o).
% 0.22/0.45 thf(func_def_15, type, sK2: ($i > $o) > $i).
% 0.22/0.45 thf(func_def_17, type, ph3: !>[X0: $tType]:(X0)).
% 0.22/0.45 thf(func_def_19, type, sK4: $i > $i).
% 0.22/0.45 thf(f718,plain,(
% 0.22/0.45 $false),
% 0.22/0.45 inference(avatar_sat_refutation,[],[f157,f652,f669,f709])).
% 0.22/0.45 thf(f709,plain,(
% 0.22/0.45 ~spl1_5),
% 0.22/0.45 inference(avatar_contradiction_clause,[],[f708])).
% 0.22/0.45 thf(f708,plain,(
% 0.22/0.45 $false | ~spl1_5),
% 0.22/0.45 inference(trivial_inequality_removal,[],[f689])).
% 0.22/0.45 thf(f689,plain,(
% 0.22/0.45 ($true != $true) | ~spl1_5),
% 0.22/0.45 inference(superposition,[],[f15,f151])).
% 0.22/0.45 thf(f151,plain,(
% 0.22/0.45 ( ! [X0 : $i] : (((r @ X0 @ X0) = $true)) ) | ~spl1_5),
% 0.22/0.45 inference(avatar_component_clause,[],[f150])).
% 0.22/0.45 thf(f150,plain,(
% 0.22/0.45 spl1_5 <=> ! [X0] : ((r @ X0 @ X0) = $true)),
% 0.22/0.45 introduced(avatar_definition,[new_symbols(naming,[spl1_5])])).
% 0.22/0.45 thf(f15,plain,(
% 0.22/0.45 ( ! [X2 : $i] : (((r @ sK0 @ X2) != $true)) )),
% 0.22/0.45 inference(cnf_transformation,[],[f12])).
% 0.22/0.45 thf(f12,plain,(
% 0.22/0.45 ! [X0] : (((r @ (cS @ X0) @ (cS @ X0)) = $true) | ((r @ X0 @ X0) != $true)) & ! [X2] : ((r @ sK0 @ X2) != $true) & (cIND = $true) & ((r @ c0 @ c0) = $true)),
% 0.22/0.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f11])).
% 0.22/0.45 thf(f11,plain,(
% 0.22/0.45 ? [X1] : ! [X2] : ((r @ X1 @ X2) != $true) => ! [X2] : ((r @ sK0 @ X2) != $true)),
% 0.22/0.45 introduced(choice_axiom,[])).
% 0.22/0.45 thf(f10,plain,(
% 0.22/0.45 ! [X0] : (((r @ (cS @ X0) @ (cS @ X0)) = $true) | ((r @ X0 @ X0) != $true)) & ? [X1] : ! [X2] : ((r @ X1 @ X2) != $true) & (cIND = $true) & ((r @ c0 @ c0) = $true)),
% 0.22/0.45 inference(flattening,[],[f9])).
% 0.22/0.45 thf(f9,plain,(
% 0.22/0.45 ? [X1] : ! [X2] : ((r @ X1 @ X2) != $true) & ((cIND = $true) & ! [X0] : (((r @ (cS @ X0) @ (cS @ X0)) = $true) | ((r @ X0 @ X0) != $true)) & ((r @ c0 @ c0) = $true))),
% 0.22/0.45 inference(ennf_transformation,[],[f8])).
% 0.22/0.45 thf(f8,plain,(
% 0.22/0.45 ~(((cIND = $true) & ! [X0] : (((r @ X0 @ X0) = $true) => ((r @ (cS @ X0) @ (cS @ X0)) = $true)) & ((r @ c0 @ c0) = $true)) => ! [X1] : ? [X2] : ((r @ X1 @ X2) = $true))),
% 0.22/0.45 inference(fool_elimination,[],[f7])).
% 0.22/0.45 thf(f7,plain,(
% 0.22/0.45 ~(((r @ c0 @ c0) & cIND & ! [X0] : ((r @ X0 @ X0) => (r @ (cS @ X0) @ (cS @ X0)))) => ! [X1] : ? [X2] : (r @ X1 @ X2))),
% 0.22/0.45 inference(rectify,[],[f3])).
% 0.22/0.45 thf(f3,negated_conjecture,(
% 0.22/0.45 ~(((r @ c0 @ c0) & cIND & ! [X1] : ((r @ X1 @ X1) => (r @ (cS @ X1) @ (cS @ X1)))) => ! [X1] : ? [X2] : (r @ X1 @ X2))),
% 0.22/0.45 inference(negated_conjecture,[],[f2])).
% 0.22/0.45 thf(f2,conjecture,(
% 0.22/0.45 ((r @ c0 @ c0) & cIND & ! [X1] : ((r @ X1 @ X1) => (r @ (cS @ X1) @ (cS @ X1)))) => ! [X1] : ? [X2] : (r @ X1 @ X2)),
% 0.22/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM130A)).
