TSTP Solution File: SEU779^2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU779^2 : 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 : n026.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 03:51:28 EDT 2024
% Result : Theorem 0.15s 0.33s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU779^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.11 % 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
% 0.10/0.31 % Computer : n026.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun May 19 16:24:53 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 This is a TH0_THM_EQU_NAR problem
% 0.15/0.31 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
% 0.15/0.32 % (23234)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.15/0.32 % (23234)Instruction limit reached!
% 0.15/0.32 % (23234)------------------------------
% 0.15/0.32 % (23234)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (23234)Termination reason: Unknown
% 0.15/0.32 % (23234)Termination phase: Function definition elimination
% 0.15/0.32
% 0.15/0.32 % (23234)Memory used [KB]: 1023
% 0.15/0.32 % (23234)Time elapsed: 0.003 s
% 0.15/0.32 % (23234)Instructions burned: 4 (million)
% 0.15/0.32 % (23234)------------------------------
% 0.15/0.32 % (23234)------------------------------
% 0.15/0.32 % (23231)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.15/0.32 % (23235)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)
% 0.15/0.32 % (23237)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.15/0.32 % (23236)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)
% 0.15/0.32 % (23233)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)
% 0.15/0.32 % (23235)Instruction limit reached!
% 0.15/0.32 % (23235)------------------------------
% 0.15/0.32 % (23235)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (23235)Termination reason: Unknown
% 0.15/0.32 % (23235)Termination phase: shuffling
% 0.15/0.32
% 0.15/0.32 % (23235)Memory used [KB]: 895
% 0.15/0.33 % (23235)Time elapsed: 0.002 s
% 0.15/0.33 % (23235)Instructions burned: 2 (million)
% 0.15/0.33 % (23235)------------------------------
% 0.15/0.33 % (23235)------------------------------
% 0.15/0.33 % (23238)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)
% 0.15/0.33 % (23236)Refutation not found, incomplete strategy
% 0.15/0.33 % (23236)------------------------------
% 0.15/0.33 % (23236)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (23236)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.33
% 0.15/0.33
% 0.15/0.33 % (23236)Memory used [KB]: 5500
% 0.15/0.33 % (23236)Time elapsed: 0.004 s
% 0.15/0.33 % (23236)Instructions burned: 5 (million)
% 0.15/0.33 % (23236)------------------------------
% 0.15/0.33 % (23236)------------------------------
% 0.15/0.33 % (23238)Instruction limit reached!
% 0.15/0.33 % (23238)------------------------------
% 0.15/0.33 % (23238)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (23238)Termination reason: Unknown
% 0.15/0.33 % (23238)Termination phase: Property scanning
% 0.15/0.33
% 0.15/0.33 % (23238)Memory used [KB]: 1023
% 0.15/0.33 % (23238)Time elapsed: 0.003 s
% 0.15/0.33 % (23238)Instructions burned: 3 (million)
% 0.15/0.33 % (23238)------------------------------
% 0.15/0.33 % (23238)------------------------------
% 0.15/0.33 % (23231)First to succeed.
% 0.15/0.33 % (23232)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)
% 0.15/0.33 % (23233)Also succeeded, but the first one will report.
% 0.15/0.33 % (23232)Instruction limit reached!
% 0.15/0.33 % (23232)------------------------------
% 0.15/0.33 % (23232)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (23232)Termination reason: Unknown
% 0.15/0.33 % (23232)Termination phase: Saturation
% 0.15/0.33
% 0.15/0.33 % (23232)Memory used [KB]: 5500
% 0.15/0.33 % (23232)Time elapsed: 0.004 s
% 0.15/0.33 % (23232)Instructions burned: 5 (million)
% 0.15/0.33 % (23232)------------------------------
% 0.15/0.33 % (23232)------------------------------
% 0.15/0.33 % (23231)Refutation found. Thanks to Tanya!
% 0.15/0.33 % SZS status Theorem for theBenchmark
% 0.15/0.33 % SZS output start Proof for theBenchmark
% 0.15/0.33 thf(func_def_0, type, in: $i > $i > $o).
