TSTP Solution File: SEU631^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU631^2 : 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 : 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 03:50:08 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU631^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % 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
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 17:30:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 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
% 0.14/0.37 % (31102)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (31102)First to succeed.
% 0.14/0.37 % (31103)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)
% 0.14/0.38 % (31103)Instruction limit reached!
% 0.14/0.38 % (31103)------------------------------
% 0.14/0.38 % (31103)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (31103)Termination reason: Unknown
% 0.14/0.38 % (31103)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (31103)Memory used [KB]: 5500
% 0.14/0.38 % (31103)Time elapsed: 0.003 s
% 0.14/0.38 % (31103)Instructions burned: 3 (million)
% 0.14/0.38 % (31103)------------------------------
% 0.14/0.38 % (31103)------------------------------
% 0.14/0.38 % (31102)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% 0.14/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.14/0.38 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.14/0.38 thf(func_def_3, type, powerset: $i > $i).
% 0.14/0.38 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 0.14/0.38 thf(func_def_7, type, binunion: $i > $i > $i).
% 0.14/0.38 thf(func_def_8, type, kpair: $i > $i > $i).
% 0.14/0.38 thf(func_def_9, type, cartprod: $i > $i > $i).
% 0.14/0.38 thf(func_def_20, type, sK0: $i > $o).
% 0.14/0.38 thf(func_def_28, type, ph7: !>[X0: $tType]:(X0)).
% 0.14/0.38 thf(f57,plain,(
% 0.14/0.38 $false),
% 0.14/0.38 inference(subsumption_resolution,[],[f56,f52])).
% 0.14/0.38 thf(f52,plain,(
% 0.14/0.38 ((setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset)) = sK3)),
% 0.14/0.38 inference(equality_proxy_clausification,[],[f50])).
% 0.14/0.38 thf(f50,plain,(
% 0.14/0.38 (((setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset)) = sK3) = $true)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f49])).
% 0.14/0.38 thf(f49,plain,(
% 0.14/0.38 ($true = ((in @ sK9 @ sK4) & ((setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset)) = sK3)))),
% 0.14/0.38 inference(beta_eta_normalization,[],[f48])).
% 0.14/0.38 thf(f48,plain,(
% 0.14/0.38 ($true = ((^[Y0 : $i]: ((in @ Y0 @ sK4) & ((setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK3))) @ sK9))),
% 0.14/0.38 inference(sigma_clausification,[],[f47])).
% 0.14/0.38 thf(f47,plain,(
% 0.14/0.38 ($true = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) & ((setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK3)))))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f45])).
% 0.14/0.38 thf(f45,plain,(
% 0.14/0.38 (((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK4) & ((setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK3)))) & (in @ sK8 @ sK5)) = $true)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f44])).
% 0.14/0.38 thf(f44,plain,(
% 0.14/0.38 ($true = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK3)))) & (in @ Y0 @ sK5))) @ sK8))),
% 0.14/0.38 inference(sigma_clausification,[],[f43])).
% 0.14/0.38 thf(f43,plain,(
% 0.14/0.38 ((?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK4) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK3)))) & (in @ Y0 @ sK5)))) = $true)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f42])).
% 0.14/0.38 thf(f42,plain,(
% 0.14/0.38 ($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ sK5))))) @ sK3))),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f41])).
% 0.14/0.38 thf(f41,plain,(
% 0.14/0.38 ($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ sK5))))) @ sK3)) | ($true != $true)),
% 0.14/0.38 inference(superposition,[],[f38,f39])).
% 0.14/0.38 thf(f39,plain,(
% 0.14/0.38 ((in @ sK3 @ (dsetconstr @ (powerset @ (powerset @ (binunion @ sK5 @ sK4))) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK4) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ sK5))))))) = $true)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f35])).
% 0.14/0.38 thf(f35,plain,(
% 0.14/0.38 ($true = (in @ sK3 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & (((^[Y5 : $i]: ((^[Y6 : $i]: (setadjoin @ (setadjoin @ Y5 @ emptyset) @ (setadjoin @ (setadjoin @ Y5 @ (setadjoin @ Y6 @ emptyset)) @ emptyset))))) @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y0))))))))) @ sK5 @ sK4)))),
% 0.14/0.38 inference(definition_unfolding,[],[f28,f31])).
