TSTP Solution File: SEU787^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU787^2 : 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 : n009.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 03:51:31 EDT 2024
% Result : Theorem 0.12s 0.37s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SEU787^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.13 % 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
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun May 19 16:26:08 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 This is a TH0_THM_EQU_NAR problem
% 0.12/0.34 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
% 0.12/0.36 % (12007)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.36 % (12013)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.36 % (12012)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)
% 0.12/0.36 % (12010)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.36 % (12009)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)
% 0.12/0.36 % (12008)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)
% 0.12/0.36 % (12011)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)
% 0.12/0.36 % (12014)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)
% 0.12/0.36 % (12010)Instruction limit reached!
% 0.12/0.36 % (12010)------------------------------
% 0.12/0.36 % (12010)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36 % (12010)Termination reason: Unknown
% 0.12/0.36 % (12010)Termination phase: Property scanning
% 0.12/0.36 % (12011)Instruction limit reached!
% 0.12/0.36 % (12011)------------------------------
% 0.12/0.36 % (12011)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36
% 0.12/0.36 % (12010)Memory used [KB]: 1023
% 0.12/0.36 % (12010)Time elapsed: 0.003 s
% 0.12/0.36 % (12010)Instructions burned: 3 (million)
% 0.12/0.36 % (12010)------------------------------
% 0.12/0.36 % (12010)------------------------------
% 0.12/0.36 % (12011)Termination reason: Unknown
% 0.12/0.36 % (12011)Termination phase: Property scanning
% 0.12/0.36
% 0.12/0.36 % (12011)Memory used [KB]: 1023
% 0.12/0.36 % (12011)Time elapsed: 0.003 s
% 0.12/0.36 % (12011)Instructions burned: 3 (million)
% 0.12/0.36 % (12011)------------------------------
% 0.12/0.36 % (12011)------------------------------
% 0.12/0.36 % (12014)Instruction limit reached!
% 0.12/0.36 % (12014)------------------------------
% 0.12/0.36 % (12014)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36 % (12014)Termination reason: Unknown
% 0.12/0.36 % (12014)Termination phase: Property scanning
% 0.12/0.36
% 0.12/0.36 % (12014)Memory used [KB]: 1023
% 0.12/0.36 % (12014)Time elapsed: 0.003 s
% 0.12/0.36 % (12014)Instructions burned: 3 (million)
% 0.12/0.36 % (12014)------------------------------
% 0.12/0.36 % (12014)------------------------------
% 0.12/0.36 % (12008)Instruction limit reached!
% 0.12/0.36 % (12008)------------------------------
% 0.12/0.36 % (12008)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36 % (12008)Termination reason: Unknown
% 0.12/0.36 % (12008)Termination phase: Saturation
% 0.12/0.36
% 0.12/0.36 % (12008)Memory used [KB]: 5500
% 0.12/0.36 % (12008)Time elapsed: 0.004 s
% 0.12/0.36 % (12008)Instructions burned: 4 (million)
% 0.12/0.36 % (12008)------------------------------
% 0.12/0.36 % (12008)------------------------------
% 0.12/0.36 % (12012)First to succeed.
% 0.12/0.37 % (12007)Also succeeded, but the first one will report.
% 0.12/0.37 % (12009)Also succeeded, but the first one will report.
% 0.12/0.37 % (12012)Refutation found. Thanks to Tanya!
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37 % SZS output start Proof for theBenchmark
% 0.12/0.37 thf(func_def_0, type, in: $i > $i > $o).
% 0.12/0.37 thf(func_def_1, type, binunion: $i > $i > $i).
% 0.12/0.37 thf(func_def_2, type, kpair: $i > $i > $i).
% 0.12/0.37 thf(func_def_3, type, breln1: $i > $i > $o).
% 0.12/0.37 thf(f78,plain,(
% 0.12/0.37 $false),
% 0.12/0.37 inference(avatar_sat_refutation,[],[f61,f66,f67,f77])).
% 0.12/0.37 thf(f77,plain,(
% 0.12/0.37 spl11_2 | spl11_3),
% 0.12/0.37 inference(avatar_contradiction_clause,[],[f76])).