% 0.22/0.45 thf(f669,plain,(
% 0.22/0.45 ~spl1_6),
% 0.22/0.45 inference(avatar_contradiction_clause,[],[f668])).
% 0.22/0.45 thf(f668,plain,(
% 0.22/0.45 $false | ~spl1_6),
% 0.22/0.45 inference(trivial_inequality_removal,[],[f659])).
% 0.22/0.45 thf(f659,plain,(
% 0.22/0.45 ($true = $false) | ~spl1_6),
% 0.22/0.45 inference(superposition,[],[f13,f155])).
% 0.22/0.45 thf(f155,plain,(
% 0.22/0.45 ((r @ c0 @ c0) = $false) | ~spl1_6),
% 0.22/0.45 inference(avatar_component_clause,[],[f153])).
% 0.22/0.45 thf(f153,plain,(
% 0.22/0.45 spl1_6 <=> ((r @ c0 @ c0) = $false)),
% 0.22/0.45 introduced(avatar_definition,[new_symbols(naming,[spl1_6])])).
% 0.22/0.45 thf(f13,plain,(
% 0.22/0.45 ((r @ c0 @ c0) = $true)),
% 0.22/0.45 inference(cnf_transformation,[],[f12])).
% 0.22/0.45 thf(f652,plain,(
% 0.22/0.45 spl1_5 | spl1_6 | spl1_4),
% 0.22/0.45 inference(avatar_split_clause,[],[f641,f146,f153,f150])).
% 0.22/0.45 thf(f146,plain,(
% 0.22/0.45 spl1_4 <=> ((r @ (sK2 @ (^[Y0 : $i]: (r @ Y0 @ Y0))) @ (sK2 @ (^[Y0 : $i]: (r @ Y0 @ Y0)))) = $true)),
% 0.22/0.45 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 0.22/0.45 thf(f641,plain,(
% 0.22/0.45 ( ! [X0 : $i] : (((r @ X0 @ X0) = $true) | ((r @ c0 @ c0) = $false)) ) | spl1_4),
% 0.22/0.45 inference(beta_eta_normalization,[],[f640])).
% 0.22/0.45 thf(f640,plain,(
% 0.22/0.45 ( ! [X0 : $i] : ((((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ c0) = $false) | (((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X0) = $true)) ) | spl1_4),
% 0.22/0.45 inference(trivial_inequality_removal,[],[f639])).
% 0.22/0.45 thf(f639,plain,(
% 0.22/0.45 ( ! [X0 : $i] : ((((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ c0) = $false) | (((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X0) = $true) | ($true != $true)) ) | spl1_4),
% 0.22/0.45 inference(superposition,[],[f148,f28])).
% 0.22/0.45 thf(f28,plain,(
% 0.22/0.45 ( ! [X2 : $i,X1 : $i > $o] : (((X1 @ (sK2 @ X1)) = $true) | ((X1 @ c0) = $false) | ((X1 @ X2) = $true)) )),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f26])).
% 0.22/0.45 thf(f26,plain,(
% 0.22/0.45 ( ! [X2 : $i,X1 : $i > $o] : (((X1 @ c0) = $false) | (((X1 @ (sK2 @ X1)) => (X1 @ (cS @ (sK2 @ X1)))) = $false) | ((X1 @ X2) = $true)) )),
% 0.22/0.45 inference(beta_eta_normalization,[],[f25])).
% 0.22/0.45 thf(f25,plain,(
% 0.22/0.45 ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0)))) @ (sK2 @ X1)) = $false) | ((X1 @ X2) = $true) | ((X1 @ c0) = $false)) )),
% 0.22/0.45 inference(sigma_clausification,[],[f24])).
% 0.22/0.45 thf(f24,plain,(
% 0.22/0.45 ( ! [X2 : $i,X1 : $i > $o] : (((X1 @ X2) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0))))) = $false) | ((X1 @ c0) = $false)) )),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f23])).
% 0.22/0.45 thf(f23,plain,(
% 0.22/0.45 ( ! [X2 : $i,X1 : $i > $o] : (((X1 @ X2) = $true) | (((X1 @ c0) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0)))))) = $false)) )),
% 0.22/0.45 inference(pi_clausification,[],[f22])).
% 0.22/0.45 thf(f22,plain,(
% 0.22/0.45 ( ! [X1 : $i > $o] : (($true = (!! @ $i @ X1)) | (((X1 @ c0) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0)))))) = $false)) )),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f21])).
% 0.22/0.45 thf(f21,plain,(
% 0.22/0.45 ( ! [X1 : $i > $o] : (((((X1 @ c0) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0)))))) => (!! @ $i @ X1)) = $true)) )),
% 0.22/0.45 inference(beta_eta_normalization,[],[f20])).
