TSTP Solution File: SEU611^2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU611^2 : 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/sandbox/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 03:49:58 EDT 2024

% Result   : Theorem 0.22s 0.41s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SEU611^2 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.14  % 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 : n026.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   : Sun May 19 16:16:23 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/sandbox/benchmark/theBenchmark.p
% 0.22/0.39  % (28074)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  % (28077)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.39  % (28075)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)
% 0.22/0.39  % (28076)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  % (28079)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  % (28080)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  % (28078)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)
% 0.22/0.39  % (28077)Instruction limit reached!
% 0.22/0.39  % (28077)------------------------------
% 0.22/0.39  % (28077)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39  % (28077)Termination reason: Unknown
% 0.22/0.39  % (28077)Termination phase: shuffling
% 0.22/0.39  % (28078)Instruction limit reached!
% 0.22/0.39  % (28078)------------------------------
% 0.22/0.39  % (28078)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39  % (28078)Termination reason: Unknown
% 0.22/0.39  % (28078)Termination phase: shuffling
% 0.22/0.39  
% 0.22/0.39  % (28078)Memory used [KB]: 895
% 0.22/0.39  % (28078)Time elapsed: 0.004 s
% 0.22/0.39  % (28078)Instructions burned: 2 (million)
% 0.22/0.39  % (28078)------------------------------
% 0.22/0.39  % (28078)------------------------------
% 0.22/0.39  
% 0.22/0.39  % (28077)Memory used [KB]: 895
% 0.22/0.39  % (28077)Time elapsed: 0.004 s
% 0.22/0.39  % (28077)Instructions burned: 2 (million)
% 0.22/0.39  % (28077)------------------------------
% 0.22/0.39  % (28077)------------------------------
% 0.22/0.39  % (28081)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)
% 0.22/0.40  % (28081)Instruction limit reached!
% 0.22/0.40  % (28081)------------------------------
% 0.22/0.40  % (28081)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40  % (28081)Termination reason: Unknown
% 0.22/0.40  % (28081)Termination phase: Function definition elimination
% 0.22/0.40  % (28075)Instruction limit reached!
% 0.22/0.40  % (28075)------------------------------
% 0.22/0.40  % (28075)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40  % (28075)Termination reason: Unknown
% 0.22/0.40  % (28075)Termination phase: Saturation
% 0.22/0.40  
% 0.22/0.40  % (28075)Memory used [KB]: 5500
% 0.22/0.40  % (28075)Time elapsed: 0.007 s
% 0.22/0.40  % (28075)Instructions burned: 4 (million)
% 0.22/0.40  % (28075)------------------------------
% 0.22/0.40  % (28075)------------------------------
% 0.22/0.40  
% 0.22/0.40  % (28081)Memory used [KB]: 1023
% 0.22/0.40  % (28081)Time elapsed: 0.005 s
% 0.22/0.40  % (28081)Instructions burned: 3 (million)
% 0.22/0.40  % (28081)------------------------------
% 0.22/0.40  % (28081)------------------------------
% 0.22/0.40  % (28079)Refutation not found, incomplete strategy
% 0.22/0.40  % (28079)------------------------------
% 0.22/0.40  % (28079)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40  % (28079)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.40  
% 0.22/0.40  
% 0.22/0.40  % (28079)Memory used [KB]: 5500
% 0.22/0.40  % (28079)Time elapsed: 0.008 s
% 0.22/0.40  % (28079)Instructions burned: 5 (million)
% 0.22/0.40  % (28079)------------------------------
% 0.22/0.40  % (28079)------------------------------
% 0.22/0.40  % (28080)First to succeed.
% 0.22/0.41  % (28076)Also succeeded, but the first one will report.
% 0.22/0.41  % (28080)Refutation found. Thanks to Tanya!
% 0.22/0.41  % SZS status Theorem for theBenchmark
% 0.22/0.41  % SZS output start Proof for theBenchmark
% 0.22/0.41  thf(func_def_0, type, in: $i > $i > $o).
% 0.22/0.41  thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.41  thf(func_def_5, type, binunion: $i > $i > $i).
% 0.22/0.41  thf(func_def_7, type, symdiff: $i > $i > $i).
% 0.22/0.41  thf(func_def_20, type, sK4: $i > $o).
% 0.22/0.41  thf(func_def_25, type, sK9: $i > $o).
% 0.22/0.41  thf(func_def_30, type, ph14: !>[X0: $tType]:(X0)).
