TSTP Solution File: SEU811^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU811^2 : 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 : n017.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 03:51:44 EDT 2024
% Result : Theorem 0.11s 0.36s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU811^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.12 % 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
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Sun May 19 16:31:08 EDT 2024
% 0.11/0.34 % CPUTime :
% 0.11/0.34 This is a TH0_THM_EQU_NAR problem
% 0.11/0.34 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
% 0.11/0.36 % (13955)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)
% 0.11/0.36 % (13957)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.36 % (13956)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)
% 0.11/0.36 % (13958)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)
% 0.11/0.36 % (13959)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)
% 0.11/0.36 % (13961)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)
% 0.11/0.36 % (13960)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.36 % (13957)Instruction limit reached!
% 0.11/0.36 % (13957)------------------------------
% 0.11/0.36 % (13957)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36 % (13957)Termination reason: Unknown
% 0.11/0.36 % (13957)Termination phase: Property scanning
% 0.11/0.36 % (13958)Instruction limit reached!
% 0.11/0.36 % (13958)------------------------------
% 0.11/0.36 % (13958)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36
% 0.11/0.36 % (13957)Memory used [KB]: 1023
% 0.11/0.36 % (13957)Time elapsed: 0.003 s
% 0.11/0.36 % (13957)Instructions burned: 3 (million)
% 0.11/0.36 % (13957)------------------------------
% 0.11/0.36 % (13957)------------------------------
% 0.11/0.36 % (13958)Termination reason: Unknown
% 0.11/0.36 % (13958)Termination phase: Property scanning
% 0.11/0.36
% 0.11/0.36 % (13958)Memory used [KB]: 1023
% 0.11/0.36 % (13958)Time elapsed: 0.003 s
% 0.11/0.36 % (13958)Instructions burned: 3 (million)
% 0.11/0.36 % (13958)------------------------------
% 0.11/0.36 % (13958)------------------------------
% 0.11/0.36 % (13961)Instruction limit reached!
% 0.11/0.36 % (13961)------------------------------
% 0.11/0.36 % (13961)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36 % (13961)Termination reason: Unknown
% 0.11/0.36 % (13961)Termination phase: Property scanning
% 0.11/0.36
% 0.11/0.36 % (13961)Memory used [KB]: 1023
% 0.11/0.36 % (13961)Time elapsed: 0.003 s
% 0.11/0.36 % (13961)Instructions burned: 3 (million)
% 0.11/0.36 % (13961)------------------------------
% 0.11/0.36 % (13961)------------------------------
% 0.11/0.36 % (13955)Instruction limit reached!
% 0.11/0.36 % (13955)------------------------------
% 0.11/0.36 % (13955)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36 % (13955)Termination reason: Unknown
% 0.11/0.36 % (13955)Termination phase: Saturation
% 0.11/0.36
% 0.11/0.36 % (13955)Memory used [KB]: 5500
% 0.11/0.36 % (13955)Time elapsed: 0.004 s
% 0.11/0.36 % (13955)Instructions burned: 4 (million)
% 0.11/0.36 % (13955)------------------------------
% 0.11/0.36 % (13955)------------------------------
% 0.11/0.36 % (13954)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.36 % (13959)Refutation not found, incomplete strategy
% 0.11/0.36 % (13959)------------------------------
% 0.11/0.36 % (13959)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36 % (13959)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.36
% 0.11/0.36
% 0.11/0.36 % (13959)Memory used [KB]: 5500
% 0.11/0.36 % (13959)Time elapsed: 0.005 s
% 0.11/0.36 % (13959)Instructions burned: 4 (million)
% 0.11/0.36 % (13959)------------------------------
% 0.11/0.36 % (13959)------------------------------
% 0.11/0.36 % (13960)First to succeed.
% 0.11/0.36 % (13960)Refutation found. Thanks to Tanya!
% 0.11/0.36 % SZS status Theorem for theBenchmark
% 0.11/0.36 % SZS output start Proof for theBenchmark
% 0.11/0.36 thf(func_def_0, type, in: $i > $i > $o).
% 0.11/0.36 thf(func_def_1, type, setadjoin: $i > $i > $i).
% 0.11/0.36 thf(func_def_8, type, omegaS: $i > $i).
% 0.11/0.36 thf(f124,plain,(
% 0.11/0.36 $false),
% 0.11/0.36 inference(subsumption_resolution,[],[f123,f119])).
% 0.11/0.36 thf(f119,plain,(
% 0.11/0.36 ($true != (in @ sK0 @ sK1))),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f118])).