% 0.15/0.33 thf(func_def_1, type, subset: $i > $i > $o).
% 0.15/0.33 thf(func_def_2, type, kpair: $i > $i > $i).
% 0.15/0.33 thf(func_def_3, type, cartprod: $i > $i > $i).
% 0.15/0.33 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 0.15/0.33 thf(func_def_6, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.15/0.33 thf(func_def_8, type, breln1: $i > $i > $o).
% 0.15/0.33 thf(func_def_9, type, breln1compset: $i > $i > $i > $i).
% 0.15/0.33 thf(func_def_31, type, ph7: !>[X0: $tType]:(X0)).
% 0.15/0.33 thf(f121,plain,(
% 0.15/0.33 $false),
% 0.15/0.33 inference(avatar_sat_refutation,[],[f80,f86,f93,f108,f114,f120])).
% 0.15/0.33 thf(f120,plain,(
% 0.15/0.33 ~spl6_4),
% 0.15/0.33 inference(avatar_contradiction_clause,[],[f119])).
% 0.15/0.33 thf(f119,plain,(
% 0.15/0.33 $false | ~spl6_4),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f116])).
% 0.15/0.33 thf(f116,plain,(
% 0.15/0.33 ($false = $true) | ~spl6_4),
% 0.15/0.33 inference(superposition,[],[f28,f102])).
% 0.15/0.33 thf(f102,plain,(
% 0.15/0.33 ((in @ sK5 @ sK0) = $false) | ~spl6_4),
% 0.15/0.33 inference(avatar_component_clause,[],[f100])).
% 0.15/0.33 thf(f100,plain,(
% 0.15/0.33 spl6_4 <=> ((in @ sK5 @ sK0) = $false)),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl6_4])])).
% 0.15/0.33 thf(f28,plain,(
% 0.15/0.33 ((in @ sK5 @ sK0) = $true)),
% 0.15/0.33 inference(cnf_transformation,[],[f24])).
% 0.15/0.33 thf(f24,plain,(
% 0.15/0.33 (dpsetconstrI = $true) & ((((breln1 @ sK0 @ sK2) = $true) & (($true = (in @ sK3 @ sK0)) & (((in @ sK4 @ sK0) = $true) & (($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) & ((in @ (kpair @ sK5 @ sK4) @ sK2) = $true) & ((in @ sK5 @ sK0) = $true) & ($true = (in @ (kpair @ sK3 @ sK5) @ sK1)))))) & ((breln1 @ sK0 @ sK1) = $true))),
% 0.15/0.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f18,f23,f22,f21,f20,f19])).
% 0.15/0.33 thf(f19,plain,(
% 0.15/0.33 ? [X0,X1] : (? [X2] : (($true = (breln1 @ X0 @ X2)) & ? [X3] : (($true = (in @ X3 @ X0)) & ? [X4] : (((in @ X4 @ X0) = $true) & ? [X5] : (($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) & ($true = (in @ (kpair @ X5 @ X4) @ X2)) & ((in @ X5 @ X0) = $true) & ((in @ (kpair @ X3 @ X5) @ X1) = $true))))) & ($true = (breln1 @ X0 @ X1))) => (? [X2] : (($true = (breln1 @ sK0 @ X2)) & ? [X3] : (((in @ X3 @ sK0) = $true) & ? [X4] : (($true = (in @ X4 @ sK0)) & ? [X5] : (($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK0 @ sK1 @ X2))) & ($true = (in @ (kpair @ X5 @ X4) @ X2)) & ((in @ X5 @ sK0) = $true) & ((in @ (kpair @ X3 @ X5) @ sK1) = $true))))) & ((breln1 @ sK0 @ sK1) = $true))),
% 0.15/0.33 introduced(choice_axiom,[])).