% 0.12/0.37 thf(f76,plain,(
% 0.12/0.37 $false | (spl11_2 | spl11_3)),
% 0.12/0.37 inference(subsumption_resolution,[],[f75,f36])).
% 0.12/0.37 thf(f36,plain,(
% 0.12/0.37 ((breln1 @ sK5 @ sK6) = $true)),
% 0.12/0.37 inference(cnf_transformation,[],[f26])).
% 0.12/0.37 thf(f26,plain,(
% 0.12/0.37 ((((((in @ (kpair @ sK8 @ sK9) @ (binunion @ sK6 @ sK7)) = $true) & (((sK10 = $true) | ((in @ (kpair @ sK8 @ sK9) @ sK7) != $true)) & (sK10 != $true) & (((in @ (kpair @ sK8 @ sK9) @ sK6) != $true) | (sK10 = $true))) & ((in @ sK9 @ sK5) = $true)) & ((in @ sK8 @ sK5) = $true)) & ((breln1 @ sK5 @ sK7) = $true)) & ((breln1 @ sK5 @ sK6) = $true)) & (breln1unionE = $true)),
% 0.12/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,sK10])],[f20,f25,f24,f23,f22,f21])).
% 0.12/0.37 thf(f21,plain,(
% 0.12/0.37 ? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) & ? [X5 : $o] : ((($true = X5) | ((in @ (kpair @ X3 @ X4) @ X2) != $true)) & ($true != X5) & (((in @ (kpair @ X3 @ X4) @ X1) != $true) | ($true = X5))) & ((in @ X4 @ X0) = $true)) & ((in @ X3 @ X0) = $true)) & ((breln1 @ X0 @ X2) = $true)) & ((breln1 @ X0 @ X1) = $true)) => (? [X2] : (? [X3] : (? [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ sK6 @ X2)) = $true) & ? [X5 : $o] : ((($true = X5) | ((in @ (kpair @ X3 @ X4) @ X2) != $true)) & ($true != X5) & (($true != (in @ (kpair @ X3 @ X4) @ sK6)) | ($true = X5))) & ((in @ X4 @ sK5) = $true)) & ($true = (in @ X3 @ sK5))) & ($true = (breln1 @ sK5 @ X2))) & ((breln1 @ sK5 @ sK6) = $true))),
% 0.12/0.37 introduced(choice_axiom,[])).
% 0.12/0.37 thf(f22,plain,(
% 0.12/0.37 ? [X2] : (? [X3] : (? [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ sK6 @ X2)) = $true) & ? [X5 : $o] : ((($true = X5) | ((in @ (kpair @ X3 @ X4) @ X2) != $true)) & ($true != X5) & (($true != (in @ (kpair @ X3 @ X4) @ sK6)) | ($true = X5))) & ((in @ X4 @ sK5) = $true)) & ($true = (in @ X3 @ sK5))) & ($true = (breln1 @ sK5 @ X2))) => (? [X3] : (? [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ sK6 @ sK7)) = $true) & ? [X5 : $o] : ((($true = X5) | ((in @ (kpair @ X3 @ X4) @ sK7) != $true)) & ($true != X5) & (($true != (in @ (kpair @ X3 @ X4) @ sK6)) | ($true = X5))) & ((in @ X4 @ sK5) = $true)) & ($true = (in @ X3 @ sK5))) & ((breln1 @ sK5 @ sK7) = $true))),
% 0.12/0.37 introduced(choice_axiom,[])).
% 0.12/0.37 thf(f23,plain,(
% 0.12/0.37 ? [X3] : (? [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ sK6 @ sK7)) = $true) & ? [X5 : $o] : ((($true = X5) | ((in @ (kpair @ X3 @ X4) @ sK7) != $true)) & ($true != X5) & (($true != (in @ (kpair @ X3 @ X4) @ sK6)) | ($true = X5))) & ((in @ X4 @ sK5) = $true)) & ($true = (in @ X3 @ sK5))) => (? [X4] : (($true = (in @ (kpair @ sK8 @ X4) @ (binunion @ sK6 @ sK7))) & ? [X5 : $o] : ((($true = X5) | ((in @ (kpair @ sK8 @ X4) @ sK7) != $true)) & ($true != X5) & (((in @ (kpair @ sK8 @ X4) @ sK6) != $true) | ($true = X5))) & ((in @ X4 @ sK5) = $true)) & ((in @ sK8 @ sK5) = $true))),
% 0.12/0.37 introduced(choice_axiom,[])).
