TSTP Solution File: SEU659^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU659^2 : 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 : n010.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 03:50:24 EDT 2024
% Result : Theorem 0.19s 0.38s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU659^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13 % 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 : n010.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 16:40:37 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.35 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
% 0.19/0.37 % (12259)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.37 % (12254)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)
% 0.19/0.37 % (12260)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)
% 0.19/0.37 % (12256)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.37 % (12257)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)
% 0.19/0.37 % (12258)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)
% 0.19/0.37 % (12255)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)
% 0.19/0.37 % (12256)Instruction limit reached!
% 0.19/0.37 % (12256)------------------------------
% 0.19/0.37 % (12256)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (12256)Termination reason: Unknown
% 0.19/0.37 % (12256)Termination phase: Property scanning
% 0.19/0.37 % (12257)Instruction limit reached!
% 0.19/0.37 % (12257)------------------------------
% 0.19/0.37 % (12257)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37
% 0.19/0.37 % (12256)Memory used [KB]: 895
% 0.19/0.37 % (12256)Time elapsed: 0.003 s
% 0.19/0.37 % (12256)Instructions burned: 2 (million)
% 0.19/0.37 % (12256)------------------------------
% 0.19/0.37 % (12256)------------------------------
% 0.19/0.37 % (12257)Termination reason: Unknown
% 0.19/0.37 % (12257)Termination phase: Property scanning
% 0.19/0.37
% 0.19/0.37 % (12257)Memory used [KB]: 895
% 0.19/0.37 % (12257)Time elapsed: 0.003 s
% 0.19/0.37 % (12257)Instructions burned: 2 (million)
% 0.19/0.37 % (12257)------------------------------
% 0.19/0.37 % (12257)------------------------------
% 0.19/0.37 % (12260)Instruction limit reached!
% 0.19/0.37 % (12260)------------------------------
% 0.19/0.37 % (12260)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (12260)Termination reason: Unknown
% 0.19/0.37 % (12260)Termination phase: Property scanning
% 0.19/0.37
% 0.19/0.37 % (12260)Memory used [KB]: 1023
% 0.19/0.37 % (12260)Time elapsed: 0.004 s
% 0.19/0.37 % (12260)Instructions burned: 3 (million)
% 0.19/0.37 % (12260)------------------------------
% 0.19/0.37 % (12260)------------------------------
% 0.19/0.37 % (12254)Instruction limit reached!
% 0.19/0.37 % (12254)------------------------------
% 0.19/0.37 % (12254)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (12254)Termination reason: Unknown
% 0.19/0.37 % (12254)Termination phase: Saturation
% 0.19/0.37
% 0.19/0.37 % (12254)Memory used [KB]: 5500
% 0.19/0.37 % (12254)Time elapsed: 0.005 s
% 0.19/0.37 % (12254)Instructions burned: 5 (million)
% 0.19/0.37 % (12254)------------------------------
% 0.19/0.37 % (12254)------------------------------
% 0.19/0.37 % (12259)First to succeed.
% 0.19/0.37 % (12258)Also succeeded, but the first one will report.
% 0.19/0.38 % (12259)Refutation found. Thanks to Tanya!
% 0.19/0.38 % SZS status Theorem for theBenchmark
% 0.19/0.38 % SZS output start Proof for theBenchmark
% 0.19/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.19/0.38 thf(func_def_1, type, kpair: $i > $i > $i).
% 0.19/0.38 thf(func_def_2, type, cartprod: $i > $i > $i).
% 0.19/0.38 thf(func_def_11, type, sK3: $i > $i > $i > $i).
% 0.19/0.38 thf(func_def_12, type, sK4: $i > $i > $i > $i).
% 0.19/0.38 thf(f66,plain,(
% 0.19/0.38 $false),
% 0.19/0.38 inference(subsumption_resolution,[],[f65,f40])).