% 0.22/0.41  thf(f128,plain,(
% 0.22/0.41    $false),
% 0.22/0.41    inference(avatar_sat_refutation,[],[f84,f86,f103,f113,f116,f124,f127])).
% 0.22/0.41  thf(f127,plain,(
% 0.22/0.41    spl13_1 | ~spl13_4),
% 0.22/0.41    inference(avatar_split_clause,[],[f126,f100,f77])).
% 0.22/0.41  thf(f77,plain,(
% 0.22/0.41    spl13_1 <=> ((in @ sK0 @ sK2) = $true)),
% 0.22/0.41    introduced(avatar_definition,[new_symbols(naming,[spl13_1])])).
% 0.22/0.41  thf(f100,plain,(
% 0.22/0.41    spl13_4 <=> ((in @ sK0 @ sK1) = $false)),
% 0.22/0.41    introduced(avatar_definition,[new_symbols(naming,[spl13_4])])).
% 0.22/0.41  thf(f126,plain,(
% 0.22/0.41    ((in @ sK0 @ sK2) = $true) | ~spl13_4),
% 0.22/0.41    inference(trivial_inequality_removal,[],[f125])).
% 0.22/0.41  thf(f125,plain,(
% 0.22/0.41    ($false = $true) | ((in @ sK0 @ sK2) = $true) | ~spl13_4),
% 0.22/0.41    inference(forward_demodulation,[],[f106,f102])).
% 0.22/0.41  thf(f102,plain,(
% 0.22/0.41    ((in @ sK0 @ sK1) = $false) | ~spl13_4),
% 0.22/0.41    inference(avatar_component_clause,[],[f100])).
% 0.22/0.41  thf(f106,plain,(
% 0.22/0.41    ((in @ sK0 @ sK1) = $true) | ((in @ sK0 @ sK2) = $true)),
% 0.22/0.41    inference(trivial_inequality_removal,[],[f105])).
% 0.22/0.41  thf(f105,plain,(
% 0.22/0.41    ((in @ sK0 @ sK1) = $true) | ($true != $true) | ((in @ sK0 @ sK2) = $true)),
% 0.22/0.41    inference(superposition,[],[f74,f89])).
% 0.22/0.41  thf(f89,plain,(
% 0.22/0.41    ((in @ sK0 @ (binunion @ sK1 @ sK2)) = $true)),
% 0.22/0.41    inference(trivial_inequality_removal,[],[f87])).
% 0.22/0.41  thf(f87,plain,(
% 0.22/0.41    ((in @ sK0 @ (binunion @ sK1 @ sK2)) = $true) | ($true != $true)),
% 0.22/0.41    inference(superposition,[],[f70,f73])).
% 0.22/0.41  thf(f73,plain,(
% 0.22/0.41    ((in @ sK0 @ (dsetconstr @ (binunion @ sK1 @ sK2) @ (^[Y0 : $i]: ((~ (in @ Y0 @ sK1)) | (~ (in @ Y0 @ sK2)))))) = $true)),
% 0.22/0.41    inference(beta_eta_normalization,[],[f58])).
% 0.22/0.41  thf(f58,plain,(
% 0.22/0.41    ($true = (in @ sK0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) | (~ (in @ Y2 @ Y1)))))))) @ sK1 @ sK2)))),
% 0.22/0.41    inference(definition_unfolding,[],[f47,f40])).
% 0.22/0.41  thf(f40,plain,(
% 0.22/0.41    (symdiff = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) | (~ (in @ Y2 @ Y1)))))))))),
% 0.22/0.41    inference(cnf_transformation,[],[f9])).
% 0.22/0.41  thf(f9,plain,(
% 0.22/0.41    (symdiff = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) | (~ (in @ Y2 @ Y1)))))))))),
% 0.22/0.41    inference(fool_elimination,[],[f8])).
% 0.22/0.41  thf(f8,plain,(
% 0.22/0.41    (symdiff = (^[X0 : $i, X1 : $i] : (dsetconstr @ (binunion @ X0 @ X1) @ (^[X2 : $i] : (~(in @ X2 @ X1) | ~(in @ X2 @ X0))))))),
% 0.22/0.41    inference(rectify,[],[f4])).
% 0.22/0.41  thf(f4,axiom,(
% 0.22/0.41    (symdiff = (^[X0 : $i, X4 : $i] : (dsetconstr @ (binunion @ X0 @ X4) @ (^[X2 : $i] : (~(in @ X2 @ X4) | ~(in @ X2 @ X0))))))),
% 0.22/0.41    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiff)).