% 0.22/0.45 thf(f20,plain,(
% 0.22/0.45 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ Y0))) @ X1) = $true)) )),
% 0.22/0.45 inference(pi_clausification,[],[f19])).
% 0.22/0.45 thf(f19,plain,(
% 0.22/0.45 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ Y0)))) = $true)),
% 0.22/0.45 inference(beta_eta_normalization,[],[f18])).
% 0.22/0.45 thf(f18,plain,(
% 0.22/0.45 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) = $true)),
% 0.22/0.45 inference(definition_unfolding,[],[f17,f14])).
% 0.22/0.45 thf(f14,plain,(
% 0.22/0.45 (cIND = $true)),
% 0.22/0.45 inference(cnf_transformation,[],[f12])).
% 0.22/0.45 thf(f17,plain,(
% 0.22/0.45 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 0.22/0.45 inference(cnf_transformation,[],[f6])).
% 0.22/0.45 thf(f6,plain,(
% 0.22/0.45 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 0.22/0.45 inference(fool_elimination,[],[f5])).
% 0.22/0.45 thf(f5,plain,(
% 0.22/0.45 (cIND = ! [X0 : $i > $o] : ((! [X1] : ((X0 @ X1) => (X0 @ (cS @ X1))) & (X0 @ c0)) => ! [X2] : (X0 @ X2)))),
% 0.22/0.45 inference(rectify,[],[f1])).
% 0.22/0.45 thf(f1,axiom,(
% 0.22/0.45 (cIND = ! [X0 : $i > $o] : ((! [X1] : ((X0 @ X1) => (X0 @ (cS @ X1))) & (X0 @ c0)) => ! [X1] : (X0 @ X1)))),
% 0.22/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cIND_def)).
% 0.22/0.45 thf(f148,plain,(
% 0.22/0.45 ((r @ (sK2 @ (^[Y0 : $i]: (r @ Y0 @ Y0))) @ (sK2 @ (^[Y0 : $i]: (r @ Y0 @ Y0)))) != $true) | spl1_4),
% 0.22/0.45 inference(avatar_component_clause,[],[f146])).
% 0.22/0.45 thf(f157,plain,(
% 0.22/0.45 spl1_5 | ~spl1_4 | spl1_6),
% 0.22/0.45 inference(avatar_split_clause,[],[f142,f153,f146,f150])).
% 0.22/0.45 thf(f142,plain,(
% 0.22/0.45 ( ! [X0 : $i] : (((r @ (sK2 @ (^[Y0 : $i]: (r @ Y0 @ Y0))) @ (sK2 @ (^[Y0 : $i]: (r @ Y0 @ Y0)))) != $true) | ((r @ X0 @ X0) = $true) | ((r @ c0 @ c0) = $false)) )),
% 0.22/0.45 inference(beta_eta_normalization,[],[f141])).
% 0.22/0.45 thf(f141,plain,(
% 0.22/0.45 ( ! [X0 : $i] : ((((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ c0) = $false) | (((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X0) = $true) | ($true != (r @ (sK2 @ (^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0)))) @ (sK2 @ (^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) )),
% 0.22/0.45 inference(trivial_inequality_removal,[],[f139])).
% 0.22/0.45 thf(f139,plain,(
% 0.22/0.45 ( ! [X0 : $i] : (($true = $false) | (((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ c0) = $false) | ($true != (r @ (sK2 @ (^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0)))) @ (sK2 @ (^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0)))))) | (((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X0) = $true)) )),
% 0.22/0.45 inference(superposition,[],[f16,f27])).
% 0.22/0.45 thf(f27,plain,(
% 0.22/0.45 ( ! [X2 : $i,X1 : $i > $o] : (($false = (X1 @ (cS @ (sK2 @ X1)))) | ((X1 @ X2) = $true) | ((X1 @ c0) = $false)) )),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f26])).
% 0.22/0.45 thf(f16,plain,(
% 0.22/0.45 ( ! [X0 : $i] : (((r @ (cS @ X0) @ (cS @ X0)) = $true) | ((r @ X0 @ X0) != $true)) )),
% 0.22/0.45 inference(cnf_transformation,[],[f12])).
% 0.22/0.45 % SZS output end Proof for theBenchmark
% 0.22/0.45 % (15365)------------------------------
% 0.22/0.45 % (15365)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (15365)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (15365)Memory used [KB]: 6012
% 0.22/0.45 % (15365)Time elapsed: 0.061 s
% 0.22/0.45 % (15365)Instructions burned: 91 (million)
% 0.22/0.45 % (15365)------------------------------
% 0.22/0.45 % (15365)------------------------------
% 0.22/0.45 % (15364)Success in time 0.075 s
% 0.22/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------