% 0.19/0.38 thf(f40,plain,(
% 0.19/0.38 ($true != (in @ sK9 @ sK10))),
% 0.19/0.38 inference(cnf_transformation,[],[f28])).
% 0.19/0.38 thf(f28,plain,(
% 0.19/0.38 (($true != (in @ sK9 @ sK10)) & ($true = (in @ (kpair @ sK9 @ sK12) @ (cartprod @ sK10 @ sK11)))) & (cartprodmempair1 = $true) & (setukpairinjL = $true)),
% 0.19/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f26,f27])).
% 0.19/0.38 thf(f27,plain,(
% 0.19/0.38 ? [X0,X1,X2,X3] : (($true != (in @ X0 @ X1)) & ((in @ (kpair @ X0 @ X3) @ (cartprod @ X1 @ X2)) = $true)) => (($true != (in @ sK9 @ sK10)) & ($true = (in @ (kpair @ sK9 @ sK12) @ (cartprod @ sK10 @ sK11))))),
% 0.19/0.38 introduced(choice_axiom,[])).
% 0.19/0.38 thf(f26,plain,(
% 0.19/0.38 ? [X0,X1,X2,X3] : (($true != (in @ X0 @ X1)) & ((in @ (kpair @ X0 @ X3) @ (cartprod @ X1 @ X2)) = $true)) & (cartprodmempair1 = $true) & (setukpairinjL = $true)),
% 0.19/0.38 inference(rectify,[],[f15])).
% 0.19/0.38 thf(f15,plain,(
% 0.19/0.38 ? [X3,X1,X0,X2] : (((in @ X3 @ X1) != $true) & ($true = (in @ (kpair @ X3 @ X2) @ (cartprod @ X1 @ X0)))) & (cartprodmempair1 = $true) & (setukpairinjL = $true)),
% 0.19/0.38 inference(flattening,[],[f14])).
% 0.19/0.38 thf(f14,plain,(
% 0.19/0.38 (? [X3,X1,X0,X2] : (((in @ X3 @ X1) != $true) & ($true = (in @ (kpair @ X3 @ X2) @ (cartprod @ X1 @ X0)))) & (setukpairinjL = $true)) & (cartprodmempair1 = $true)),
% 0.19/0.38 inference(ennf_transformation,[],[f9])).
% 0.19/0.38 thf(f9,plain,(
% 0.19/0.38 ~((cartprodmempair1 = $true) => ((setukpairinjL = $true) => ! [X1,X3,X2,X0] : (($true = (in @ (kpair @ X3 @ X2) @ (cartprod @ X1 @ X0))) => ((in @ X3 @ X1) = $true))))),
% 0.19/0.38 inference(fool_elimination,[],[f8])).
% 0.19/0.38 thf(f8,plain,(
% 0.19/0.38 ~(cartprodmempair1 => (setukpairinjL => ! [X0,X1,X2,X3] : ((in @ (kpair @ X3 @ X2) @ (cartprod @ X1 @ X0)) => (in @ X3 @ X1))))),
% 0.19/0.38 inference(rectify,[],[f4])).
% 0.19/0.38 thf(f4,negated_conjecture,(
% 0.19/0.38 ~(cartprodmempair1 => (setukpairinjL => ! [X1,X0,X4,X3] : ((in @ (kpair @ X3 @ X4) @ (cartprod @ X0 @ X1)) => (in @ X3 @ X0))))),
% 0.19/0.38 inference(negated_conjecture,[],[f3])).
% 0.19/0.38 thf(f3,conjecture,(
% 0.19/0.38 cartprodmempair1 => (setukpairinjL => ! [X1,X0,X4,X3] : ((in @ (kpair @ X3 @ X4) @ (cartprod @ X0 @ X1)) => (in @ X3 @ X0)))),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemEL)).
% 0.19/0.38 thf(f65,plain,(
% 0.19/0.38 ($true = (in @ sK9 @ sK10))),
% 0.19/0.38 inference(backward_demodulation,[],[f57,f63])).