% 0.15/0.33 thf(f20,plain,(
% 0.15/0.33 ? [X2] : (($true = (breln1 @ sK0 @ X2)) & ? [X3] : (((in @ X3 @ sK0) = $true) & ? [X4] : (($true = (in @ X4 @ sK0)) & ? [X5] : (($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK0 @ sK1 @ X2))) & ($true = (in @ (kpair @ X5 @ X4) @ X2)) & ((in @ X5 @ sK0) = $true) & ((in @ (kpair @ X3 @ X5) @ sK1) = $true))))) => (((breln1 @ sK0 @ sK2) = $true) & ? [X3] : (((in @ X3 @ sK0) = $true) & ? [X4] : (($true = (in @ X4 @ sK0)) & ? [X5] : (((in @ (kpair @ X3 @ X4) @ (breln1compset @ sK0 @ sK1 @ sK2)) != $true) & ($true = (in @ (kpair @ X5 @ X4) @ sK2)) & ((in @ X5 @ sK0) = $true) & ((in @ (kpair @ X3 @ X5) @ sK1) = $true)))))),
% 0.15/0.33 introduced(choice_axiom,[])).
% 0.15/0.33 thf(f21,plain,(
% 0.15/0.33 ? [X3] : (((in @ X3 @ sK0) = $true) & ? [X4] : (($true = (in @ X4 @ sK0)) & ? [X5] : (((in @ (kpair @ X3 @ X4) @ (breln1compset @ sK0 @ sK1 @ sK2)) != $true) & ($true = (in @ (kpair @ X5 @ X4) @ sK2)) & ((in @ X5 @ sK0) = $true) & ((in @ (kpair @ X3 @ X5) @ sK1) = $true)))) => (($true = (in @ sK3 @ sK0)) & ? [X4] : (($true = (in @ X4 @ sK0)) & ? [X5] : (($true != (in @ (kpair @ sK3 @ X4) @ (breln1compset @ sK0 @ sK1 @ sK2))) & ($true = (in @ (kpair @ X5 @ X4) @ sK2)) & ((in @ X5 @ sK0) = $true) & ($true = (in @ (kpair @ sK3 @ X5) @ sK1)))))),
% 0.15/0.33 introduced(choice_axiom,[])).
% 0.15/0.33 thf(f22,plain,(
% 0.15/0.33 ? [X4] : (($true = (in @ X4 @ sK0)) & ? [X5] : (($true != (in @ (kpair @ sK3 @ X4) @ (breln1compset @ sK0 @ sK1 @ sK2))) & ($true = (in @ (kpair @ X5 @ X4) @ sK2)) & ((in @ X5 @ sK0) = $true) & ($true = (in @ (kpair @ sK3 @ X5) @ sK1)))) => (((in @ sK4 @ sK0) = $true) & ? [X5] : (($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) & ($true = (in @ (kpair @ X5 @ sK4) @ sK2)) & ((in @ X5 @ sK0) = $true) & ($true = (in @ (kpair @ sK3 @ X5) @ sK1))))),
% 0.15/0.33 introduced(choice_axiom,[])).
% 0.15/0.33 thf(f23,plain,(
% 0.15/0.33 ? [X5] : (($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) & ($true = (in @ (kpair @ X5 @ sK4) @ sK2)) & ((in @ X5 @ sK0) = $true) & ($true = (in @ (kpair @ sK3 @ X5) @ sK1))) => (($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))) & ((in @ (kpair @ sK5 @ sK4) @ sK2) = $true) & ((in @ sK5 @ sK0) = $true) & ($true = (in @ (kpair @ sK3 @ sK5) @ sK1)))),
% 0.15/0.33 introduced(choice_axiom,[])).
% 0.15/0.33 thf(f18,plain,(
% 0.15/0.33 (dpsetconstrI = $true) & ? [X0,X1] : (? [X2] : (($true = (breln1 @ X0 @ X2)) & ? [X3] : (($true = (in @ X3 @ X0)) & ? [X4] : (((in @ X4 @ X0) = $true) & ? [X5] : (($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) & ($true = (in @ (kpair @ X5 @ X4) @ X2)) & ((in @ X5 @ X0) = $true) & ((in @ (kpair @ X3 @ X5) @ X1) = $true))))) & ($true = (breln1 @ X0 @ X1)))),
% 0.15/0.33 inference(flattening,[],[f17])).