% 0.11/0.36 thf(f118,plain,(
% 0.11/0.36 ($true != $true) | ($true != (in @ sK0 @ sK1))),
% 0.11/0.36 inference(superposition,[],[f101,f117])).
% 0.11/0.36 thf(f117,plain,(
% 0.11/0.36 ($true = (in @ sK1 @ sK0))),
% 0.11/0.36 inference(subsumption_resolution,[],[f116,f49])).
% 0.11/0.36 thf(f49,plain,(
% 0.11/0.36 (sK0 != sK1)),
% 0.11/0.36 inference(cnf_transformation,[],[f29])).
% 0.11/0.36 thf(f29,plain,(
% 0.11/0.36 (notinself2 = $true) & (in__Cong = $true) & (setadjoinIL = $true) & (setadjoinE = $true) & (($true = (in @ sK0 @ omega)) & (($true = (in @ sK1 @ omega)) & (sK0 != sK1) & ((omegaS @ sK1) = (omegaS @ sK0))))),
% 0.11/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f24,f28,f27])).
% 0.11/0.36 thf(f27,plain,(
% 0.11/0.36 ? [X0] : (((in @ X0 @ omega) = $true) & ? [X1] : (((in @ X1 @ omega) = $true) & (X0 != X1) & ((omegaS @ X0) = (omegaS @ X1)))) => (($true = (in @ sK0 @ omega)) & ? [X1] : (((in @ X1 @ omega) = $true) & (sK0 != X1) & ((omegaS @ X1) = (omegaS @ sK0))))),
% 0.11/0.36 introduced(choice_axiom,[])).
% 0.11/0.36 thf(f28,plain,(
% 0.11/0.36 ? [X1] : (((in @ X1 @ omega) = $true) & (sK0 != X1) & ((omegaS @ X1) = (omegaS @ sK0))) => (($true = (in @ sK1 @ omega)) & (sK0 != sK1) & ((omegaS @ sK1) = (omegaS @ sK0)))),
% 0.11/0.36 introduced(choice_axiom,[])).
% 0.11/0.36 thf(f24,plain,(
% 0.11/0.36 (notinself2 = $true) & (in__Cong = $true) & (setadjoinIL = $true) & (setadjoinE = $true) & ? [X0] : (((in @ X0 @ omega) = $true) & ? [X1] : (((in @ X1 @ omega) = $true) & (X0 != X1) & ((omegaS @ X0) = (omegaS @ X1))))),
% 0.11/0.36 inference(flattening,[],[f23])).
% 0.11/0.36 thf(f23,plain,(
% 0.11/0.36 (((? [X0] : (? [X1] : (((X0 != X1) & ((omegaS @ X0) = (omegaS @ X1))) & ((in @ X1 @ omega) = $true)) & ((in @ X0 @ omega) = $true)) & (notinself2 = $true)) & (in__Cong = $true)) & (setadjoinE = $true)) & (setadjoinIL = $true)),
% 0.11/0.36 inference(ennf_transformation,[],[f19])).
% 0.11/0.36 thf(f19,plain,(
% 0.11/0.36 ~((setadjoinIL = $true) => ((setadjoinE = $true) => ((in__Cong = $true) => ((notinself2 = $true) => ! [X0] : (((in @ X0 @ omega) = $true) => ! [X1] : (((in @ X1 @ omega) = $true) => (((omegaS @ X0) = (omegaS @ X1)) => (X0 = X1))))))))),
% 0.11/0.36 inference(fool_elimination,[],[f18])).
% 0.11/0.36 thf(f18,plain,(
% 0.11/0.36 ~(setadjoinIL => (setadjoinE => (in__Cong => (notinself2 => ! [X0] : ((in @ X0 @ omega) => ! [X1] : ((in @ X1 @ omega) => (((omegaS @ X0) = (omegaS @ X1)) => (X0 = X1))))))))),
% 0.11/0.36 inference(rectify,[],[f7])).
% 0.11/0.36 thf(f7,negated_conjecture,(
% 0.11/0.36 ~(setadjoinIL => (setadjoinE => (in__Cong => (notinself2 => ! [X0] : ((in @ X0 @ omega) => ! [X1] : ((in @ X1 @ omega) => (((omegaS @ X0) = (omegaS @ X1)) => (X0 = X1))))))))),
% 0.11/0.36 inference(negated_conjecture,[],[f6])).