% 0.22/0.41  thf(f47,plain,(
% 0.22/0.41    ((in @ sK0 @ (symdiff @ sK1 @ sK2)) = $true)),
% 0.22/0.41    inference(cnf_transformation,[],[f27])).
% 0.22/0.41  thf(f27,plain,(
% 0.22/0.41    (((in @ sK0 @ (symdiff @ sK1 @ sK2)) = $true) & ((((in @ sK0 @ sK1) != $true) | (sK3 = $true) | ((in @ sK0 @ sK2) = $true)) & (((in @ sK0 @ sK1) = $true) | (sK3 = $true) | ((in @ sK0 @ sK2) != $true)) & (sK3 != $true))) & (dsetconstrEL = $true) & (binunionE = $true) & (dsetconstrER = $true)),
% 0.22/0.41    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f26,f25])).
% 0.22/0.41  thf(f25,plain,(
% 0.22/0.41    ? [X0,X1,X2] : (($true = (in @ X0 @ (symdiff @ X1 @ X2))) & ? [X3 : $o] : ((((in @ X0 @ X1) != $true) | ($true = X3) | ((in @ X0 @ X2) = $true)) & (((in @ X0 @ X1) = $true) | ($true = X3) | ((in @ X0 @ X2) != $true)) & ($true != X3))) => (((in @ sK0 @ (symdiff @ sK1 @ sK2)) = $true) & ? [X3 : $o] : ((((in @ sK0 @ sK1) != $true) | ($true = X3) | ((in @ sK0 @ sK2) = $true)) & (((in @ sK0 @ sK1) = $true) | ($true = X3) | ((in @ sK0 @ sK2) != $true)) & ($true != X3)))),
% 0.22/0.41    introduced(choice_axiom,[])).
% 0.22/0.41  thf(f26,plain,(
% 0.22/0.41    ? [X3 : $o] : ((((in @ sK0 @ sK1) != $true) | ($true = X3) | ((in @ sK0 @ sK2) = $true)) & (((in @ sK0 @ sK1) = $true) | ($true = X3) | ((in @ sK0 @ sK2) != $true)) & ($true != X3)) => ((((in @ sK0 @ sK1) != $true) | (sK3 = $true) | ((in @ sK0 @ sK2) = $true)) & (((in @ sK0 @ sK1) = $true) | (sK3 = $true) | ((in @ sK0 @ sK2) != $true)) & (sK3 != $true))),
% 0.22/0.41    introduced(choice_axiom,[])).
% 0.22/0.41  thf(f20,plain,(
% 0.22/0.41    ? [X0,X1,X2] : (($true = (in @ X0 @ (symdiff @ X1 @ X2))) & ? [X3 : $o] : ((((in @ X0 @ X1) != $true) | ($true = X3) | ((in @ X0 @ X2) = $true)) & (((in @ X0 @ X1) = $true) | ($true = X3) | ((in @ X0 @ X2) != $true)) & ($true != X3))) & (dsetconstrEL = $true) & (binunionE = $true) & (dsetconstrER = $true)),
% 0.22/0.41    inference(flattening,[],[f19])).
% 0.22/0.41  thf(f19,plain,(
% 0.22/0.41    ((? [X0,X1,X2] : (? [X3 : $o] : ((($true != X3) & ((($true = X3) | ((in @ X0 @ X2) != $true)) | ((in @ X0 @ X1) = $true))) & ((($true = X3) | ((in @ X0 @ X2) = $true)) | ((in @ X0 @ X1) != $true))) & ($true = (in @ X0 @ (symdiff @ X1 @ X2)))) & (binunionE = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)),
% 0.22/0.41    inference(ennf_transformation,[],[f18])).
% 0.22/0.41  thf(f18,plain,(
% 0.22/0.41    ~((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((binunionE = $true) => ! [X0,X1,X2] : (($true = (in @ X0 @ (symdiff @ X1 @ X2))) => ! [X3 : $o] : ((((in @ X0 @ X1) = $true) => (((in @ X0 @ X2) != $true) => ($true = X3))) => ((((in @ X0 @ X1) != $true) => (((in @ X0 @ X2) = $true) => ($true = X3))) => ($true = X3)))))))),
% 0.22/0.41    inference(flattening,[],[f17])).