% 0.15/0.33 thf(f17,plain,(
% 0.15/0.33 ? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : (? [X5] : (((($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) & ($true = (in @ (kpair @ X5 @ X4) @ X2))) & ((in @ (kpair @ X3 @ X5) @ X1) = $true)) & ((in @ X5 @ X0) = $true)) & ((in @ X4 @ X0) = $true)) & ($true = (in @ X3 @ X0))) & ($true = (breln1 @ X0 @ X2))) & ($true = (breln1 @ X0 @ X1))) & (dpsetconstrI = $true)),
% 0.15/0.33 inference(ennf_transformation,[],[f9])).
% 0.15/0.33 thf(f9,plain,(
% 0.15/0.33 ~((dpsetconstrI = $true) => ! [X0,X1] : (($true = (breln1 @ X0 @ X1)) => ! [X2] : (($true = (breln1 @ X0 @ X2)) => ! [X3] : (($true = (in @ X3 @ X0)) => ! [X4] : (((in @ X4 @ X0) = $true) => ! [X5] : (((in @ X5 @ X0) = $true) => (((in @ (kpair @ X3 @ X5) @ X1) = $true) => (($true = (in @ (kpair @ X5 @ X4) @ X2)) => ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))))))))))),
% 0.15/0.33 inference(fool_elimination,[],[f8])).
% 0.15/0.33 thf(f8,plain,(
% 0.15/0.33 ~(dpsetconstrI => ! [X0,X1] : ((breln1 @ X0 @ X1) => ! [X2] : ((breln1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X0) => ((in @ (kpair @ X3 @ X5) @ X1) => ((in @ (kpair @ X5 @ X4) @ X2) => (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))))))))))),
% 0.15/0.33 inference(rectify,[],[f6])).
% 0.15/0.33 thf(f6,negated_conjecture,(
% 0.15/0.33 ~(dpsetconstrI => ! [X0,X8] : ((breln1 @ X0 @ X8) => ! [X9] : ((breln1 @ X0 @ X9) => ! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X0) => ! [X6] : ((in @ X6 @ X0) => ((in @ (kpair @ X4 @ X6) @ X8) => ((in @ (kpair @ X6 @ X5) @ X9) => (in @ (kpair @ X4 @ X5) @ (breln1compset @ X0 @ X8 @ X9))))))))))),
% 0.15/0.33 inference(negated_conjecture,[],[f5])).
% 0.15/0.33 thf(f5,conjecture,(
% 0.15/0.33 dpsetconstrI => ! [X0,X8] : ((breln1 @ X0 @ X8) => ! [X9] : ((breln1 @ X0 @ X9) => ! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X0) => ! [X6] : ((in @ X6 @ X0) => ((in @ (kpair @ X4 @ X6) @ X8) => ((in @ (kpair @ X6 @ X5) @ X9) => (in @ (kpair @ X4 @ X5) @ (breln1compset @ X0 @ X8 @ X9)))))))))),
% 0.15/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compI)).
% 0.15/0.33 thf(f114,plain,(
% 0.15/0.33 ~spl6_5),
% 0.15/0.33 inference(avatar_contradiction_clause,[],[f113])).
% 0.15/0.33 thf(f113,plain,(
% 0.15/0.33 $false | ~spl6_5),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f109])).
% 0.15/0.33 thf(f109,plain,(
% 0.15/0.33 ($false = $true) | ~spl6_5),
% 0.15/0.33 inference(superposition,[],[f106,f29])).
% 0.15/0.33 thf(f29,plain,(
% 0.15/0.33 ((in @ (kpair @ sK5 @ sK4) @ sK2) = $true)),
% 0.15/0.33 inference(cnf_transformation,[],[f24])).
% 0.15/0.33 thf(f106,plain,(
% 0.15/0.33 ((in @ (kpair @ sK5 @ sK4) @ sK2) = $false) | ~spl6_5),
% 0.15/0.33 inference(avatar_component_clause,[],[f104])).
% 0.15/0.33 thf(f104,plain,(
% 0.15/0.33 spl6_5 <=> ((in @ (kpair @ sK5 @ sK4) @ sK2) = $false)),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl6_5])])).