% 0.14/0.38 thf(f31,plain,(
% 0.14/0.38 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & (((^[Y5 : $i]: ((^[Y6 : $i]: (setadjoin @ (setadjoin @ Y5 @ emptyset) @ (setadjoin @ (setadjoin @ Y5 @ (setadjoin @ Y6 @ emptyset)) @ emptyset))))) @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y0))))))))))),
% 0.14/0.38 inference(definition_unfolding,[],[f29,f30])).
% 0.14/0.38 thf(f30,plain,(
% 0.14/0.38 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f14])).
% 0.14/0.38 thf(f14,plain,(
% 0.14/0.38 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.14/0.38 inference(fool_elimination,[],[f13])).
% 0.14/0.38 thf(f13,plain,(
% 0.14/0.38 (kpair = (^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))),
% 0.14/0.38 inference(rectify,[],[f2])).
% 0.14/0.38 thf(f2,axiom,(
% 0.14/0.38 (kpair = (^[X2 : $i, X3 : $i] : (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair)).
% 0.14/0.38 thf(f29,plain,(
% 0.14/0.38 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y0))))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f10])).
% 0.14/0.38 thf(f10,plain,(
% 0.14/0.38 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y0))))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f9])).
% 0.14/0.38 thf(f9,plain,(
% 0.14/0.38 (cartprod = (^[X0 : $i, X1 : $i] : (dsetconstr @ (powerset @ (powerset @ (binunion @ X0 @ X1))) @ (^[X2 : $i] : (? [X3] : ((in @ X3 @ X0) & ? [X4] : (((kpair @ X3 @ X4) = X2) & (in @ X4 @ X1))))))))),
% 0.14/0.38 inference(rectify,[],[f3])).
% 0.14/0.38 thf(f3,axiom,(
% 0.14/0.38 (cartprod = (^[X0 : $i, X4 : $i] : (dsetconstr @ (powerset @ (powerset @ (binunion @ X0 @ X4))) @ (^[X2 : $i] : (? [X3] : ((in @ X3 @ X0) & ? [X5] : (((kpair @ X3 @ X5) = X2) & (in @ X5 @ X4))))))))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprod)).
% 0.14/0.38 thf(f28,plain,(
% 0.14/0.38 ($true = (in @ sK3 @ (cartprod @ sK5 @ sK4)))),
% 0.14/0.38 inference(cnf_transformation,[],[f22])).
% 0.14/0.38 thf(f22,plain,(
% 0.14/0.38 (($true = (in @ sK3 @ (cartprod @ sK5 @ sK4))) & ! [X3] : (((in @ X3 @ sK5) != $true) | ! [X4] : (($true != (in @ X4 @ sK4)) | ((kpair @ X3 @ X4) != sK3)))) & (dsetconstrER = $true)),
% 0.14/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f15,f21])).
% 0.14/0.38 thf(f21,plain,(
% 0.14/0.38 ? [X0,X1,X2] : (((in @ X0 @ (cartprod @ X2 @ X1)) = $true) & ! [X3] : (($true != (in @ X3 @ X2)) | ! [X4] : (($true != (in @ X4 @ X1)) | ((kpair @ X3 @ X4) != X0)))) => (($true = (in @ sK3 @ (cartprod @ sK5 @ sK4))) & ! [X3] : (((in @ X3 @ sK5) != $true) | ! [X4] : (($true != (in @ X4 @ sK4)) | ((kpair @ X3 @ X4) != sK3))))),
% 0.14/0.38 introduced(choice_axiom,[])).
% 0.14/0.38 thf(f15,plain,(
% 0.14/0.38 ? [X0,X1,X2] : (((in @ X0 @ (cartprod @ X2 @ X1)) = $true) & ! [X3] : (($true != (in @ X3 @ X2)) | ! [X4] : (($true != (in @ X4 @ X1)) | ((kpair @ X3 @ X4) != X0)))) & (dsetconstrER = $true)),
% 0.14/0.38 inference(ennf_transformation,[],[f8])).