% 0.19/0.38 thf(f63,plain,(
% 0.19/0.38 (sK9 = (sK3 @ sK11 @ (kpair @ sK9 @ sK12) @ sK10))),
% 0.19/0.38 inference(equality_resolution,[],[f60])).
% 0.19/0.38 thf(f60,plain,(
% 0.19/0.38 ( ! [X0 : $i,X1 : $i] : (((kpair @ X0 @ X1) != (kpair @ sK9 @ sK12)) | ((sK3 @ sK11 @ (kpair @ sK9 @ sK12) @ sK10) = X0)) )),
% 0.19/0.38 inference(superposition,[],[f50,f59])).
% 0.19/0.38 thf(f59,plain,(
% 0.19/0.38 ((kpair @ (sK3 @ sK11 @ (kpair @ sK9 @ sK12) @ sK10) @ (sK4 @ sK11 @ (kpair @ sK9 @ sK12) @ sK10)) = (kpair @ sK9 @ sK12))),
% 0.19/0.38 inference(trivial_inequality_removal,[],[f58])).
% 0.19/0.38 thf(f58,plain,(
% 0.19/0.38 ($true != $true) | ((kpair @ (sK3 @ sK11 @ (kpair @ sK9 @ sK12) @ sK10) @ (sK4 @ sK11 @ (kpair @ sK9 @ sK12) @ sK10)) = (kpair @ sK9 @ sK12))),
% 0.19/0.38 inference(superposition,[],[f51,f39])).
% 0.19/0.38 thf(f39,plain,(
% 0.19/0.38 ($true = (in @ (kpair @ sK9 @ sK12) @ (cartprod @ sK10 @ sK11)))),
% 0.19/0.38 inference(cnf_transformation,[],[f28])).
% 0.19/0.38 thf(f51,plain,(
% 0.19/0.38 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X6 @ (cartprod @ X5 @ X7))) | ((kpair @ (sK3 @ X7 @ X6 @ X5) @ (sK4 @ X7 @ X6 @ X5)) = X6)) )),
% 0.19/0.38 inference(trivial_inequality_removal,[],[f45])).
% 0.19/0.38 thf(f45,plain,(
% 0.19/0.38 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != $true) | ((kpair @ (sK3 @ X7 @ X6 @ X5) @ (sK4 @ X7 @ X6 @ X5)) = X6) | ($true != (in @ X6 @ (cartprod @ X5 @ X7)))) )),
% 0.19/0.38 inference(definition_unfolding,[],[f29,f38])).
% 0.19/0.38 thf(f38,plain,(
% 0.19/0.38 (cartprodmempair1 = $true)),
% 0.19/0.38 inference(cnf_transformation,[],[f28])).
% 0.19/0.38 thf(f29,plain,(
% 0.19/0.38 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X6 @ (cartprod @ X5 @ X7))) | ((kpair @ (sK3 @ X7 @ X6 @ X5) @ (sK4 @ X7 @ X6 @ X5)) = X6) | (cartprodmempair1 != $true)) )),
% 0.19/0.38 inference(cnf_transformation,[],[f21])).
% 0.19/0.38 thf(f21,plain,(
% 0.19/0.38 ((cartprodmempair1 = $true) | (($true = (in @ sK1 @ (cartprod @ sK0 @ sK2))) & ! [X3] : (($true != (in @ X3 @ sK0)) | ! [X4] : (($true != (in @ X4 @ sK2)) | ((kpair @ X3 @ X4) != sK1))))) & (! [X5,X6,X7] : (($true != (in @ X6 @ (cartprod @ X5 @ X7))) | (($true = (in @ (sK3 @ X7 @ X6 @ X5) @ X5)) & (($true = (in @ (sK4 @ X7 @ X6 @ X5) @ X7)) & ((kpair @ (sK3 @ X7 @ X6 @ X5) @ (sK4 @ X7 @ X6 @ X5)) = X6)))) | (cartprodmempair1 != $true))),
% 0.19/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f17,f20,f19,f18])).
