TSTP Solution File: SEU669^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU669^2 : 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 : n004.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 03:50:28 EDT 2024
% Result : Theorem 0.17s 0.35s
% Output : Refutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU669^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.12 % 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
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 15:57:53 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 This is a TH0_THM_EQU_NAR problem
% 0.11/0.33 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
% 0.17/0.34 % (11690)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.17/0.34 % (11686)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.17/0.34 % (11684)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (3000ds/4Mi)
% 0.17/0.34 % (11683)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.17/0.34 % (11687)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.17/0.34 % (11689)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.17/0.34 % (11688)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (3000ds/275Mi)
% 0.17/0.34 % (11685)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (3000ds/27Mi)
% 0.17/0.34 % (11686)Instruction limit reached!
% 0.17/0.34 % (11686)------------------------------
% 0.17/0.34 % (11686)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34 % (11686)Termination reason: Unknown
% 0.17/0.34 % (11686)Termination phase: Preprocessing 3
% 0.17/0.34
% 0.17/0.34 % (11687)Instruction limit reached!
% 0.17/0.34 % (11687)------------------------------
% 0.17/0.34 % (11687)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34 % (11686)Memory used [KB]: 895
% 0.17/0.34 % (11686)Time elapsed: 0.003 s
% 0.17/0.34 % (11686)Instructions burned: 2 (million)
% 0.17/0.34 % (11686)------------------------------
% 0.17/0.34 % (11686)------------------------------
% 0.17/0.34 % (11687)Termination reason: Unknown
% 0.17/0.34 % (11687)Termination phase: Property scanning
% 0.17/0.34
% 0.17/0.34 % (11687)Memory used [KB]: 895
% 0.17/0.34 % (11687)Time elapsed: 0.002 s
% 0.17/0.34 % (11687)Instructions burned: 2 (million)
% 0.17/0.34 % (11687)------------------------------
% 0.17/0.34 % (11687)------------------------------
% 0.17/0.34 % (11690)Instruction limit reached!
% 0.17/0.34 % (11690)------------------------------
% 0.17/0.34 % (11690)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34 % (11690)Termination reason: Unknown
% 0.17/0.34 % (11690)Termination phase: Property scanning
% 0.17/0.34
% 0.17/0.34 % (11690)Memory used [KB]: 1023
% 0.17/0.34 % (11690)Time elapsed: 0.003 s
% 0.17/0.34 % (11690)Instructions burned: 3 (million)
% 0.17/0.34 % (11690)------------------------------
% 0.17/0.34 % (11690)------------------------------
% 0.17/0.34 % (11684)Instruction limit reached!
% 0.17/0.34 % (11684)------------------------------
% 0.17/0.34 % (11684)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34 % (11684)Termination reason: Unknown
% 0.17/0.34 % (11684)Termination phase: Saturation
% 0.17/0.34
% 0.17/0.34 % (11684)Memory used [KB]: 5500
% 0.17/0.34 % (11684)Time elapsed: 0.003 s
% 0.17/0.34 % (11684)Instructions burned: 4 (million)
% 0.17/0.34 % (11684)------------------------------
% 0.17/0.34 % (11684)------------------------------
% 0.17/0.34 % (11688)Refutation not found, incomplete strategy
% 0.17/0.34 % (11688)------------------------------
% 0.17/0.34 % (11688)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34 % (11688)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.34
% 0.17/0.34
% 0.17/0.34 % (11688)Memory used [KB]: 5500
% 0.17/0.34 % (11688)Time elapsed: 0.003 s
% 0.17/0.34 % (11688)Instructions burned: 3 (million)
% 0.17/0.34 % (11688)------------------------------
% 0.17/0.34 % (11688)------------------------------
% 0.17/0.34 % (11689)First to succeed.
% 0.17/0.35 % (11683)Also succeeded, but the first one will report.
% 0.17/0.35 % (11689)Refutation found. Thanks to Tanya!
% 0.17/0.35 % SZS status Theorem for theBenchmark
% 0.17/0.35 % SZS output start Proof for theBenchmark
% 0.17/0.35 thf(func_def_0, type, in: $i > $i > $o).
% 0.17/0.35 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 0.17/0.35 thf(func_def_4, type, kpair: $i > $i > $i).
% 0.17/0.35 thf(func_def_5, type, cartprod: $i > $i > $i).