% 0.15/0.33 thf(f108,plain,(
% 0.15/0.33 spl6_4 | spl6_5 | ~spl6_1),
% 0.15/0.33 inference(avatar_split_clause,[],[f97,f70,f104,f100])).
% 0.15/0.33 thf(f70,plain,(
% 0.15/0.33 spl6_1 <=> ! [X1] : (((in @ (kpair @ sK3 @ X1) @ sK1) = $false) | ((in @ X1 @ sK0) = $false) | ((in @ (kpair @ X1 @ sK4) @ sK2) = $false))),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl6_1])])).
% 0.15/0.33 thf(f97,plain,(
% 0.15/0.33 ((in @ (kpair @ sK5 @ sK4) @ sK2) = $false) | ((in @ sK5 @ sK0) = $false) | ~spl6_1),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f96])).
% 0.15/0.33 thf(f96,plain,(
% 0.15/0.33 ((in @ (kpair @ sK5 @ sK4) @ sK2) = $false) | ($false = $true) | ((in @ sK5 @ sK0) = $false) | ~spl6_1),
% 0.15/0.33 inference(superposition,[],[f27,f71])).
% 0.15/0.33 thf(f71,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((in @ (kpair @ sK3 @ X1) @ sK1) = $false) | ((in @ (kpair @ X1 @ sK4) @ sK2) = $false) | ((in @ X1 @ sK0) = $false)) ) | ~spl6_1),
% 0.15/0.33 inference(avatar_component_clause,[],[f70])).
% 0.15/0.33 thf(f27,plain,(
% 0.15/0.33 ($true = (in @ (kpair @ sK3 @ sK5) @ sK1))),
% 0.15/0.33 inference(cnf_transformation,[],[f24])).
% 0.15/0.33 thf(f93,plain,(
% 0.15/0.33 ~spl6_3),
% 0.15/0.33 inference(avatar_contradiction_clause,[],[f92])).
% 0.15/0.33 thf(f92,plain,(
% 0.15/0.33 $false | ~spl6_3),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f88])).
% 0.15/0.33 thf(f88,plain,(
% 0.15/0.33 ($false = $true) | ~spl6_3),
% 0.15/0.33 inference(superposition,[],[f79,f31])).
% 0.15/0.33 thf(f31,plain,(
% 0.15/0.33 ((in @ sK4 @ sK0) = $true)),
% 0.15/0.33 inference(cnf_transformation,[],[f24])).
% 0.15/0.33 thf(f79,plain,(
% 0.15/0.33 ((in @ sK4 @ sK0) = $false) | ~spl6_3),
% 0.15/0.33 inference(avatar_component_clause,[],[f77])).
% 0.15/0.33 thf(f77,plain,(
% 0.15/0.33 spl6_3 <=> ((in @ sK4 @ sK0) = $false)),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl6_3])])).
% 0.15/0.33 thf(f86,plain,(
% 0.15/0.33 ~spl6_2),
% 0.15/0.33 inference(avatar_contradiction_clause,[],[f85])).
% 0.15/0.33 thf(f85,plain,(
% 0.15/0.33 $false | ~spl6_2),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f82])).
% 0.15/0.33 thf(f82,plain,(
% 0.15/0.33 ($false = $true) | ~spl6_2),
% 0.15/0.33 inference(superposition,[],[f32,f75])).
% 0.15/0.33 thf(f75,plain,(
% 0.15/0.33 ($false = (in @ sK3 @ sK0)) | ~spl6_2),
% 0.15/0.33 inference(avatar_component_clause,[],[f73])).
% 0.15/0.33 thf(f73,plain,(
% 0.15/0.33 spl6_2 <=> ($false = (in @ sK3 @ sK0))),
% 0.15/0.33 introduced(avatar_definition,[new_symbols(naming,[spl6_2])])).
% 0.15/0.33 thf(f32,plain,(
% 0.15/0.33 ($true = (in @ sK3 @ sK0))),
% 0.15/0.33 inference(cnf_transformation,[],[f24])).