% 0.11/0.36 thf(f6,conjecture,(
% 0.11/0.36 setadjoinIL => (setadjoinE => (in__Cong => (notinself2 => ! [X0] : ((in @ X0 @ omega) => ! [X1] : ((in @ X1 @ omega) => (((omegaS @ X0) = (omegaS @ X1)) => (X0 = X1)))))))),
% 0.11/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',peanoSinj)).
% 0.11/0.36 thf(f116,plain,(
% 0.11/0.36 (sK0 = sK1) | ($true = (in @ sK1 @ sK0))),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f115])).
% 0.11/0.36 thf(f115,plain,(
% 0.11/0.36 ($true != $true) | (sK0 = sK1) | ($true = (in @ sK1 @ sK0))),
% 0.11/0.36 inference(superposition,[],[f100,f103])).
% 0.11/0.36 thf(f103,plain,(
% 0.11/0.36 ($true = (in @ sK1 @ (setadjoin @ sK0 @ sK0)))),
% 0.11/0.36 inference(superposition,[],[f98,f102])).
% 0.11/0.36 thf(f102,plain,(
% 0.11/0.36 ((setadjoin @ sK1 @ sK1) = (setadjoin @ sK0 @ sK0))),
% 0.11/0.36 inference(beta_eta_normalization,[],[f74])).
% 0.11/0.36 thf(f74,plain,(
% 0.11/0.36 (((^[Y0 : $i]: (setadjoin @ Y0 @ Y0)) @ sK0) = ((^[Y0 : $i]: (setadjoin @ Y0 @ Y0)) @ sK1))),
% 0.11/0.36 inference(definition_unfolding,[],[f48,f61,f61])).
% 0.11/0.36 thf(f61,plain,(
% 0.11/0.36 (omegaS = (^[Y0 : $i]: (setadjoin @ Y0 @ Y0)))),
% 0.11/0.36 inference(cnf_transformation,[],[f15])).
% 0.11/0.36 thf(f15,plain,(
% 0.11/0.36 (omegaS = (^[Y0 : $i]: (setadjoin @ Y0 @ Y0)))),
% 0.11/0.36 inference(fool_elimination,[],[f5])).
% 0.11/0.36 thf(f5,axiom,(
% 0.11/0.36 (omegaS = (^[X0 : $i] : (setadjoin @ X0 @ X0)))),
% 0.11/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaS)).
% 0.11/0.36 thf(f48,plain,(
% 0.11/0.36 ((omegaS @ sK1) = (omegaS @ sK0))),
% 0.11/0.36 inference(cnf_transformation,[],[f29])).
% 0.11/0.36 thf(f98,plain,(
% 0.11/0.36 ( ! [X2 : $i,X3 : $i] : (($true = (in @ X3 @ (setadjoin @ X3 @ X2)))) )),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f76])).
% 0.11/0.36 thf(f76,plain,(
% 0.11/0.36 ( ! [X2 : $i,X3 : $i] : (($true != $true) | ($true = (in @ X3 @ (setadjoin @ X3 @ X2)))) )),
% 0.11/0.36 inference(definition_unfolding,[],[f56,f53])).
% 0.11/0.36 thf(f53,plain,(
% 0.11/0.36 (setadjoinIL = $true)),
% 0.11/0.36 inference(cnf_transformation,[],[f29])).
% 0.11/0.36 thf(f56,plain,(
% 0.11/0.36 ( ! [X2 : $i,X3 : $i] : (($true = (in @ X3 @ (setadjoin @ X3 @ X2))) | (setadjoinIL != $true)) )),
% 0.11/0.36 inference(cnf_transformation,[],[f33])).
% 0.11/0.36 thf(f33,plain,(
% 0.11/0.36 ((setadjoinIL = $true) | ($true != (in @ sK3 @ (setadjoin @ sK3 @ sK2)))) & (! [X2,X3] : ($true = (in @ X3 @ (setadjoin @ X3 @ X2))) | (setadjoinIL != $true))),
% 0.11/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f31,f32])).
% 0.11/0.36 thf(f32,plain,(
% 0.11/0.36 ? [X0,X1] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0))) => ($true != (in @ sK3 @ (setadjoin @ sK3 @ sK2)))),
% 0.11/0.36 introduced(choice_axiom,[])).
% 0.11/0.36 thf(f31,plain,(
% 0.11/0.36 ((setadjoinIL = $true) | ? [X0,X1] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0)))) & (! [X2,X3] : ($true = (in @ X3 @ (setadjoin @ X3 @ X2))) | (setadjoinIL != $true))),
% 0.11/0.36 inference(rectify,[],[f30])).