% 0.22/0.41  thf(f17,plain,(
% 0.22/0.41    ~((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((binunionE = $true) => ! [X0,X1,X2] : (($true = (in @ X0 @ (symdiff @ X1 @ X2))) => ! [X3 : $o] : ((((in @ X0 @ X1) = $true) => (~((in @ X0 @ X2) = $true) => ($true = X3))) => ((~((in @ X0 @ X1) = $true) => (((in @ X0 @ X2) = $true) => ($true = X3))) => ($true = X3)))))))),
% 0.22/0.41    inference(fool_elimination,[],[f16])).
% 0.22/0.41  thf(f16,plain,(
% 0.22/0.41    ~(dsetconstrEL => (dsetconstrER => (binunionE => ! [X0,X1,X2] : ((in @ X0 @ (symdiff @ X1 @ X2)) => ! [X3 : $o] : (((in @ X0 @ X1) => (~(in @ X0 @ X2) => X3)) => ((~(in @ X0 @ X1) => ((in @ X0 @ X2) => X3)) => X3))))))),
% 0.22/0.41    inference(rectify,[],[f6])).
% 0.22/0.41  thf(f6,negated_conjecture,(
% 0.22/0.41    ~(dsetconstrEL => (dsetconstrER => (binunionE => ! [X2,X0,X4] : ((in @ X2 @ (symdiff @ X0 @ X4)) => ! [X1 : $o] : (((in @ X2 @ X0) => (~(in @ X2 @ X4) => X1)) => ((~(in @ X2 @ X0) => ((in @ X2 @ X4) => X1)) => X1))))))),
% 0.22/0.41    inference(negated_conjecture,[],[f5])).
% 0.22/0.41  thf(f5,conjecture,(
% 0.22/0.41    dsetconstrEL => (dsetconstrER => (binunionE => ! [X2,X0,X4] : ((in @ X2 @ (symdiff @ X0 @ X4)) => ! [X1 : $o] : (((in @ X2 @ X0) => (~(in @ X2 @ X4) => X1)) => ((~(in @ X2 @ X0) => ((in @ X2 @ X4) => X1)) => X1)))))),
% 0.22/0.41    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE)).
% 0.22/0.41  thf(f70,plain,(
% 0.22/0.41    ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X4 @ (dsetconstr @ X5 @ X3)) != $true) | ($true = (in @ X4 @ X5))) )),
% 0.22/0.41    inference(beta_eta_normalization,[],[f69])).
% 0.22/0.41  thf(f69,plain,(
% 0.22/0.41    ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true) | ($true = (in @ X4 @ X5))) )),
% 0.22/0.41    inference(trivial_inequality_removal,[],[f61])).
% 0.22/0.41  thf(f61,plain,(
% 0.22/0.41    ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (($true != $true) | ($true = (in @ X4 @ X5)) | ((in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true)) )),
% 0.22/0.41    inference(definition_unfolding,[],[f48,f43])).
% 0.22/0.41  thf(f43,plain,(
% 0.22/0.41    (dsetconstrEL = $true)),
% 0.22/0.41    inference(cnf_transformation,[],[f27])).
% 0.22/0.41  thf(f48,plain,(
% 0.22/0.41    ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (($true = (in @ X4 @ X5)) | ((in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true) | (dsetconstrEL != $true)) )),
% 0.22/0.41    inference(cnf_transformation,[],[f31])).
% 0.22/0.41  thf(f31,plain,(
% 0.22/0.41    ((dsetconstrEL = $true) | (($true != (in @ sK5 @ sK6)) & ($true = (in @ sK5 @ (dsetconstr @ sK6 @ (^[Y0 : $i]: (sK4 @ Y0))))))) & (! [X3 : $i > $o,X4,X5] : (($true = (in @ X4 @ X5)) | ((in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true)) | (dsetconstrEL != $true))),
% 0.22/0.41    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f29,f30])).
% 0.22/0.41  thf(f30,plain,(
% 0.22/0.41    ? [X0 : $i > $o,X1,X2] : (((in @ X1 @ X2) != $true) & ($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) => (($true != (in @ sK5 @ sK6)) & ($true = (in @ sK5 @ (dsetconstr @ sK6 @ (^[Y0 : $i]: (sK4 @ Y0))))))),
% 0.22/0.41    introduced(choice_axiom,[])).