% 0.17/0.35 thf(func_def_7, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.17/0.35 thf(func_def_21, type, sK2: $i > $o).
% 0.17/0.35 thf(func_def_26, type, sK7: $i > $i > $o).
% 0.17/0.35 thf(func_def_33, type, ph13: !>[X0: $tType]:(X0)).
% 0.17/0.35 thf(f55,plain,(
% 0.17/0.35 $false),
% 0.17/0.35 inference(subsumption_resolution,[],[f54,f35])).
% 0.17/0.35 thf(f35,plain,(
% 0.17/0.35 ($true != (in @ sK3 @ sK4))),
% 0.17/0.35 inference(cnf_transformation,[],[f24])).
% 0.17/0.35 thf(f24,plain,(
% 0.17/0.35 (cartprodpairmemEL = $true) & (($true != (in @ sK3 @ sK4)) & ($true = (in @ (kpair @ sK3 @ sK6) @ (dpsetconstr @ sK4 @ sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK7 @ Y0 @ Y1)))))))) & (dsetconstrEL = $true)),
% 0.17/0.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f17,f23])).
% 0.17/0.35 thf(f23,plain,(
% 0.17/0.35 ? [X0,X1,X2,X3,X4 : $i > $i > $o] : (($true != (in @ X0 @ X1)) & ($true = (in @ (kpair @ X0 @ X3) @ (dpsetconstr @ X1 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X4 @ Y0 @ Y1)))))))) => (($true != (in @ sK3 @ sK4)) & ($true = (in @ (kpair @ sK3 @ sK6) @ (dpsetconstr @ sK4 @ sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK7 @ Y0 @ Y1))))))))),
% 0.17/0.35 introduced(choice_axiom,[])).
% 0.17/0.35 thf(f17,plain,(
% 0.17/0.35 (cartprodpairmemEL = $true) & ? [X0,X1,X2,X3,X4 : $i > $i > $o] : (($true != (in @ X0 @ X1)) & ($true = (in @ (kpair @ X0 @ X3) @ (dpsetconstr @ X1 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X4 @ Y0 @ Y1)))))))) & (dsetconstrEL = $true)),
% 0.17/0.35 inference(flattening,[],[f16])).
% 0.17/0.35 thf(f16,plain,(
% 0.17/0.35 (? [X0,X1,X2,X3,X4 : $i > $i > $o] : (($true != (in @ X0 @ X1)) & ($true = (in @ (kpair @ X0 @ X3) @ (dpsetconstr @ X1 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X4 @ Y0 @ Y1)))))))) & (cartprodpairmemEL = $true)) & (dsetconstrEL = $true)),
% 0.17/0.35 inference(ennf_transformation,[],[f12])).
% 0.17/0.35 thf(f12,plain,(
% 0.17/0.35 ~((dsetconstrEL = $true) => ((cartprodpairmemEL = $true) => ! [X0,X1,X2,X3,X4 : $i > $i > $o] : (($true = (in @ (kpair @ X0 @ X3) @ (dpsetconstr @ X1 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X4 @ Y0 @ Y1))))))) => ($true = (in @ X0 @ X1)))))),
% 0.17/0.35 inference(fool_elimination,[],[f11])).
% 0.17/0.35 thf(f11,plain,(
% 0.17/0.35 ~(dsetconstrEL => (cartprodpairmemEL => ! [X0,X1,X2,X3,X4 : $i > $i > $o] : ((in @ (kpair @ X0 @ X3) @ (dpsetconstr @ X1 @ X2 @ (^[X5 : $i, X6 : $i] : (X4 @ X5 @ X6)))) => (in @ X0 @ X1))))),
% 0.17/0.35 inference(rectify,[],[f5])).
% 0.17/0.35 thf(f5,negated_conjecture,(
% 0.17/0.35 ~(dsetconstrEL => (cartprodpairmemEL => ! [X2,X0,X4,X3,X1 : $i > $i > $o] : ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X4 @ (^[X6 : $i, X5 : $i] : (X1 @ X6 @ X5)))) => (in @ X2 @ X0))))),
% 0.17/0.35 inference(negated_conjecture,[],[f4])).
% 0.17/0.35 thf(f4,conjecture,(
% 0.17/0.35 dsetconstrEL => (cartprodpairmemEL => ! [X2,X0,X4,X3,X1 : $i > $i > $o] : ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X4 @ (^[X6 : $i, X5 : $i] : (X1 @ X6 @ X5)))) => (in @ X2 @ X0)))),
% 0.17/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL1)).