% 0.11/0.36 thf(f30,plain,(
% 0.11/0.36 ((setadjoinIL = $true) | ? [X0,X1] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0)))) & (! [X0,X1] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true))),
% 0.11/0.36 inference(nnf_transformation,[],[f10])).
% 0.11/0.36 thf(f10,plain,(
% 0.11/0.36 (setadjoinIL = $true) <=> ! [X0,X1] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0)))),
% 0.11/0.36 inference(fool_elimination,[],[f9])).
% 0.11/0.36 thf(f9,plain,(
% 0.11/0.36 (setadjoinIL = ! [X0,X1] : (in @ X1 @ (setadjoin @ X1 @ X0)))),
% 0.11/0.36 inference(rectify,[],[f1])).
% 0.11/0.36 thf(f1,axiom,(
% 0.11/0.36 (setadjoinIL = ! [X1,X0] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 0.11/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL)).
% 0.11/0.36 thf(f100,plain,(
% 0.11/0.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setadjoin @ X2 @ X1))) | ($true = (in @ X0 @ X1)) | (X0 = X2)) )),
% 0.11/0.36 inference(condensation,[],[f99])).
% 0.11/0.36 thf(f99,plain,(
% 0.11/0.36 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ X2)) != $true) | ($true = X3) | ((in @ X1 @ X2) = $true) | (X0 = X1)) )),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f87])).
% 0.11/0.36 thf(f87,plain,(
% 0.11/0.36 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (($true = X3) | ((in @ X1 @ X2) = $true) | ((in @ X1 @ (setadjoin @ X0 @ X2)) != $true) | (X0 = X1) | ($true != $true)) )),
% 0.11/0.36 inference(definition_unfolding,[],[f70,f52])).
% 0.11/0.36 thf(f52,plain,(
% 0.11/0.36 (setadjoinE = $true)),
% 0.11/0.36 inference(cnf_transformation,[],[f29])).
% 0.11/0.36 thf(f70,plain,(
% 0.11/0.36 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (($true = X3) | (X0 = X1) | ((in @ X1 @ X2) = $true) | ((in @ X1 @ (setadjoin @ X0 @ X2)) != $true) | (setadjoinE != $true)) )),
% 0.11/0.36 inference(cnf_transformation,[],[f47])).
% 0.11/0.36 thf(f47,plain,(
% 0.11/0.36 (! [X0,X1,X2] : (! [X3 : $o] : (($true = X3) | (($true != X3) & (X0 = X1)) | (($true != X3) & ((in @ X1 @ X2) = $true))) | ((in @ X1 @ (setadjoin @ X0 @ X2)) != $true)) | (setadjoinE != $true)) & ((setadjoinE = $true) | ((($true != sK13) & (($true = sK13) | (sK11 != sK10)) & (($true = sK13) | ((in @ sK11 @ sK12) != $true))) & ($true = (in @ sK11 @ (setadjoin @ sK10 @ sK12)))))),
% 0.11/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f44,f46,f45])).
% 0.11/0.36 thf(f45,plain,(
% 0.11/0.36 ? [X4,X5,X6] : (? [X7 : $o] : (($true != X7) & (($true = X7) | (X4 != X5)) & (($true = X7) | ($true != (in @ X5 @ X6)))) & ($true = (in @ X5 @ (setadjoin @ X4 @ X6)))) => (? [X7 : $o] : (($true != X7) & (($true = X7) | (sK11 != sK10)) & (($true = X7) | ((in @ sK11 @ sK12) != $true))) & ($true = (in @ sK11 @ (setadjoin @ sK10 @ sK12))))),
% 0.11/0.36 introduced(choice_axiom,[])).
% 0.11/0.36 thf(f46,plain,(
% 0.11/0.36 ? [X7 : $o] : (($true != X7) & (($true = X7) | (sK11 != sK10)) & (($true = X7) | ((in @ sK11 @ sK12) != $true))) => (($true != sK13) & (($true = sK13) | (sK11 != sK10)) & (($true = sK13) | ((in @ sK11 @ sK12) != $true)))),
% 0.11/0.36 introduced(choice_axiom,[])).