% 0.12/0.37 thf(f24,plain,(
% 0.12/0.37 ? [X4] : (($true = (in @ (kpair @ sK8 @ X4) @ (binunion @ sK6 @ sK7))) & ? [X5 : $o] : ((($true = X5) | ((in @ (kpair @ sK8 @ X4) @ sK7) != $true)) & ($true != X5) & (((in @ (kpair @ sK8 @ X4) @ sK6) != $true) | ($true = X5))) & ((in @ X4 @ sK5) = $true)) => (((in @ (kpair @ sK8 @ sK9) @ (binunion @ sK6 @ sK7)) = $true) & ? [X5 : $o] : ((($true = X5) | ((in @ (kpair @ sK8 @ sK9) @ sK7) != $true)) & ($true != X5) & (((in @ (kpair @ sK8 @ sK9) @ sK6) != $true) | ($true = X5))) & ((in @ sK9 @ sK5) = $true))),
% 0.12/0.37 introduced(choice_axiom,[])).
% 0.12/0.37 thf(f25,plain,(
% 0.12/0.37 ? [X5 : $o] : ((($true = X5) | ((in @ (kpair @ sK8 @ sK9) @ sK7) != $true)) & ($true != X5) & (((in @ (kpair @ sK8 @ sK9) @ sK6) != $true) | ($true = X5))) => (((sK10 = $true) | ((in @ (kpair @ sK8 @ sK9) @ sK7) != $true)) & (sK10 != $true) & (((in @ (kpair @ sK8 @ sK9) @ sK6) != $true) | (sK10 = $true)))),
% 0.12/0.37 introduced(choice_axiom,[])).
% 0.12/0.37 thf(f20,plain,(
% 0.12/0.37 ? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) & ? [X5 : $o] : ((($true = X5) | ((in @ (kpair @ X3 @ X4) @ X2) != $true)) & ($true != X5) & (((in @ (kpair @ X3 @ X4) @ X1) != $true) | ($true = X5))) & ((in @ X4 @ X0) = $true)) & ((in @ X3 @ X0) = $true)) & ((breln1 @ X0 @ X2) = $true)) & ((breln1 @ X0 @ X1) = $true)) & (breln1unionE = $true)),
% 0.12/0.37 inference(rectify,[],[f12])).
% 0.12/0.37 thf(f12,plain,(
% 0.12/0.37 ? [X1,X0] : (? [X2] : (? [X3] : (? [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true) & ? [X5 : $o] : ((($true = X5) | ((in @ (kpair @ X3 @ X4) @ X2) != $true)) & ($true != X5) & (((in @ (kpair @ X3 @ X4) @ X0) != $true) | ($true = X5))) & ($true = (in @ X4 @ X1))) & ($true = (in @ X3 @ X1))) & ($true = (breln1 @ X1 @ X2))) & ((breln1 @ X1 @ X0) = $true)) & (breln1unionE = $true)),
% 0.12/0.37 inference(flattening,[],[f11])).
% 0.12/0.37 thf(f11,plain,(
% 0.12/0.37 ? [X1,X0] : (? [X2] : (? [X3] : (? [X4] : ((? [X5 : $o] : ((($true != X5) & (($true = X5) | ((in @ (kpair @ X3 @ X4) @ X2) != $true))) & (((in @ (kpair @ X3 @ X4) @ X0) != $true) | ($true = X5))) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true)) & ($true = (in @ X4 @ X1))) & ($true = (in @ X3 @ X1))) & ($true = (breln1 @ X1 @ X2))) & ((breln1 @ X1 @ X0) = $true)) & (breln1unionE = $true)),
% 0.12/0.37 inference(ennf_transformation,[],[f6])).