% 0.19/0.38 thf(f18,plain,(
% 0.19/0.38 ? [X0,X1,X2] : (($true = (in @ X1 @ (cartprod @ X0 @ X2))) & ! [X3] : (((in @ X3 @ X0) != $true) | ! [X4] : (($true != (in @ X4 @ X2)) | ((kpair @ X3 @ X4) != X1)))) => (($true = (in @ sK1 @ (cartprod @ sK0 @ sK2))) & ! [X3] : (($true != (in @ X3 @ sK0)) | ! [X4] : (($true != (in @ X4 @ sK2)) | ((kpair @ X3 @ X4) != sK1))))),
% 0.19/0.38 introduced(choice_axiom,[])).
% 0.19/0.38 thf(f19,plain,(
% 0.19/0.38 ! [X5,X6,X7] : (? [X8] : (($true = (in @ X8 @ X5)) & ? [X9] : (($true = (in @ X9 @ X7)) & ((kpair @ X8 @ X9) = X6))) => (($true = (in @ (sK3 @ X7 @ X6 @ X5) @ X5)) & ? [X9] : (($true = (in @ X9 @ X7)) & ((kpair @ (sK3 @ X7 @ X6 @ X5) @ X9) = X6))))),
% 0.19/0.38 introduced(choice_axiom,[])).
% 0.19/0.38 thf(f20,plain,(
% 0.19/0.38 ! [X5,X6,X7] : (? [X9] : (($true = (in @ X9 @ X7)) & ((kpair @ (sK3 @ X7 @ X6 @ X5) @ X9) = X6)) => (($true = (in @ (sK4 @ X7 @ X6 @ X5) @ X7)) & ((kpair @ (sK3 @ X7 @ X6 @ X5) @ (sK4 @ X7 @ X6 @ X5)) = X6)))),
% 0.19/0.38 introduced(choice_axiom,[])).
% 0.19/0.38 thf(f17,plain,(
% 0.19/0.38 ((cartprodmempair1 = $true) | ? [X0,X1,X2] : (($true = (in @ X1 @ (cartprod @ X0 @ X2))) & ! [X3] : (((in @ X3 @ X0) != $true) | ! [X4] : (($true != (in @ X4 @ X2)) | ((kpair @ X3 @ X4) != X1))))) & (! [X5,X6,X7] : (($true != (in @ X6 @ (cartprod @ X5 @ X7))) | ? [X8] : (($true = (in @ X8 @ X5)) & ? [X9] : (($true = (in @ X9 @ X7)) & ((kpair @ X8 @ X9) = X6)))) | (cartprodmempair1 != $true))),
% 0.19/0.38 inference(rectify,[],[f16])).
% 0.19/0.38 thf(f16,plain,(
% 0.19/0.38 ((cartprodmempair1 = $true) | ? [X1,X2,X0] : (($true = (in @ X2 @ (cartprod @ X1 @ X0))) & ! [X3] : (((in @ X3 @ X1) != $true) | ! [X4] : (($true != (in @ X4 @ X0)) | ((kpair @ X3 @ X4) != X2))))) & (! [X1,X2,X0] : (($true != (in @ X2 @ (cartprod @ X1 @ X0))) | ? [X3] : (((in @ X3 @ X1) = $true) & ? [X4] : (($true = (in @ X4 @ X0)) & ((kpair @ X3 @ X4) = X2)))) | (cartprodmempair1 != $true))),
% 0.19/0.38 inference(nnf_transformation,[],[f12])).
% 0.19/0.38 thf(f12,plain,(
% 0.19/0.38 (cartprodmempair1 = $true) <=> ! [X1,X2,X0] : (($true != (in @ X2 @ (cartprod @ X1 @ X0))) | ? [X3] : (((in @ X3 @ X1) = $true) & ? [X4] : (($true = (in @ X4 @ X0)) & ((kpair @ X3 @ X4) = X2))))),
% 0.19/0.38 inference(ennf_transformation,[],[f7])).