% 0.11/0.36 thf(f44,plain,(
% 0.11/0.36 (! [X0,X1,X2] : (! [X3 : $o] : (($true = X3) | (($true != X3) & (X0 = X1)) | (($true != X3) & ((in @ X1 @ X2) = $true))) | ((in @ X1 @ (setadjoin @ X0 @ X2)) != $true)) | (setadjoinE != $true)) & ((setadjoinE = $true) | ? [X4,X5,X6] : (? [X7 : $o] : (($true != X7) & (($true = X7) | (X4 != X5)) & (($true = X7) | ($true != (in @ X5 @ X6)))) & ($true = (in @ X5 @ (setadjoin @ X4 @ X6)))))),
% 0.11/0.36 inference(rectify,[],[f43])).
% 0.11/0.36 thf(f43,plain,(
% 0.11/0.36 (! [X0,X1,X2] : (! [X3 : $o] : (($true = X3) | (($true != X3) & (X0 = X1)) | (($true != X3) & ((in @ X1 @ X2) = $true))) | ((in @ X1 @ (setadjoin @ X0 @ X2)) != $true)) | (setadjoinE != $true)) & ((setadjoinE = $true) | ? [X0,X1,X2] : (? [X3 : $o] : (($true != X3) & (($true = X3) | (X0 != X1)) & (($true = X3) | ((in @ X1 @ X2) != $true))) & ((in @ X1 @ (setadjoin @ X0 @ X2)) = $true)))),
% 0.11/0.36 inference(nnf_transformation,[],[f22])).
% 0.11/0.36 thf(f22,plain,(
% 0.11/0.36 ! [X0,X1,X2] : (! [X3 : $o] : (($true = X3) | (($true != X3) & (X0 = X1)) | (($true != X3) & ((in @ X1 @ X2) = $true))) | ((in @ X1 @ (setadjoin @ X0 @ X2)) != $true)) <=> (setadjoinE = $true)),
% 0.11/0.36 inference(flattening,[],[f21])).
% 0.11/0.36 thf(f21,plain,(
% 0.11/0.36 ! [X0,X1,X2] : (! [X3 : $o] : ((($true = X3) | (($true != X3) & ((in @ X1 @ X2) = $true))) | (($true != X3) & (X0 = X1))) | ((in @ X1 @ (setadjoin @ X0 @ X2)) != $true)) <=> (setadjoinE = $true)),
% 0.11/0.36 inference(ennf_transformation,[],[f17])).
% 0.11/0.36 thf(f17,plain,(
% 0.11/0.36 ! [X0,X1,X2] : (((in @ X1 @ (setadjoin @ X0 @ X2)) = $true) => ! [X3 : $o] : (((X0 = X1) => ($true = X3)) => ((((in @ X1 @ X2) = $true) => ($true = X3)) => ($true = X3)))) <=> (setadjoinE = $true)),
% 0.11/0.36 inference(fool_elimination,[],[f16])).
% 0.11/0.36 thf(f16,plain,(
% 0.11/0.36 (! [X0,X1,X2] : ((in @ X1 @ (setadjoin @ X0 @ X2)) => ! [X3 : $o] : (((X0 = X1) => X3) => (((in @ X1 @ X2) => X3) => X3))) = setadjoinE)),
% 0.11/0.36 inference(rectify,[],[f2])).
% 0.11/0.36 thf(f2,axiom,(
% 0.11/0.36 (! [X0,X1,X2] : ((in @ X1 @ (setadjoin @ X0 @ X2)) => ! [X3 : $o] : (((X0 = X1) => X3) => (((in @ X1 @ X2) => X3) => X3))) = setadjoinE)),
% 0.11/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE)).
% 0.11/0.36 thf(f101,plain,(
% 0.11/0.36 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | ($true != (in @ X0 @ X1))) )),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f77])).
% 0.11/0.36 thf(f77,plain,(
% 0.11/0.36 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ($true != $true) | ($true != (in @ X1 @ X0))) )),
% 0.11/0.36 inference(definition_unfolding,[],[f60,f55])).
% 0.11/0.36 thf(f55,plain,(
% 0.11/0.36 (notinself2 = $true)),
% 0.11/0.36 inference(cnf_transformation,[],[f29])).
% 0.11/0.36 thf(f60,plain,(
% 0.11/0.36 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ($true != (in @ X1 @ X0)) | (notinself2 != $true)) )),
% 0.11/0.36 inference(cnf_transformation,[],[f37])).
% 0.11/0.36 thf(f37,plain,(
% 0.11/0.36 (! [X0,X1] : (($true != (in @ X0 @ X1)) | ($true != (in @ X1 @ X0))) | (notinself2 != $true)) & ((notinself2 = $true) | (($true = (in @ sK4 @ sK5)) & ($true = (in @ sK5 @ sK4))))),
% 0.11/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f35,f36])).