% 0.12/0.37 thf(f6,plain,(
% 0.12/0.37 ~((breln1unionE = $true) => ! [X1,X0] : (((breln1 @ X1 @ X0) = $true) => ! [X2] : (($true = (breln1 @ X1 @ X2)) => ! [X3] : (($true = (in @ X3 @ X1)) => ! [X4] : (($true = (in @ X4 @ X1)) => (((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true) => ! [X5 : $o] : ((((in @ (kpair @ X3 @ X4) @ X0) = $true) => ($true = X5)) => ((((in @ (kpair @ X3 @ X4) @ X2) = $true) => ($true = X5)) => ($true = X5)))))))))),
% 0.12/0.37 inference(fool_elimination,[],[f5])).
% 0.12/0.37 thf(f5,plain,(
% 0.12/0.37 ~(breln1unionE => ! [X0,X1] : ((breln1 @ X1 @ X0) => ! [X2] : ((breln1 @ X1 @ X2) => ! [X3] : ((in @ X3 @ X1) => ! [X4] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) => ! [X5 : $o] : (((in @ (kpair @ X3 @ X4) @ X0) => X5) => (((in @ (kpair @ X3 @ X4) @ X2) => X5) => X5))))))))),
% 0.12/0.37 inference(rectify,[],[f3])).
% 0.12/0.37 thf(f3,negated_conjecture,(
% 0.12/0.37 ~(breln1unionE => ! [X1,X0] : ((breln1 @ X0 @ X1) => ! [X2] : ((breln1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) => ! [X5 : $o] : (((in @ (kpair @ X3 @ X4) @ X1) => X5) => (((in @ (kpair @ X3 @ X4) @ X2) => X5) => X5))))))))),
% 0.12/0.37 inference(negated_conjecture,[],[f2])).
% 0.12/0.37 thf(f2,conjecture,(
% 0.12/0.37 breln1unionE => ! [X1,X0] : ((breln1 @ X0 @ X1) => ! [X2] : ((breln1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) => ! [X5 : $o] : (((in @ (kpair @ X3 @ X4) @ X1) => X5) => (((in @ (kpair @ X3 @ X4) @ X2) => X5) => X5)))))))),
% 0.12/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionEcases)).
% 0.12/0.37 thf(f75,plain,(
% 0.12/0.37 ((breln1 @ sK5 @ sK6) != $true) | (spl11_2 | spl11_3)),
% 0.12/0.37 inference(subsumption_resolution,[],[f74,f38])).
% 0.12/0.37 thf(f38,plain,(
% 0.12/0.37 ((in @ sK8 @ sK5) = $true)),
% 0.12/0.37 inference(cnf_transformation,[],[f26])).
% 0.12/0.37 thf(f74,plain,(
% 0.12/0.37 ((in @ sK8 @ sK5) != $true) | ((breln1 @ sK5 @ sK6) != $true) | (spl11_2 | spl11_3)),
% 0.12/0.37 inference(subsumption_resolution,[],[f73,f39])).
% 0.12/0.37 thf(f39,plain,(
% 0.12/0.37 ((in @ sK9 @ sK5) = $true)),
% 0.12/0.37 inference(cnf_transformation,[],[f26])).
% 0.12/0.37 thf(f73,plain,(
% 0.12/0.37 ((in @ sK9 @ sK5) != $true) | ((breln1 @ sK5 @ sK6) != $true) | ((in @ sK8 @ sK5) != $true) | (spl11_2 | spl11_3)),
% 0.12/0.37 inference(trivial_inequality_removal,[],[f72])).
% 0.12/0.37 thf(f72,plain,(
% 0.12/0.37 ((in @ sK8 @ sK5) != $true) | ((breln1 @ sK5 @ sK6) != $true) | ((in @ sK9 @ sK5) != $true) | ($true != $true) | (spl11_2 | spl11_3)),
% 0.12/0.37 inference(superposition,[],[f71,f37])).
% 0.12/0.37 thf(f37,plain,(
% 0.12/0.37 ((breln1 @ sK5 @ sK7) = $true)),
% 0.12/0.37 inference(cnf_transformation,[],[f26])).