% 0.22/0.41  thf(f29,plain,(
% 0.22/0.41    ((dsetconstrEL = $true) | ? [X0 : $i > $o,X1,X2] : (((in @ X1 @ X2) != $true) & ($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))))) & (! [X3 : $i > $o,X4,X5] : (($true = (in @ X4 @ X5)) | ((in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true)) | (dsetconstrEL != $true))),
% 0.22/0.41    inference(rectify,[],[f28])).
% 0.22/0.41  thf(f28,plain,(
% 0.22/0.41    ((dsetconstrEL = $true) | ? [X0 : $i > $o,X1,X2] : (((in @ X1 @ X2) != $true) & ($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))))) & (! [X0 : $i > $o,X1,X2] : (((in @ X1 @ X2) = $true) | ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) | (dsetconstrEL != $true))),
% 0.22/0.41    inference(nnf_transformation,[],[f21])).
% 0.22/0.41  thf(f21,plain,(
% 0.22/0.41    (dsetconstrEL = $true) <=> ! [X0 : $i > $o,X1,X2] : (((in @ X1 @ X2) = $true) | ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))))),
% 0.22/0.41    inference(ennf_transformation,[],[f11])).
% 0.22/0.41  thf(f11,plain,(
% 0.22/0.41    (dsetconstrEL = $true) <=> ! [X0 : $i > $o,X1,X2] : (($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) => ((in @ X1 @ X2) = $true))),
% 0.22/0.41    inference(fool_elimination,[],[f10])).
% 0.22/0.41  thf(f10,plain,(
% 0.22/0.41    (dsetconstrEL = ! [X0 : $i > $o,X1,X2] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))) => (in @ X1 @ X2)))),
% 0.22/0.41    inference(rectify,[],[f1])).
% 0.22/0.41  thf(f1,axiom,(
% 0.22/0.41    (dsetconstrEL = ! [X1 : $i > $o,X2,X0] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)))),
% 0.22/0.41    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL)).
% 0.22/0.41  thf(f74,plain,(
% 0.22/0.41    ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binunion @ X5 @ X4)) != $true) | ((in @ X3 @ X5) = $true) | ((in @ X3 @ X4) = $true)) )),
% 0.22/0.41    inference(trivial_inequality_removal,[],[f68])).
% 0.22/0.41  thf(f68,plain,(
% 0.22/0.41    ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ((in @ X3 @ X5) = $true) | ($true != $true) | ((in @ X3 @ (binunion @ X5 @ X4)) != $true)) )),
% 0.22/0.41    inference(definition_unfolding,[],[f54,f42])).
% 0.22/0.41  thf(f42,plain,(
% 0.22/0.41    (binunionE = $true)),
% 0.22/0.41    inference(cnf_transformation,[],[f27])).
% 0.22/0.41  thf(f54,plain,(
% 0.22/0.41    ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) = $true) | ((in @ X3 @ (binunion @ X5 @ X4)) != $true) | ((in @ X3 @ X4) = $true) | (binunionE != $true)) )),
% 0.22/0.41    inference(cnf_transformation,[],[f39])).
% 0.22/0.41  thf(f39,plain,(
% 0.22/0.41    ((binunionE = $true) | (((in @ sK10 @ sK12) != $true) & ($true = (in @ sK10 @ (binunion @ sK12 @ sK11))) & ((in @ sK10 @ sK11) != $true))) & (! [X3,X4,X5] : (((in @ X3 @ X5) = $true) | ((in @ X3 @ (binunion @ X5 @ X4)) != $true) | ((in @ X3 @ X4) = $true)) | (binunionE != $true))),
% 0.22/0.41    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f37,f38])).
% 0.22/0.41  thf(f38,plain,(
% 0.22/0.41    ? [X0,X1,X2] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ (binunion @ X2 @ X1)) = $true) & ((in @ X0 @ X1) != $true)) => (((in @ sK10 @ sK12) != $true) & ($true = (in @ sK10 @ (binunion @ sK12 @ sK11))) & ((in @ sK10 @ sK11) != $true))),
% 0.22/0.41    introduced(choice_axiom,[])).
% 0.22/0.41  thf(f37,plain,(
% 0.22/0.41    ((binunionE = $true) | ? [X0,X1,X2] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ (binunion @ X2 @ X1)) = $true) & ((in @ X0 @ X1) != $true))) & (! [X3,X4,X5] : (((in @ X3 @ X5) = $true) | ((in @ X3 @ (binunion @ X5 @ X4)) != $true) | ((in @ X3 @ X4) = $true)) | (binunionE != $true))),
% 0.22/0.41    inference(rectify,[],[f36])).