% 0.17/0.35 thf(f54,plain,(
% 0.17/0.35 ($true = (in @ sK3 @ sK4))),
% 0.17/0.35 inference(trivial_inequality_removal,[],[f53])).
% 0.17/0.35 thf(f53,plain,(
% 0.17/0.35 ($true = (in @ sK3 @ sK4)) | ($true != $true)),
% 0.17/0.35 inference(superposition,[],[f50,f52])).
% 0.17/0.35 thf(f52,plain,(
% 0.17/0.35 ($true = (in @ (kpair @ sK3 @ sK6) @ (cartprod @ sK4 @ sK5)))),
% 0.17/0.35 inference(trivial_inequality_removal,[],[f51])).
% 0.17/0.35 thf(f51,plain,(
% 0.17/0.35 ($true != $true) | ($true = (in @ (kpair @ sK3 @ sK6) @ (cartprod @ sK4 @ sK5)))),
% 0.17/0.35 inference(superposition,[],[f49,f47])).
% 0.17/0.35 thf(f47,plain,(
% 0.17/0.35 ($true = (in @ (kpair @ sK3 @ sK6) @ (dsetconstr @ (cartprod @ sK4 @ sK5) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((((kpair @ Y1 @ Y2) = Y0) & (sK7 @ Y1 @ Y2)) & (in @ Y2 @ sK5)))) & (in @ Y1 @ sK4))))))))),
% 0.17/0.35 inference(beta_eta_normalization,[],[f43])).
% 0.17/0.35 thf(f43,plain,(
% 0.17/0.35 ($true = (in @ (kpair @ sK3 @ sK6) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: ((((kpair @ Y4 @ Y5) = Y3) & (Y2 @ Y4 @ Y5)) & (in @ Y5 @ Y1)))) & (in @ Y4 @ Y0))))))))))) @ sK4 @ sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK7 @ Y0 @ Y1)))))))),
% 0.17/0.35 inference(definition_unfolding,[],[f34,f32])).
% 0.17/0.35 thf(f32,plain,(
% 0.17/0.35 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: ((((kpair @ Y4 @ Y5) = Y3) & (Y2 @ Y4 @ Y5)) & (in @ Y5 @ Y1)))) & (in @ Y4 @ Y0))))))))))))),
% 0.17/0.35 inference(cnf_transformation,[],[f8])).
% 0.17/0.35 thf(f8,plain,(
% 0.17/0.35 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: ((((kpair @ Y4 @ Y5) = Y3) & (Y2 @ Y4 @ Y5)) & (in @ Y5 @ Y1)))) & (in @ Y4 @ Y0))))))))))))),
% 0.17/0.35 inference(fool_elimination,[],[f7])).
% 0.17/0.35 thf(f7,plain,(
% 0.17/0.35 (dpsetconstr = (^[X0 : $i, X1 : $i, X2 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4] : ((in @ X4 @ X0) & ? [X5] : ((in @ X5 @ X1) & (X2 @ X4 @ X5) & ((kpair @ X4 @ X5) = X3))))))))),
% 0.17/0.35 inference(rectify,[],[f3])).
% 0.17/0.35 thf(f3,axiom,(
% 0.17/0.35 (dpsetconstr = (^[X0 : $i, X4 : $i, X1 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X4) @ (^[X5 : $i] : (? [X2] : ((in @ X2 @ X0) & ? [X3] : ((in @ X3 @ X4) & (X1 @ X2 @ X3) & ((kpair @ X2 @ X3) = X5))))))))),
% 0.17/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstr)).
% 0.17/0.35 thf(f34,plain,(
% 0.17/0.35 ($true = (in @ (kpair @ sK3 @ sK6) @ (dpsetconstr @ sK4 @ sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK7 @ Y0 @ Y1)))))))),
% 0.17/0.35 inference(cnf_transformation,[],[f24])).
% 0.17/0.35 thf(f49,plain,(
% 0.17/0.35 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != (in @ X4 @ (dsetconstr @ X3 @ X5))) | ($true = (in @ X4 @ X3))) )),
% 0.17/0.35 inference(beta_eta_normalization,[],[f48])).
% 0.17/0.35 thf(f48,plain,(
% 0.17/0.35 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true = (in @ X4 @ X3)) | ($true != (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))))) )),
% 0.17/0.35 inference(trivial_inequality_removal,[],[f42])).