% 0.12/0.37 thf(f71,plain,(
% 0.12/0.37 ( ! [X0 : $i] : (($true != (breln1 @ X0 @ sK7)) | ($true != (breln1 @ X0 @ sK6)) | ($true != (in @ sK9 @ X0)) | ((in @ sK8 @ X0) != $true)) ) | (spl11_2 | spl11_3)),
% 0.12/0.37 inference(subsumption_resolution,[],[f70,f65])).
% 0.12/0.37 thf(f65,plain,(
% 0.12/0.37 ((in @ (kpair @ sK8 @ sK9) @ sK6) != $true) | spl11_3),
% 0.12/0.37 inference(avatar_component_clause,[],[f63])).
% 0.12/0.37 thf(f63,plain,(
% 0.12/0.37 spl11_3 <=> ((in @ (kpair @ sK8 @ sK9) @ sK6) = $true)),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl11_3])])).
% 0.12/0.37 thf(f70,plain,(
% 0.12/0.37 ( ! [X0 : $i] : (((in @ (kpair @ sK8 @ sK9) @ sK6) = $true) | ($true != (breln1 @ X0 @ sK6)) | ($true != (in @ sK9 @ X0)) | ((in @ sK8 @ X0) != $true) | ($true != (breln1 @ X0 @ sK7))) ) | spl11_2),
% 0.12/0.37 inference(subsumption_resolution,[],[f69,f60])).
% 0.12/0.37 thf(f60,plain,(
% 0.12/0.37 ((in @ (kpair @ sK8 @ sK9) @ sK7) != $true) | spl11_2),
% 0.12/0.37 inference(avatar_component_clause,[],[f58])).
% 0.12/0.37 thf(f58,plain,(
% 0.12/0.37 spl11_2 <=> ((in @ (kpair @ sK8 @ sK9) @ sK7) = $true)),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl11_2])])).
% 0.12/0.37 thf(f69,plain,(
% 0.12/0.37 ( ! [X0 : $i] : (($true != (breln1 @ X0 @ sK7)) | ((in @ (kpair @ sK8 @ sK9) @ sK7) = $true) | ($true != (breln1 @ X0 @ sK6)) | ($true != (in @ sK9 @ X0)) | ((in @ (kpair @ sK8 @ sK9) @ sK6) = $true) | ((in @ sK8 @ X0) != $true)) )),
% 0.12/0.37 inference(trivial_inequality_removal,[],[f68])).
% 0.12/0.37 thf(f68,plain,(
% 0.12/0.37 ( ! [X0 : $i] : (((in @ sK8 @ X0) != $true) | ($true != (in @ sK9 @ X0)) | ($true != (breln1 @ X0 @ sK7)) | ((in @ (kpair @ sK8 @ sK9) @ sK7) = $true) | ($true != $true) | ((in @ (kpair @ sK8 @ sK9) @ sK6) = $true) | ($true != (breln1 @ X0 @ sK6))) )),
% 0.12/0.37 inference(superposition,[],[f52,f43])).
% 0.12/0.37 thf(f43,plain,(
% 0.12/0.37 ((in @ (kpair @ sK8 @ sK9) @ (binunion @ sK6 @ sK7)) = $true)),
% 0.12/0.37 inference(cnf_transformation,[],[f26])).
% 0.12/0.37 thf(f52,plain,(
% 0.12/0.37 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((in @ (kpair @ X8 @ X9) @ (binunion @ X6 @ X7)) != $true) | ((in @ X9 @ X5) != $true) | ((in @ (kpair @ X8 @ X9) @ X7) = $true) | ((in @ X8 @ X5) != $true) | ($true != (breln1 @ X5 @ X7)) | ((in @ (kpair @ X8 @ X9) @ X6) = $true) | ((breln1 @ X5 @ X6) != $true)) )),
% 0.12/0.37 inference(trivial_inequality_removal,[],[f51])).