% 0.22/0.41  thf(f36,plain,(
% 0.22/0.41    ((binunionE = $true) | ? [X0,X1,X2] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ (binunion @ X2 @ X1)) = $true) & ((in @ X0 @ X1) != $true))) & (! [X0,X1,X2] : (((in @ X0 @ X2) = $true) | ((in @ X0 @ (binunion @ X2 @ X1)) != $true) | ((in @ X0 @ X1) = $true)) | (binunionE != $true))),
% 0.22/0.41    inference(nnf_transformation,[],[f24])).
% 0.22/0.41  thf(f24,plain,(
% 0.22/0.41    (binunionE = $true) <=> ! [X0,X1,X2] : (((in @ X0 @ X2) = $true) | ((in @ X0 @ (binunion @ X2 @ X1)) != $true) | ((in @ X0 @ X1) = $true))),
% 0.22/0.41    inference(flattening,[],[f23])).
% 0.22/0.41  thf(f23,plain,(
% 0.22/0.41    (binunionE = $true) <=> ! [X0,X1,X2] : ((((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) = $true)) | ((in @ X0 @ (binunion @ X2 @ X1)) != $true))),
% 0.22/0.41    inference(ennf_transformation,[],[f13])).
% 0.22/0.41  thf(f13,plain,(
% 0.22/0.41    (binunionE = $true) <=> ! [X0,X1,X2] : (((in @ X0 @ (binunion @ X2 @ X1)) = $true) => (((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) = $true)))),
% 0.22/0.41    inference(fool_elimination,[],[f12])).
% 0.22/0.41  thf(f12,plain,(
% 0.22/0.41    (binunionE = ! [X0,X1,X2] : ((in @ X0 @ (binunion @ X2 @ X1)) => ((in @ X0 @ X2) | (in @ X0 @ X1))))),
% 0.22/0.41    inference(rectify,[],[f3])).
% 0.22/0.41  thf(f3,axiom,(
% 0.22/0.41    (binunionE = ! [X2,X4,X0] : ((in @ X2 @ (binunion @ X0 @ X4)) => ((in @ X2 @ X0) | (in @ X2 @ X4))))),
% 0.22/0.41    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE)).
% 0.22/0.41  thf(f124,plain,(
% 0.22/0.41    ~spl13_2 | ~spl13_4),
% 0.22/0.41    inference(avatar_contradiction_clause,[],[f123])).
% 0.22/0.41  thf(f123,plain,(
% 0.22/0.41    $false | (~spl13_2 | ~spl13_4)),
% 0.22/0.41    inference(trivial_inequality_removal,[],[f122])).
% 0.22/0.41  thf(f122,plain,(
% 0.22/0.41    ($false = $true) | (~spl13_2 | ~spl13_4)),
% 0.22/0.41    inference(forward_demodulation,[],[f82,f102])).
% 0.22/0.41  thf(f82,plain,(
% 0.22/0.41    ((in @ sK0 @ sK1) = $true) | ~spl13_2),
% 0.22/0.41    inference(avatar_component_clause,[],[f81])).
% 0.22/0.41  thf(f81,plain,(
% 0.22/0.41    spl13_2 <=> ((in @ sK0 @ sK1) = $true)),
% 0.22/0.41    introduced(avatar_definition,[new_symbols(naming,[spl13_2])])).
% 0.22/0.41  thf(f116,plain,(
% 0.22/0.41    ~spl13_1 | ~spl13_3),
% 0.22/0.41    inference(avatar_contradiction_clause,[],[f115])).
% 0.22/0.41  thf(f115,plain,(
% 0.22/0.41    $false | (~spl13_1 | ~spl13_3)),
% 0.22/0.41    inference(trivial_inequality_removal,[],[f114])).
% 0.22/0.41  thf(f114,plain,(
% 0.22/0.41    ($false = $true) | (~spl13_1 | ~spl13_3)),
% 0.22/0.41    inference(forward_demodulation,[],[f79,f98])).
% 0.22/0.41  thf(f98,plain,(
% 0.22/0.41    ((in @ sK0 @ sK2) = $false) | ~spl13_3),
% 0.22/0.41    inference(avatar_component_clause,[],[f96])).
% 0.22/0.41  thf(f96,plain,(
% 0.22/0.41    spl13_3 <=> ((in @ sK0 @ sK2) = $false)),
% 0.22/0.41    introduced(avatar_definition,[new_symbols(naming,[spl13_3])])).