% 0.17/0.35 thf(f42,plain,(
% 0.17/0.35 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != $true) | ($true != (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0))))) | ($true = (in @ X4 @ X3))) )),
% 0.17/0.35 inference(definition_unfolding,[],[f29,f33])).
% 0.17/0.35 thf(f33,plain,(
% 0.17/0.35 (dsetconstrEL = $true)),
% 0.17/0.35 inference(cnf_transformation,[],[f24])).
% 0.17/0.35 thf(f29,plain,(
% 0.17/0.35 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true = (in @ X4 @ X3)) | ($true != (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0))))) | (dsetconstrEL != $true)) )),
% 0.17/0.35 inference(cnf_transformation,[],[f22])).
% 0.17/0.35 thf(f22,plain,(
% 0.17/0.35 ((dsetconstrEL = $true) | (($true != (in @ sK1 @ sK0)) & ($true = (in @ sK1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK2 @ Y0))))))) & (! [X3,X4,X5 : $i > $o] : (($true = (in @ X4 @ X3)) | ($true != (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))))) | (dsetconstrEL != $true))),
% 0.17/0.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f21])).
% 0.17/0.35 thf(f21,plain,(
% 0.17/0.35 ? [X0,X1,X2 : $i > $o] : (($true != (in @ X1 @ X0)) & ($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) => (($true != (in @ sK1 @ sK0)) & ($true = (in @ sK1 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK2 @ Y0))))))),
% 0.17/0.35 introduced(choice_axiom,[])).
% 0.17/0.35 thf(f20,plain,(
% 0.17/0.35 ((dsetconstrEL = $true) | ? [X0,X1,X2 : $i > $o] : (($true != (in @ X1 @ X0)) & ($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))))) & (! [X3,X4,X5 : $i > $o] : (($true = (in @ X4 @ X3)) | ($true != (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))))) | (dsetconstrEL != $true))),
% 0.17/0.35 inference(rectify,[],[f19])).
% 0.17/0.35 thf(f19,plain,(
% 0.17/0.35 ((dsetconstrEL = $true) | ? [X0,X1,X2 : $i > $o] : (($true != (in @ X1 @ X0)) & ($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))))) & (! [X0,X1,X2 : $i > $o] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) | (dsetconstrEL != $true))),
% 0.17/0.35 inference(nnf_transformation,[],[f18])).
% 0.17/0.35 thf(f18,plain,(
% 0.17/0.35 (dsetconstrEL = $true) <=> ! [X0,X1,X2 : $i > $o] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))))),
% 0.17/0.35 inference(ennf_transformation,[],[f14])).
% 0.17/0.35 thf(f14,plain,(
% 0.17/0.35 (dsetconstrEL = $true) <=> ! [X0,X1,X2 : $i > $o] : (($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) => ($true = (in @ X1 @ X0)))),
% 0.17/0.35 inference(fool_elimination,[],[f13])).
% 0.17/0.35 thf(f13,plain,(
% 0.17/0.35 (dsetconstrEL = ! [X0,X1,X2 : $i > $o] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => (in @ X1 @ X0)))),
% 0.17/0.35 inference(rectify,[],[f1])).
% 0.17/0.35 thf(f1,axiom,(
% 0.17/0.35 (dsetconstrEL = ! [X0,X2,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)))),
% 0.17/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL)).
% 0.17/0.35 thf(f50,plain,(
% 0.17/0.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ X1 @ X2) @ (cartprod @ X0 @ X3))) | ($true = (in @ X1 @ X0))) )),
% 0.17/0.35 inference(trivial_inequality_removal,[],[f44])).
% 0.17/0.35 thf(f44,plain,(
% 0.17/0.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = (in @ X1 @ X0)) | ($true != (in @ (kpair @ X1 @ X2) @ (cartprod @ X0 @ X3)))) )),
% 0.17/0.35 inference(definition_unfolding,[],[f39,f36])).
% 0.17/0.35 thf(f36,plain,(
% 0.17/0.35 (cartprodpairmemEL = $true)),
% 0.17/0.35 inference(cnf_transformation,[],[f24])).
% 0.17/0.35 thf(f39,plain,(
% 0.17/0.35 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ X1 @ X2) @ (cartprod @ X0 @ X3))) | ($true = (in @ X1 @ X0)) | (cartprodpairmemEL != $true)) )),
% 0.17/0.35 inference(cnf_transformation,[],[f28])).