% 0.14/0.38 thf(f8,plain,(
% 0.14/0.38 ~((dsetconstrER = $true) => ! [X0,X1,X2] : (((in @ X0 @ (cartprod @ X2 @ X1)) = $true) => ? [X3] : (($true = (in @ X3 @ X2)) & ? [X4] : (((kpair @ X3 @ X4) = X0) & ($true = (in @ X4 @ X1))))))),
% 0.14/0.38 inference(fool_elimination,[],[f7])).
% 0.14/0.38 thf(f7,plain,(
% 0.14/0.38 ~(dsetconstrER => ! [X0,X1,X2] : ((in @ X0 @ (cartprod @ X2 @ X1)) => ? [X3] : ((in @ X3 @ X2) & ? [X4] : (((kpair @ X3 @ X4) = X0) & (in @ X4 @ X1)))))),
% 0.14/0.38 inference(rectify,[],[f5])).
% 0.14/0.38 thf(f5,negated_conjecture,(
% 0.14/0.38 ~(dsetconstrER => ! [X6,X4,X0] : ((in @ X6 @ (cartprod @ X0 @ X4)) => ? [X2] : ((in @ X2 @ X0) & ? [X3] : (((kpair @ X2 @ X3) = X6) & (in @ X3 @ X4)))))),
% 0.14/0.38 inference(negated_conjecture,[],[f4])).
% 0.14/0.38 thf(f4,conjecture,(
% 0.14/0.38 dsetconstrER => ! [X6,X4,X0] : ((in @ X6 @ (cartprod @ X0 @ X4)) => ? [X2] : ((in @ X2 @ X0) & ? [X3] : (((kpair @ X2 @ X3) = X6) & (in @ X3 @ X4))))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1)).
% 0.14/0.38 thf(f38,plain,(
% 0.14/0.38 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X5 @ (dsetconstr @ X4 @ X3)) != $true) | ((X3 @ X5) = $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f37])).
% 0.14/0.38 thf(f37,plain,(
% 0.14/0.38 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0))))) | ((X3 @ X5) = $true)) )),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f34])).
% 0.14/0.38 thf(f34,plain,(
% 0.14/0.38 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((X3 @ X5) = $true) | ($true != $true) | ($true != (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))))) )),
% 0.14/0.38 inference(definition_unfolding,[],[f23,f26])).
% 0.14/0.38 thf(f26,plain,(
% 0.14/0.38 (dsetconstrER = $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f22])).
% 0.14/0.38 thf(f23,plain,(
% 0.14/0.38 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((X3 @ X5) = $true) | ($true != (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0))))) | (dsetconstrER != $true)) )),
% 0.14/0.38 inference(cnf_transformation,[],[f20])).
% 0.14/0.38 thf(f20,plain,(
% 0.14/0.38 ((dsetconstrER = $true) | (((sK0 @ sK2) != $true) & ($true = (in @ sK2 @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (sK0 @ Y0))))))) & (! [X3 : $i > $o,X4,X5] : (((X3 @ X5) = $true) | ($true != (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))))) | (dsetconstrER != $true))),
% 0.14/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f19])).
% 0.14/0.38 thf(f19,plain,(
% 0.14/0.38 ? [X0 : $i > $o,X1,X2] : (($true != (X0 @ X2)) & ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true)) => (((sK0 @ sK2) != $true) & ($true = (in @ sK2 @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (sK0 @ Y0))))))),
% 0.14/0.38 introduced(choice_axiom,[])).
% 0.14/0.38 thf(f18,plain,(
% 0.14/0.38 ((dsetconstrER = $true) | ? [X0 : $i > $o,X1,X2] : (($true != (X0 @ X2)) & ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true))) & (! [X3 : $i > $o,X4,X5] : (((X3 @ X5) = $true) | ($true != (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))))) | (dsetconstrER != $true))),
% 0.14/0.38 inference(rectify,[],[f17])).