% 0.12/0.37 thf(f51,plain,(
% 0.12/0.37 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((in @ (kpair @ X8 @ X9) @ X7) = $true) | ((in @ (kpair @ X8 @ X9) @ X6) = $true) | ((in @ (kpair @ X8 @ X9) @ (binunion @ X6 @ X7)) != $true) | ((breln1 @ X5 @ X6) != $true) | ($true != $true) | ((in @ X8 @ X5) != $true) | ($true != (breln1 @ X5 @ X7)) | ((in @ X9 @ X5) != $true)) )),
% 0.12/0.37 inference(definition_unfolding,[],[f27,f35])).
% 0.12/0.37 thf(f35,plain,(
% 0.12/0.37 (breln1unionE = $true)),
% 0.12/0.37 inference(cnf_transformation,[],[f26])).
% 0.12/0.37 thf(f27,plain,(
% 0.12/0.37 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((breln1 @ X5 @ X6) != $true) | ((in @ X8 @ X5) != $true) | ((in @ (kpair @ X8 @ X9) @ (binunion @ X6 @ X7)) != $true) | ((in @ X9 @ X5) != $true) | ((in @ (kpair @ X8 @ X9) @ X6) = $true) | ((in @ (kpair @ X8 @ X9) @ X7) = $true) | ($true != (breln1 @ X5 @ X7)) | (breln1unionE != $true)) )),
% 0.12/0.37 inference(cnf_transformation,[],[f19])).
% 0.12/0.37 thf(f19,plain,(
% 0.12/0.37 ((breln1unionE = $true) | (((breln1 @ sK0 @ sK1) = $true) & ((((in @ sK3 @ sK0) = $true) & (($true = (in @ (kpair @ sK3 @ sK4) @ (binunion @ sK1 @ sK2))) & ((in @ sK4 @ sK0) = $true) & ((in @ (kpair @ sK3 @ sK4) @ sK1) != $true) & ((in @ (kpair @ sK3 @ sK4) @ sK2) != $true))) & ((breln1 @ sK0 @ sK2) = $true)))) & (! [X5,X6] : (((breln1 @ X5 @ X6) != $true) | ! [X7] : (! [X8] : (((in @ X8 @ X5) != $true) | ! [X9] : (((in @ (kpair @ X8 @ X9) @ (binunion @ X6 @ X7)) != $true) | ((in @ X9 @ X5) != $true) | ((in @ (kpair @ X8 @ X9) @ X6) = $true) | ((in @ (kpair @ X8 @ X9) @ X7) = $true))) | ($true != (breln1 @ X5 @ X7)))) | (breln1unionE != $true))),
% 0.12/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f14,f18,f17,f16,f15])).
% 0.12/0.37 thf(f15,plain,(
% 0.12/0.37 ? [X0,X1] : (((breln1 @ X0 @ X1) = $true) & ? [X2] : (? [X3] : (((in @ X3 @ X0) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) & ((in @ X4 @ X0) = $true) & ((in @ (kpair @ X3 @ X4) @ X1) != $true) & ((in @ (kpair @ X3 @ X4) @ X2) != $true))) & ((breln1 @ X0 @ X2) = $true))) => (((breln1 @ sK0 @ sK1) = $true) & ? [X2] : (? [X3] : (((in @ X3 @ sK0) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ sK1 @ X2)) = $true) & ((in @ X4 @ sK0) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ sK1)) & ((in @ (kpair @ X3 @ X4) @ X2) != $true))) & ((breln1 @ sK0 @ X2) = $true)))),
% 0.12/0.37 introduced(choice_axiom,[])).
% 0.12/0.37 thf(f16,plain,(
% 0.12/0.37 ? [X2] : (? [X3] : (((in @ X3 @ sK0) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ sK1 @ X2)) = $true) & ((in @ X4 @ sK0) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ sK1)) & ((in @ (kpair @ X3 @ X4) @ X2) != $true))) & ((breln1 @ sK0 @ X2) = $true)) => (? [X3] : (((in @ X3 @ sK0) = $true) & ? [X4] : (($true = (in @ (kpair @ X3 @ X4) @ (binunion @ sK1 @ sK2))) & ((in @ X4 @ sK0) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ sK1)) & ((in @ (kpair @ X3 @ X4) @ sK2) != $true))) & ((breln1 @ sK0 @ sK2) = $true))),
% 0.12/0.37 introduced(choice_axiom,[])).