% 0.17/0.35 thf(f28,plain,(
% 0.17/0.35 (! [X0,X1,X2,X3] : (($true != (in @ (kpair @ X1 @ X2) @ (cartprod @ X0 @ X3))) | ($true = (in @ X1 @ X0))) | (cartprodpairmemEL != $true)) & ((cartprodpairmemEL = $true) | (($true = (in @ (kpair @ sK9 @ sK10) @ (cartprod @ sK8 @ sK11))) & ($true != (in @ sK9 @ sK8))))),
% 0.17/0.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f26,f27])).
% 0.17/0.35 thf(f27,plain,(
% 0.17/0.35 ? [X4,X5,X6,X7] : (($true = (in @ (kpair @ X5 @ X6) @ (cartprod @ X4 @ X7))) & ($true != (in @ X5 @ X4))) => (($true = (in @ (kpair @ sK9 @ sK10) @ (cartprod @ sK8 @ sK11))) & ($true != (in @ sK9 @ sK8)))),
% 0.17/0.35 introduced(choice_axiom,[])).
% 0.17/0.35 thf(f26,plain,(
% 0.17/0.35 (! [X0,X1,X2,X3] : (($true != (in @ (kpair @ X1 @ X2) @ (cartprod @ X0 @ X3))) | ($true = (in @ X1 @ X0))) | (cartprodpairmemEL != $true)) & ((cartprodpairmemEL = $true) | ? [X4,X5,X6,X7] : (($true = (in @ (kpair @ X5 @ X6) @ (cartprod @ X4 @ X7))) & ($true != (in @ X5 @ X4))))),
% 0.17/0.35 inference(rectify,[],[f25])).
% 0.17/0.35 thf(f25,plain,(
% 0.17/0.35 (! [X0,X1,X2,X3] : (($true != (in @ (kpair @ X1 @ X2) @ (cartprod @ X0 @ X3))) | ($true = (in @ X1 @ X0))) | (cartprodpairmemEL != $true)) & ((cartprodpairmemEL = $true) | ? [X0,X1,X2,X3] : (($true = (in @ (kpair @ X1 @ X2) @ (cartprod @ X0 @ X3))) & ($true != (in @ X1 @ X0))))),
% 0.17/0.35 inference(nnf_transformation,[],[f15])).
% 0.17/0.35 thf(f15,plain,(
% 0.17/0.35 ! [X0,X1,X2,X3] : (($true != (in @ (kpair @ X1 @ X2) @ (cartprod @ X0 @ X3))) | ($true = (in @ X1 @ X0))) <=> (cartprodpairmemEL = $true)),
% 0.17/0.35 inference(ennf_transformation,[],[f10])).
% 0.17/0.35 thf(f10,plain,(
% 0.17/0.35 (cartprodpairmemEL = $true) <=> ! [X0,X1,X2,X3] : (($true = (in @ (kpair @ X1 @ X2) @ (cartprod @ X0 @ X3))) => ($true = (in @ X1 @ X0)))),
% 0.17/0.35 inference(fool_elimination,[],[f9])).
% 0.17/0.35 thf(f9,plain,(
% 0.17/0.35 (! [X0,X1,X2,X3] : ((in @ (kpair @ X1 @ X2) @ (cartprod @ X0 @ X3)) => (in @ X1 @ X0)) = cartprodpairmemEL)),
% 0.17/0.35 inference(rectify,[],[f2])).
% 0.17/0.35 thf(f2,axiom,(
% 0.17/0.35 (! [X0,X2,X3,X4] : ((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X4)) => (in @ X2 @ X0)) = cartprodpairmemEL)),
% 0.17/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemEL)).
% 0.17/0.35 % SZS output end Proof for theBenchmark
% 0.17/0.35 % (11689)------------------------------
% 0.17/0.35 % (11689)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.35 % (11689)Termination reason: Refutation
% 0.17/0.35
% 0.17/0.35 % (11689)Memory used [KB]: 5500
% 0.17/0.35 % (11689)Time elapsed: 0.007 s
% 0.17/0.35 % (11689)Instructions burned: 5 (million)
% 0.17/0.35 % (11689)------------------------------
% 0.17/0.35 % (11689)------------------------------
% 0.17/0.35 % (11682)Success in time 0.006 s
% 0.17/0.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------