% 0.11/0.36 thf(f36,plain,(
% 0.11/0.36 ? [X2,X3] : (($true = (in @ X2 @ X3)) & ($true = (in @ X3 @ X2))) => (($true = (in @ sK4 @ sK5)) & ($true = (in @ sK5 @ sK4)))),
% 0.11/0.36 introduced(choice_axiom,[])).
% 0.11/0.36 thf(f35,plain,(
% 0.11/0.36 (! [X0,X1] : (($true != (in @ X0 @ X1)) | ($true != (in @ X1 @ X0))) | (notinself2 != $true)) & ((notinself2 = $true) | ? [X2,X3] : (($true = (in @ X2 @ X3)) & ($true = (in @ X3 @ X2))))),
% 0.11/0.36 inference(rectify,[],[f34])).
% 0.11/0.36 thf(f34,plain,(
% 0.11/0.36 (! [X0,X1] : (($true != (in @ X0 @ X1)) | ($true != (in @ X1 @ X0))) | (notinself2 != $true)) & ((notinself2 = $true) | ? [X0,X1] : (($true = (in @ X0 @ X1)) & ($true = (in @ X1 @ X0))))),
% 0.11/0.36 inference(nnf_transformation,[],[f26])).
% 0.11/0.36 thf(f26,plain,(
% 0.11/0.36 ! [X0,X1] : (($true != (in @ X0 @ X1)) | ($true != (in @ X1 @ X0))) <=> (notinself2 = $true)),
% 0.11/0.36 inference(ennf_transformation,[],[f20])).
% 0.11/0.36 thf(f20,plain,(
% 0.11/0.36 (notinself2 = $true) <=> ! [X0,X1] : (($true = (in @ X0 @ X1)) => ($true != (in @ X1 @ X0)))),
% 0.11/0.36 inference(flattening,[],[f12])).
% 0.11/0.36 thf(f12,plain,(
% 0.11/0.36 ! [X0,X1] : (($true = (in @ X0 @ X1)) => ~($true = (in @ X1 @ X0))) <=> (notinself2 = $true)),
% 0.11/0.36 inference(fool_elimination,[],[f11])).
% 0.11/0.36 thf(f11,plain,(
% 0.11/0.36 (! [X0,X1] : ((in @ X0 @ X1) => ~(in @ X1 @ X0)) = notinself2)),
% 0.11/0.36 inference(rectify,[],[f4])).
% 0.11/0.36 thf(f4,axiom,(
% 0.11/0.36 (! [X2,X4] : ((in @ X2 @ X4) => ~(in @ X4 @ X2)) = notinself2)),
% 0.11/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinself2)).
% 0.11/0.36 thf(f123,plain,(
% 0.11/0.36 ($true = (in @ sK0 @ sK1))),
% 0.11/0.36 inference(subsumption_resolution,[],[f122,f49])).
% 0.11/0.36 thf(f122,plain,(
% 0.11/0.36 (sK0 = sK1) | ($true = (in @ sK0 @ sK1))),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f120])).
% 0.11/0.36 thf(f120,plain,(
% 0.11/0.36 ($true != $true) | ($true = (in @ sK0 @ sK1)) | (sK0 = sK1)),
% 0.11/0.36 inference(superposition,[],[f113,f98])).
% 0.11/0.36 thf(f113,plain,(
% 0.11/0.36 ( ! [X0 : $i] : (($true != (in @ X0 @ (setadjoin @ sK0 @ sK0))) | ($true = (in @ X0 @ sK1)) | (sK1 = X0)) )),
% 0.11/0.36 inference(superposition,[],[f100,f102])).
% 0.11/0.36 % SZS output end Proof for theBenchmark
% 0.11/0.36 % (13960)------------------------------
% 0.11/0.36 % (13960)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36 % (13960)Termination reason: Refutation
% 0.11/0.36
% 0.11/0.36 % (13960)Memory used [KB]: 5500
% 0.11/0.36 % (13960)Time elapsed: 0.008 s
% 0.11/0.36 % (13960)Instructions burned: 7 (million)
% 0.11/0.36 % (13960)------------------------------
% 0.11/0.36 % (13960)------------------------------
% 0.11/0.36 % (13953)Success in time 0.019 s
% 0.11/0.36 % Vampire---4.8 exiting
%------------------------------------------------------------------------------