% 0.12/0.37 thf(f17,plain,(
% 0.12/0.37 ? [X3] : (((in @ X3 @ sK0) = $true) & ? [X4] : (($true = (in @ (kpair @ X3 @ X4) @ (binunion @ sK1 @ sK2))) & ((in @ X4 @ sK0) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ sK1)) & ((in @ (kpair @ X3 @ X4) @ sK2) != $true))) => (((in @ sK3 @ sK0) = $true) & ? [X4] : (((in @ (kpair @ sK3 @ X4) @ (binunion @ sK1 @ sK2)) = $true) & ((in @ X4 @ sK0) = $true) & ((in @ (kpair @ sK3 @ X4) @ sK1) != $true) & ($true != (in @ (kpair @ sK3 @ X4) @ sK2))))),
% 0.12/0.37 introduced(choice_axiom,[])).
% 0.12/0.37 thf(f18,plain,(
% 0.12/0.37 ? [X4] : (((in @ (kpair @ sK3 @ X4) @ (binunion @ sK1 @ sK2)) = $true) & ((in @ X4 @ sK0) = $true) & ((in @ (kpair @ sK3 @ X4) @ sK1) != $true) & ($true != (in @ (kpair @ sK3 @ X4) @ sK2))) => (($true = (in @ (kpair @ sK3 @ sK4) @ (binunion @ sK1 @ sK2))) & ((in @ sK4 @ sK0) = $true) & ((in @ (kpair @ sK3 @ sK4) @ sK1) != $true) & ((in @ (kpair @ sK3 @ sK4) @ sK2) != $true))),
% 0.12/0.37 introduced(choice_axiom,[])).
% 0.12/0.37 thf(f14,plain,(
% 0.12/0.37 ((breln1unionE = $true) | ? [X0,X1] : (((breln1 @ X0 @ X1) = $true) & ? [X2] : (? [X3] : (((in @ X3 @ X0) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) & ((in @ X4 @ X0) = $true) & ((in @ (kpair @ X3 @ X4) @ X1) != $true) & ((in @ (kpair @ X3 @ X4) @ X2) != $true))) & ((breln1 @ X0 @ X2) = $true)))) & (! [X5,X6] : (((breln1 @ X5 @ X6) != $true) | ! [X7] : (! [X8] : (((in @ X8 @ X5) != $true) | ! [X9] : (((in @ (kpair @ X8 @ X9) @ (binunion @ X6 @ X7)) != $true) | ((in @ X9 @ X5) != $true) | ((in @ (kpair @ X8 @ X9) @ X6) = $true) | ((in @ (kpair @ X8 @ X9) @ X7) = $true))) | ($true != (breln1 @ X5 @ X7)))) | (breln1unionE != $true))),
% 0.12/0.37 inference(rectify,[],[f13])).
% 0.12/0.37 thf(f13,plain,(
% 0.12/0.37 ((breln1unionE = $true) | ? [X0,X1] : (((breln1 @ X0 @ X1) = $true) & ? [X2] : (? [X3] : (((in @ X3 @ X0) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) & ((in @ X4 @ X0) = $true) & ((in @ (kpair @ X3 @ X4) @ X1) != $true) & ((in @ (kpair @ X3 @ X4) @ X2) != $true))) & ((breln1 @ X0 @ X2) = $true)))) & (! [X0,X1] : (((breln1 @ X0 @ X1) != $true) | ! [X2] : (! [X3] : (((in @ X3 @ X0) != $true) | ! [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) != $true) | ((in @ X4 @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ X1) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true))) | ((breln1 @ X0 @ X2) != $true))) | (breln1unionE != $true))),
% 0.12/0.37 inference(nnf_transformation,[],[f10])).
% 0.12/0.37 thf(f10,plain,(
% 0.12/0.37 (breln1unionE = $true) <=> ! [X0,X1] : (((breln1 @ X0 @ X1) != $true) | ! [X2] : (! [X3] : (((in @ X3 @ X0) != $true) | ! [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) != $true) | ((in @ X4 @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ X1) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true))) | ((breln1 @ X0 @ X2) != $true)))),
% 0.12/0.37 inference(flattening,[],[f9])).