% 0.22/0.41  thf(f79,plain,(
% 0.22/0.41    ((in @ sK0 @ sK2) = $true) | ~spl13_1),
% 0.22/0.41    inference(avatar_component_clause,[],[f77])).
% 0.22/0.41  thf(f113,plain,(
% 0.22/0.41    spl13_2 | ~spl13_3),
% 0.22/0.41    inference(avatar_split_clause,[],[f112,f96,f81])).
% 0.22/0.41  thf(f112,plain,(
% 0.22/0.41    ((in @ sK0 @ sK1) = $true) | ~spl13_3),
% 0.22/0.41    inference(trivial_inequality_removal,[],[f111])).
% 0.22/0.41  thf(f111,plain,(
% 0.22/0.41    ((in @ sK0 @ sK1) = $true) | ($false = $true) | ~spl13_3),
% 0.22/0.41    inference(forward_demodulation,[],[f106,f98])).
% 0.22/0.41  thf(f103,plain,(
% 0.22/0.41    spl13_3 | spl13_4),
% 0.22/0.41    inference(avatar_split_clause,[],[f94,f100,f96])).
% 0.22/0.41  thf(f94,plain,(
% 0.22/0.41    ((in @ sK0 @ sK2) = $false) | ((in @ sK0 @ sK1) = $false)),
% 0.22/0.41    inference(not_proxy_clausification,[],[f93])).
% 0.22/0.41  thf(f93,plain,(
% 0.22/0.41    ((in @ sK0 @ sK1) = $false) | ((~ (in @ sK0 @ sK2)) = $true)),
% 0.22/0.41    inference(not_proxy_clausification,[],[f92])).
% 0.22/0.41  thf(f92,plain,(
% 0.22/0.41    ((~ (in @ sK0 @ sK1)) = $true) | ((~ (in @ sK0 @ sK2)) = $true)),
% 0.22/0.41    inference(binary_proxy_clausification,[],[f91])).
% 0.22/0.41  thf(f91,plain,(
% 0.22/0.41    (((~ (in @ sK0 @ sK1)) | (~ (in @ sK0 @ sK2))) = $true)),
% 0.22/0.41    inference(beta_eta_normalization,[],[f90])).
% 0.22/0.41  thf(f90,plain,(
% 0.22/0.41    (((^[Y0 : $i]: ((~ (in @ Y0 @ sK1)) | (~ (in @ Y0 @ sK2)))) @ sK0) = $true)),
% 0.22/0.41    inference(trivial_inequality_removal,[],[f88])).
% 0.22/0.41  thf(f88,plain,(
% 0.22/0.41    ($true != $true) | (((^[Y0 : $i]: ((~ (in @ Y0 @ sK1)) | (~ (in @ Y0 @ sK2)))) @ sK0) = $true)),
% 0.22/0.41    inference(superposition,[],[f72,f73])).
% 0.22/0.41  thf(f72,plain,(
% 0.22/0.41    ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((in @ X0 @ (dsetconstr @ X1 @ X2)) != $true) | ($true = (X2 @ X0))) )),
% 0.22/0.41    inference(beta_eta_normalization,[],[f71])).
% 0.22/0.41  thf(f71,plain,(
% 0.22/0.41    ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true = (X2 @ X0)) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) )),
% 0.22/0.41    inference(trivial_inequality_removal,[],[f62])).
% 0.22/0.41  thf(f62,plain,(
% 0.22/0.41    ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true = (X2 @ X0)) | ($true != $true) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) )),
% 0.22/0.41    inference(definition_unfolding,[],[f53,f41])).
% 0.22/0.41  thf(f41,plain,(
% 0.22/0.41    (dsetconstrER = $true)),
% 0.22/0.41    inference(cnf_transformation,[],[f27])).
% 0.22/0.41  thf(f53,plain,(
% 0.22/0.41    ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true = (X2 @ X0)) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) | (dsetconstrER != $true)) )),
% 0.22/0.41    inference(cnf_transformation,[],[f35])).
% 0.22/0.41  thf(f35,plain,(
% 0.22/0.41    (! [X0,X1,X2 : $i > $o] : (($true = (X2 @ X0)) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | (((sK9 @ sK7) != $true) & ((in @ sK7 @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (sK9 @ Y0)))) = $true)))),
% 0.22/0.41    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f33,f34])).