% 0.15/0.33 thf(f80,plain,(
% 0.15/0.33 spl6_1 | spl6_2 | spl6_3),
% 0.15/0.33 inference(avatar_split_clause,[],[f68,f77,f73,f70])).
% 0.15/0.33 thf(f68,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((in @ sK4 @ sK0) = $false) | ((in @ (kpair @ sK3 @ X1) @ sK1) = $false) | ((in @ (kpair @ X1 @ sK4) @ sK2) = $false) | ((in @ X1 @ sK0) = $false) | ($false = (in @ sK3 @ sK0))) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f67])).
% 0.15/0.33 thf(f67,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((in @ X1 @ sK0) = $false) | ((in @ sK4 @ sK0) = $false) | ($false = (in @ sK3 @ sK0)) | (((in @ (kpair @ X1 @ sK4) @ sK2) & (in @ (kpair @ sK3 @ X1) @ sK1)) = $false)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f66])).
% 0.15/0.33 thf(f66,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (((((in @ (kpair @ X1 @ sK4) @ sK2) & (in @ (kpair @ sK3 @ X1) @ sK1)) & (in @ X1 @ sK0)) = $false) | ((in @ sK4 @ sK0) = $false) | ($false = (in @ sK3 @ sK0))) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f65])).
% 0.15/0.33 thf(f65,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (($false = (in @ sK3 @ sK0)) | ((in @ sK4 @ sK0) = $false) | (((^[Y0 : $i]: (((in @ (kpair @ Y0 @ sK4) @ sK2) & (in @ (kpair @ sK3 @ Y0) @ sK1)) & (in @ Y0 @ sK0))) @ X1) = $false)) )),
% 0.15/0.33 inference(pi_clausification,[],[f64])).
% 0.15/0.33 thf(f64,plain,(
% 0.15/0.33 ($false = (in @ sK3 @ sK0)) | ((?? @ $i @ (^[Y0 : $i]: (((in @ (kpair @ Y0 @ sK4) @ sK2) & (in @ (kpair @ sK3 @ Y0) @ sK1)) & (in @ Y0 @ sK0)))) = $false) | ((in @ sK4 @ sK0) = $false)),
% 0.15/0.33 inference(beta_eta_normalization,[],[f63])).
% 0.15/0.33 thf(f63,plain,(
% 0.15/0.33 ((in @ sK4 @ sK0) = $false) | (((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ (kpair @ Y2 @ Y1) @ sK2) & (in @ (kpair @ Y0 @ Y2) @ sK1)) & (in @ Y2 @ sK0))))))) @ sK3 @ sK4) = $false) | ($false = (in @ sK3 @ sK0))),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f62])).
% 0.15/0.33 thf(f62,plain,(
% 0.15/0.33 ($false = (in @ sK3 @ sK0)) | ((in @ sK4 @ sK0) = $false) | ($true != $true) | (((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ (kpair @ Y2 @ Y1) @ sK2) & (in @ (kpair @ Y0 @ Y2) @ sK1)) & (in @ Y2 @ sK0))))))) @ sK3 @ sK4) = $false)),
% 0.15/0.33 inference(superposition,[],[f59,f58])).
% 0.15/0.33 thf(f58,plain,(
% 0.15/0.33 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (((in @ (kpair @ X1 @ X5) @ (dpsetconstr @ X3 @ X4 @ X2)) = $true) | ($false = (X2 @ X1 @ X5)) | ($false = (in @ X1 @ X3)) | ($false = (in @ X5 @ X4))) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f57])).
% 0.15/0.33 thf(f57,plain,(
% 0.15/0.33 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (in @ X5 @ X4)) | (((X2 @ X1 @ X5) => (in @ (kpair @ X1 @ X5) @ (dpsetconstr @ X3 @ X4 @ X2))) = $true) | ($false = (in @ X1 @ X3))) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f56])).
% 0.15/0.33 thf(f56,plain,(
% 0.15/0.33 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (in @ X1 @ X3)) | ($true = ((in @ X5 @ X4) => ((X2 @ X1 @ X5) => (in @ (kpair @ X1 @ X5) @ (dpsetconstr @ X3 @ X4 @ X2)))))) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f55])).