% 0.19/0.38 thf(f7,plain,(
% 0.19/0.38 ! [X1,X2,X0] : (($true = (in @ X2 @ (cartprod @ X1 @ X0))) => ? [X3] : (((in @ X3 @ X1) = $true) & ? [X4] : (($true = (in @ X4 @ X0)) & ((kpair @ X3 @ X4) = X2)))) <=> (cartprodmempair1 = $true)),
% 0.19/0.38 inference(fool_elimination,[],[f6])).
% 0.19/0.38 thf(f6,plain,(
% 0.19/0.38 (! [X0,X1,X2] : ((in @ X2 @ (cartprod @ X1 @ X0)) => ? [X3] : (? [X4] : ((in @ X4 @ X0) & ((kpair @ X3 @ X4) = X2)) & (in @ X3 @ X1))) = cartprodmempair1)),
% 0.19/0.38 inference(rectify,[],[f1])).
% 0.19/0.38 thf(f1,axiom,(
% 0.19/0.38 (! [X1,X0,X2] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ? [X3] : (? [X4] : ((in @ X4 @ X1) & ((kpair @ X3 @ X4) = X2)) & (in @ X3 @ X0))) = cartprodmempair1)),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1)).
% 0.19/0.38 thf(f50,plain,(
% 0.19/0.38 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((kpair @ X6 @ X7) != (kpair @ X5 @ X4)) | (X5 = X6)) )),
% 0.19/0.38 inference(trivial_inequality_removal,[],[f48])).
% 0.19/0.38 thf(f48,plain,(
% 0.19/0.38 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != $true) | (X5 = X6) | ((kpair @ X6 @ X7) != (kpair @ X5 @ X4))) )),
% 0.19/0.38 inference(definition_unfolding,[],[f34,f37])).
% 0.19/0.38 thf(f37,plain,(
% 0.19/0.38 (setukpairinjL = $true)),
% 0.19/0.38 inference(cnf_transformation,[],[f28])).
% 0.19/0.38 thf(f34,plain,(
% 0.19/0.38 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((kpair @ X6 @ X7) != (kpair @ X5 @ X4)) | (X5 = X6) | (setukpairinjL != $true)) )),
% 0.19/0.38 inference(cnf_transformation,[],[f25])).
% 0.19/0.38 thf(f25,plain,(
% 0.19/0.38 ((setukpairinjL = $true) | (((kpair @ sK6 @ sK5) = (kpair @ sK7 @ sK8)) & (sK6 != sK7))) & (! [X4,X5,X6,X7] : (((kpair @ X6 @ X7) != (kpair @ X5 @ X4)) | (X5 = X6)) | (setukpairinjL != $true))),
% 0.19/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f23,f24])).
% 0.19/0.38 thf(f24,plain,(
% 0.19/0.38 ? [X0,X1,X2,X3] : (((kpair @ X1 @ X0) = (kpair @ X2 @ X3)) & (X1 != X2)) => (((kpair @ sK6 @ sK5) = (kpair @ sK7 @ sK8)) & (sK6 != sK7))),
% 0.19/0.38 introduced(choice_axiom,[])).
% 0.19/0.38 thf(f23,plain,(
% 0.19/0.38 ((setukpairinjL = $true) | ? [X0,X1,X2,X3] : (((kpair @ X1 @ X0) = (kpair @ X2 @ X3)) & (X1 != X2))) & (! [X4,X5,X6,X7] : (((kpair @ X6 @ X7) != (kpair @ X5 @ X4)) | (X5 = X6)) | (setukpairinjL != $true))),
% 0.19/0.38 inference(rectify,[],[f22])).