% 0.22/0.41  thf(f34,plain,(
% 0.22/0.41    ? [X3,X4,X5 : $i > $o] : (((X5 @ X3) != $true) & ((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true)) => (((sK9 @ sK7) != $true) & ((in @ sK7 @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (sK9 @ Y0)))) = $true))),
% 0.22/0.41    introduced(choice_axiom,[])).
% 0.22/0.41  thf(f33,plain,(
% 0.22/0.41    (! [X0,X1,X2 : $i > $o] : (($true = (X2 @ X0)) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X3,X4,X5 : $i > $o] : (((X5 @ X3) != $true) & ((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true)))),
% 0.22/0.41    inference(rectify,[],[f32])).
% 0.22/0.41  thf(f32,plain,(
% 0.22/0.41    (! [X0,X1,X2 : $i > $o] : (($true = (X2 @ X0)) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X0,X1,X2 : $i > $o] : (($true != (X2 @ X0)) & ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true)))),
% 0.22/0.41    inference(nnf_transformation,[],[f22])).
% 0.22/0.41  thf(f22,plain,(
% 0.22/0.41    ! [X0,X1,X2 : $i > $o] : (($true = (X2 @ X0)) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) <=> (dsetconstrER = $true)),
% 0.22/0.41    inference(ennf_transformation,[],[f15])).
% 0.22/0.41  thf(f15,plain,(
% 0.22/0.41    (dsetconstrER = $true) <=> ! [X0,X1,X2 : $i > $o] : (((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) => ($true = (X2 @ X0)))),
% 0.22/0.41    inference(fool_elimination,[],[f14])).
% 0.22/0.41  thf(f14,plain,(
% 0.22/0.41    (dsetconstrER = ! [X0,X1,X2 : $i > $o] : ((in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))) => (X2 @ X0)))),
% 0.22/0.41    inference(rectify,[],[f2])).
% 0.22/0.41  thf(f2,axiom,(
% 0.22/0.41    (dsetconstrER = ! [X2,X0,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)))),
% 0.22/0.41    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER)).
% 0.22/0.41  thf(f86,plain,(
% 0.22/0.41    spl13_2 | ~spl13_1),
% 0.22/0.41    inference(avatar_split_clause,[],[f85,f77,f81])).
% 0.22/0.41  thf(f85,plain,(
% 0.22/0.41    ((in @ sK0 @ sK1) = $true) | ((in @ sK0 @ sK2) != $true)),
% 0.22/0.41    inference(subsumption_resolution,[],[f45,f44])).
% 0.22/0.41  thf(f44,plain,(
% 0.22/0.41    (sK3 != $true)),
% 0.22/0.41    inference(cnf_transformation,[],[f27])).
% 0.22/0.41  thf(f45,plain,(
% 0.22/0.41    ((in @ sK0 @ sK2) != $true) | ((in @ sK0 @ sK1) = $true) | (sK3 = $true)),
% 0.22/0.41    inference(cnf_transformation,[],[f27])).
% 0.22/0.41  thf(f84,plain,(
% 0.22/0.41    spl13_1 | ~spl13_2),
% 0.22/0.41    inference(avatar_split_clause,[],[f75,f81,f77])).
% 0.22/0.41  thf(f75,plain,(
% 0.22/0.41    ((in @ sK0 @ sK1) != $true) | ((in @ sK0 @ sK2) = $true)),
% 0.22/0.41    inference(subsumption_resolution,[],[f46,f44])).
% 0.22/0.41  thf(f46,plain,(
% 0.22/0.41    ((in @ sK0 @ sK2) = $true) | (sK3 = $true) | ((in @ sK0 @ sK1) != $true)),
% 0.22/0.41    inference(cnf_transformation,[],[f27])).
% 0.22/0.41  % SZS output end Proof for theBenchmark
% 0.22/0.41  % (28080)------------------------------
% 0.22/0.41  % (28080)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41  % (28080)Termination reason: Refutation
% 0.22/0.41  
% 0.22/0.41  % (28080)Memory used [KB]: 5628
% 0.22/0.41  % (28080)Time elapsed: 0.017 s
% 0.22/0.41  % (28080)Instructions burned: 7 (million)
% 0.22/0.41  % (28080)------------------------------
% 0.22/0.41  % (28080)------------------------------
% 0.22/0.41  % (28073)Success in time 0.04 s
% 0.22/0.41  % Vampire---4.8 exiting
%------------------------------------------------------------------------------