% 0.15/0.33 thf(f55,plain,(
% 0.15/0.33 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (in @ X1 @ X3)) | ($true = ((^[Y0 : $i]: ((in @ Y0 @ X4) => ((X2 @ X1 @ Y0) => (in @ (kpair @ X1 @ Y0) @ (dpsetconstr @ X3 @ X4 @ X2))))) @ X5))) )),
% 0.15/0.33 inference(pi_clausification,[],[f54])).
% 0.15/0.33 thf(f54,plain,(
% 0.15/0.33 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X4) => ((X2 @ X1 @ Y0) => (in @ (kpair @ X1 @ Y0) @ (dpsetconstr @ X3 @ X4 @ X2)))))) = $true) | ($false = (in @ X1 @ X3))) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f53])).
% 0.15/0.33 thf(f53,plain,(
% 0.15/0.33 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i] : (($true = ((in @ X1 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X4) => ((X2 @ X1 @ Y0) => (in @ (kpair @ X1 @ Y0) @ (dpsetconstr @ X3 @ X4 @ X2))))))))) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f52])).
% 0.15/0.33 thf(f52,plain,(
% 0.15/0.33 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X2 @ X1 @ Y1) => (in @ (kpair @ X1 @ Y1) @ (dpsetconstr @ X3 @ Y0 @ X2)))))))) @ X4) = $true)) )),
% 0.15/0.33 inference(pi_clausification,[],[f51])).
% 0.15/0.33 thf(f51,plain,(
% 0.15/0.33 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X2 @ X1 @ Y1) => (in @ (kpair @ X1 @ Y1) @ (dpsetconstr @ X3 @ Y0 @ X2))))))))))) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f50])).
% 0.15/0.33 thf(f50,plain,(
% 0.15/0.33 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((X2 @ X1 @ Y2) => (in @ (kpair @ X1 @ Y2) @ (dpsetconstr @ Y0 @ Y1 @ X2)))))))))) @ X3))) )),
% 0.15/0.33 inference(pi_clausification,[],[f49])).
% 0.15/0.33 thf(f49,plain,(
% 0.15/0.33 ( ! [X2 : $i > $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((X2 @ X1 @ Y2) => (in @ (kpair @ X1 @ Y2) @ (dpsetconstr @ Y0 @ Y1 @ X2))))))))))) = $true)) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f48])).
% 0.15/0.33 thf(f48,plain,(
% 0.15/0.33 ( ! [X2 : $i > $i > $o,X1 : $i] : ((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y0 @ X1 @ Y3) => (in @ (kpair @ X1 @ Y3) @ (dpsetconstr @ Y1 @ Y2 @ Y0)))))))))))) @ X2) = $true)) )),
% 0.15/0.33 inference(pi_clausification,[],[f47])).
% 0.15/0.33 thf(f47,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y0 @ X1 @ Y3) => (in @ (kpair @ X1 @ Y3) @ (dpsetconstr @ Y1 @ Y2 @ Y0))))))))))))))) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f46])).
% 0.15/0.33 thf(f46,plain,(
% 0.15/0.33 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y1 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ Y1)))))))))))))) @ X1))) )),
% 0.15/0.33 inference(pi_clausification,[],[f45])).
% 0.15/0.33 thf(f45,plain,(
% 0.15/0.33 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y1 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ Y1))))))))))))))))),
% 0.15/0.33 inference(beta_eta_normalization,[],[f42])).
% 0.15/0.33 thf(f42,plain,(
% 0.15/0.33 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y1 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6))))))))))))))))))))),
% 0.15/0.33 inference(definition_unfolding,[],[f36,f34])).
% 0.15/0.33 thf(f34,plain,(
% 0.15/0.33 (dpsetconstrI = $true)),
% 0.15/0.33 inference(cnf_transformation,[],[f24])).
% 0.15/0.33 thf(f36,plain,(
% 0.15/0.33 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y1 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6))))))))))))))))))))),
% 0.15/0.33 inference(cnf_transformation,[],[f16])).