% 0.19/0.38 thf(f22,plain,(
% 0.19/0.38 ((setukpairinjL = $true) | ? [X3,X1,X0,X2] : (((kpair @ X0 @ X2) = (kpair @ X1 @ X3)) & (X0 != X1))) & (! [X3,X1,X0,X2] : (((kpair @ X0 @ X2) != (kpair @ X1 @ X3)) | (X0 = X1)) | (setukpairinjL != $true))),
% 0.19/0.38 inference(nnf_transformation,[],[f13])).
% 0.19/0.38 thf(f13,plain,(
% 0.19/0.38 (setukpairinjL = $true) <=> ! [X3,X1,X0,X2] : (((kpair @ X0 @ X2) != (kpair @ X1 @ X3)) | (X0 = X1))),
% 0.19/0.38 inference(ennf_transformation,[],[f11])).
% 0.19/0.38 thf(f11,plain,(
% 0.19/0.38 (setukpairinjL = $true) <=> ! [X0,X2,X3,X1] : (((kpair @ X0 @ X2) = (kpair @ X1 @ X3)) => (X0 = X1))),
% 0.19/0.38 inference(fool_elimination,[],[f10])).
% 0.19/0.38 thf(f10,plain,(
% 0.19/0.38 (setukpairinjL = ! [X0,X1,X2,X3] : (((kpair @ X0 @ X2) = (kpair @ X1 @ X3)) => (X0 = X1)))),
% 0.19/0.38 inference(rectify,[],[f2])).
% 0.19/0.38 thf(f2,axiom,(
% 0.19/0.38 (setukpairinjL = ! [X3,X5,X4,X2] : (((kpair @ X3 @ X4) = (kpair @ X5 @ X2)) => (X3 = X5)))),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL)).
% 0.19/0.38 thf(f57,plain,(
% 0.19/0.38 ($true = (in @ (sK3 @ sK11 @ (kpair @ sK9 @ sK12) @ sK10) @ sK10))),
% 0.19/0.38 inference(trivial_inequality_removal,[],[f56])).
% 0.19/0.38 thf(f56,plain,(
% 0.19/0.38 ($true != $true) | ($true = (in @ (sK3 @ sK11 @ (kpair @ sK9 @ sK12) @ sK10) @ sK10))),
% 0.19/0.38 inference(superposition,[],[f52,f39])).
% 0.19/0.38 thf(f52,plain,(
% 0.19/0.38 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X6 @ (cartprod @ X5 @ X7))) | ($true = (in @ (sK3 @ X7 @ X6 @ X5) @ X5))) )),
% 0.19/0.38 inference(trivial_inequality_removal,[],[f43])).
% 0.19/0.38 thf(f43,plain,(
% 0.19/0.38 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true = (in @ (sK3 @ X7 @ X6 @ X5) @ X5)) | ($true != (in @ X6 @ (cartprod @ X5 @ X7))) | ($true != $true)) )),
% 0.19/0.38 inference(definition_unfolding,[],[f31,f38])).
% 0.19/0.38 thf(f31,plain,(
% 0.19/0.38 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X6 @ (cartprod @ X5 @ X7))) | ($true = (in @ (sK3 @ X7 @ X6 @ X5) @ X5)) | (cartprodmempair1 != $true)) )),
% 0.19/0.38 inference(cnf_transformation,[],[f21])).
% 0.19/0.38 % SZS output end Proof for theBenchmark
% 0.19/0.38 % (12259)------------------------------
% 0.19/0.38 % (12259)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.38 % (12259)Termination reason: Refutation
% 0.19/0.38
% 0.19/0.38 % (12259)Memory used [KB]: 5500
% 0.19/0.38 % (12259)Time elapsed: 0.008 s
% 0.19/0.38 % (12259)Instructions burned: 6 (million)
% 0.19/0.38 % (12259)------------------------------
% 0.19/0.38 % (12259)------------------------------
% 0.19/0.38 % (12252)Success in time 0.022 s
% 0.19/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------