% 0.12/0.37 thf(f9,plain,(
% 0.12/0.37 ! [X1,X0] : (! [X2] : (! [X3] : (! [X4] : (((((in @ (kpair @ X3 @ X4) @ X1) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true)) | ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) != $true)) | ((in @ X4 @ X0) != $true)) | ((in @ X3 @ X0) != $true)) | ((breln1 @ X0 @ X2) != $true)) | ((breln1 @ X0 @ X1) != $true)) <=> (breln1unionE = $true)),
% 0.12/0.37 inference(ennf_transformation,[],[f8])).
% 0.12/0.37 thf(f8,plain,(
% 0.12/0.37 ! [X1,X0] : (((breln1 @ X0 @ X1) = $true) => ! [X2] : (((breln1 @ X0 @ X2) = $true) => ! [X3] : (((in @ X3 @ X0) = $true) => ! [X4] : (((in @ X4 @ X0) = $true) => (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) => (((in @ (kpair @ X3 @ X4) @ X1) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true))))))) <=> (breln1unionE = $true)),
% 0.12/0.37 inference(fool_elimination,[],[f7])).
% 0.12/0.37 thf(f7,plain,(
% 0.12/0.37 (breln1unionE = ! [X0,X1] : ((breln1 @ X0 @ X1) => ! [X2] : ((breln1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) => ((in @ (kpair @ X3 @ X4) @ X2) | (in @ (kpair @ X3 @ X4) @ X1))))))))),
% 0.12/0.37 inference(rectify,[],[f1])).
% 0.12/0.37 thf(f1,axiom,(
% 0.12/0.37 (breln1unionE = ! [X0,X1] : ((breln1 @ X0 @ X1) => ! [X2] : ((breln1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) => ((in @ (kpair @ X3 @ X4) @ X2) | (in @ (kpair @ X3 @ X4) @ X1))))))))),
% 0.12/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionE)).
% 0.12/0.37 thf(f67,plain,(
% 0.12/0.37 ~spl11_1),
% 0.12/0.37 inference(avatar_split_clause,[],[f41,f54])).
% 0.12/0.37 thf(f54,plain,(
% 0.12/0.37 spl11_1 <=> (sK10 = $true)),
% 0.12/0.37 introduced(avatar_definition,[new_symbols(naming,[spl11_1])])).
% 0.12/0.37 thf(f41,plain,(
% 0.12/0.37 (sK10 != $true)),
% 0.12/0.37 inference(cnf_transformation,[],[f26])).
% 0.12/0.37 thf(f66,plain,(
% 0.12/0.37 spl11_1 | ~spl11_3),
% 0.12/0.37 inference(avatar_split_clause,[],[f40,f63,f54])).
% 0.12/0.37 thf(f40,plain,(
% 0.12/0.37 (sK10 = $true) | ((in @ (kpair @ sK8 @ sK9) @ sK6) != $true)),
% 0.12/0.37 inference(cnf_transformation,[],[f26])).
% 0.12/0.37 thf(f61,plain,(
% 0.12/0.37 spl11_1 | ~spl11_2),
% 0.12/0.37 inference(avatar_split_clause,[],[f42,f58,f54])).
% 0.12/0.37 thf(f42,plain,(
% 0.12/0.37 ((in @ (kpair @ sK8 @ sK9) @ sK7) != $true) | (sK10 = $true)),
% 0.12/0.37 inference(cnf_transformation,[],[f26])).
% 0.12/0.37 % SZS output end Proof for theBenchmark
% 0.12/0.37 % (12012)------------------------------
% 0.12/0.37 % (12012)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37 % (12012)Termination reason: Refutation
% 0.12/0.37
% 0.12/0.37 % (12012)Memory used [KB]: 5628
% 0.12/0.37 % (12012)Time elapsed: 0.009 s
% 0.12/0.37 % (12012)Instructions burned: 6 (million)
% 0.12/0.37 % (12012)------------------------------
% 0.12/0.37 % (12012)------------------------------
% 0.12/0.37 % (12006)Success in time 0.023 s
% 0.12/0.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------