% 0.15/0.33 thf(f16,plain,(
% 0.15/0.33 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y1 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6))))))))))))))))))))),
% 0.15/0.33 inference(fool_elimination,[],[f15])).
% 0.15/0.33 thf(f15,plain,(
% 0.15/0.33 (dpsetconstrI = ! [X0,X1,X2 : $i > $i > $o,X3] : ((in @ X3 @ X1) => ! [X4] : ((in @ X4 @ X0) => ((X2 @ X3 @ X4) => (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[X5 : $i, X6 : $i] : (X2 @ X5 @ X6))))))))),
% 0.15/0.33 inference(rectify,[],[f2])).
% 0.15/0.33 thf(f2,axiom,(
% 0.15/0.33 (dpsetconstrI = ! [X1,X0,X3 : $i > $i > $o,X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X1) => ((X3 @ X4 @ X5) => (in @ (kpair @ X4 @ X5) @ (dpsetconstr @ X0 @ X1 @ (^[X6 : $i, X7 : $i] : (X3 @ X6 @ X7))))))))),
% 0.15/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI)).
% 0.15/0.33 thf(f59,plain,(
% 0.15/0.33 ((in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK0 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ (kpair @ Y2 @ Y1) @ sK2) & (in @ (kpair @ Y0 @ Y2) @ sK1)) & (in @ Y2 @ sK0))))))))) != $true)),
% 0.15/0.33 inference(beta_eta_normalization,[],[f40])).
% 0.15/0.33 thf(f40,plain,(
% 0.15/0.33 ($true != (in @ (kpair @ sK3 @ sK4) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y5 @ Y4) @ Y2) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ Y5 @ Y0))))))))))))) @ sK0 @ sK1 @ sK2)))),
% 0.15/0.33 inference(definition_unfolding,[],[f30,f37])).
% 0.15/0.33 thf(f37,plain,(
% 0.15/0.33 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y5 @ Y4) @ Y2) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ Y5 @ Y0))))))))))))))),
% 0.15/0.33 inference(cnf_transformation,[],[f11])).
% 0.15/0.33 thf(f11,plain,(
% 0.15/0.33 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y5 @ Y4) @ Y2) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ Y5 @ Y0))))))))))))))),
% 0.15/0.33 inference(fool_elimination,[],[f10])).
% 0.15/0.33 thf(f10,plain,(
% 0.15/0.33 ((^[X0 : $i, X1 : $i, X2 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X3 : $i, X4 : $i] : (? [X5] : ((in @ X5 @ X0) & (in @ (kpair @ X3 @ X5) @ X1) & (in @ (kpair @ X5 @ X4) @ X2)))))) = breln1compset)),
% 0.15/0.33 inference(rectify,[],[f4])).
% 0.15/0.33 thf(f4,axiom,(
% 0.15/0.33 ((^[X0 : $i, X8 : $i, X9 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X4 : $i, X5 : $i] : (? [X6] : ((in @ X6 @ X0) & (in @ (kpair @ X4 @ X6) @ X8) & (in @ (kpair @ X6 @ X5) @ X9)))))) = breln1compset)),
% 0.15/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compset)).
% 0.15/0.33 thf(f30,plain,(
% 0.15/0.33 ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2)))),
% 0.15/0.33 inference(cnf_transformation,[],[f24])).
% 0.15/0.33 % SZS output end Proof for theBenchmark
% 0.15/0.33 % (23231)------------------------------
% 0.15/0.33 % (23231)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (23231)Termination reason: Refutation
% 0.15/0.33
% 0.15/0.33 % (23231)Memory used [KB]: 5628
% 0.15/0.33 % (23231)Time elapsed: 0.009 s
% 0.15/0.33 % (23231)Instructions burned: 12 (million)
% 0.15/0.33 % (23231)------------------------------
% 0.15/0.33 % (23231)------------------------------
% 0.15/0.33 % (23230)Success in time 0.018 s
% 0.15/0.33 % Vampire---4.8 exiting
%------------------------------------------------------------------------------