% 0.14/0.38 thf(f17,plain,(
% 0.14/0.38 ((dsetconstrER = $true) | ? [X0 : $i > $o,X1,X2] : (($true != (X0 @ X2)) & ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true))) & (! [X0 : $i > $o,X1,X2] : (($true = (X0 @ X2)) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) | (dsetconstrER != $true))),
% 0.14/0.38 inference(nnf_transformation,[],[f16])).
% 0.14/0.38 thf(f16,plain,(
% 0.14/0.38 (dsetconstrER = $true) <=> ! [X0 : $i > $o,X1,X2] : (($true = (X0 @ X2)) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true))),
% 0.14/0.38 inference(ennf_transformation,[],[f12])).
% 0.14/0.38 thf(f12,plain,(
% 0.14/0.38 (dsetconstrER = $true) <=> ! [X0 : $i > $o,X1,X2] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ($true = (X0 @ X2)))),
% 0.14/0.38 inference(fool_elimination,[],[f11])).
% 0.14/0.38 thf(f11,plain,(
% 0.14/0.38 (! [X0 : $i > $o,X1,X2] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X2)) = dsetconstrER)),
% 0.14/0.38 inference(rectify,[],[f1])).
% 0.14/0.38 thf(f1,axiom,(
% 0.14/0.38 (! [X1 : $i > $o,X0,X2] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER)).
% 0.14/0.38 thf(f56,plain,(
% 0.14/0.38 ((setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset)) != sK3)),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f55])).
% 0.14/0.38 thf(f55,plain,(
% 0.14/0.38 ((setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset)) != sK3) | ($true != $true)),
% 0.14/0.38 inference(superposition,[],[f54,f46])).
% 0.14/0.38 thf(f46,plain,(
% 0.14/0.38 ($true = (in @ sK8 @ sK5))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f45])).
% 0.14/0.38 thf(f54,plain,(
% 0.14/0.38 ( ! [X0 : $i] : (((in @ X0 @ sK5) != $true) | ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ sK9 @ emptyset)) @ emptyset)) != sK3)) )),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f53])).
% 0.14/0.38 thf(f53,plain,(
% 0.14/0.38 ( ! [X0 : $i] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ sK9 @ emptyset)) @ emptyset)) != sK3) | ($true != $true) | ((in @ X0 @ sK5) != $true)) )),
% 0.14/0.38 inference(superposition,[],[f40,f51])).
% 0.14/0.38 thf(f51,plain,(
% 0.14/0.38 ($true = (in @ sK9 @ sK4))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f49])).
% 0.14/0.38 thf(f40,plain,(
% 0.14/0.38 ( ! [X3 : $i,X4 : $i] : (($true != (in @ X4 @ sK4)) | ((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) != sK3) | ((in @ X3 @ sK5) != $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f36])).
% 0.14/0.38 thf(f36,plain,(
% 0.14/0.38 ( ! [X3 : $i,X4 : $i] : (((in @ X3 @ sK5) != $true) | ($true != (in @ X4 @ sK4)) | (((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ X3 @ X4) != sK3)) )),
% 0.14/0.38 inference(definition_unfolding,[],[f27,f30])).
% 0.14/0.38 thf(f27,plain,(
% 0.14/0.38 ( ! [X3 : $i,X4 : $i] : (((in @ X3 @ sK5) != $true) | ($true != (in @ X4 @ sK4)) | ((kpair @ X3 @ X4) != sK3)) )),
% 0.14/0.38 inference(cnf_transformation,[],[f22])).
% 0.14/0.38 % SZS output end Proof for theBenchmark
% 0.14/0.38 % (31102)------------------------------
% 0.14/0.38 % (31102)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (31102)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (31102)Memory used [KB]: 5500
% 0.14/0.38 % (31102)Time elapsed: 0.010 s
% 0.14/0.38 % (31102)Instructions burned: 6 (million)
% 0.14/0.38 % (31102)------------------------------
% 0.14/0.38 % (31102)------------------------------
% 0.14/0.38 % (31095)Success in time 0.025 s
% 0.14/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------