TSTP Solution File: SEU671^2 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEU671^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n020.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 : Mon Jun 24 15:42:13 EDT 2024
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU671^2 : TPTP v8.2.0. Released v3.7.0.
% 0.00/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 16:34:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.20/0.35 This is a TH0_THM_EQU_NAR problem
% 0.20/0.35 Running higher-order theorem proving
% 0.20/0.35 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.20/0.37 % (14809)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.37 % (14810)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)
% 0.20/0.37 % (14811)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)
% 0.20/0.37 % (14813)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)
% 0.20/0.37 % (14812)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (14814)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)
% 0.20/0.37 % (14815)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.37 % (14813)Instruction limit reached!
% 0.20/0.37 % (14813)------------------------------
% 0.20/0.37 % (14813)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (14813)Termination reason: Unknown
% 0.20/0.37 % (14813)Termination phase: shuffling
% 0.20/0.37
% 0.20/0.37 % (14813)Memory used [KB]: 1023
% 0.20/0.37 % (14813)Time elapsed: 0.003 s
% 0.20/0.37 % (14813)Instructions burned: 2 (million)
% 0.20/0.37 % (14813)------------------------------
% 0.20/0.37 % (14813)------------------------------
% 0.20/0.37 % (14812)Instruction limit reached!
% 0.20/0.37 % (14812)------------------------------
% 0.20/0.37 % (14812)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (14812)Termination reason: Unknown
% 0.20/0.37 % (14812)Termination phase: Function definition elimination
% 0.20/0.37
% 0.20/0.37 % (14812)Memory used [KB]: 1023
% 0.20/0.37 % (14812)Time elapsed: 0.004 s
% 0.20/0.37 % (14812)Instructions burned: 3 (million)
% 0.20/0.37 % (14812)------------------------------
% 0.20/0.37 % (14812)------------------------------
% 0.20/0.37 % (14810)Instruction limit reached!
% 0.20/0.37 % (14810)------------------------------
% 0.20/0.37 % (14810)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (14810)Termination reason: Unknown
% 0.20/0.37 % (14810)Termination phase: Saturation
% 0.20/0.37
% 0.20/0.37 % (14810)Memory used [KB]: 5500
% 0.20/0.37 % (14810)Time elapsed: 0.005 s
% 0.20/0.37 % (14810)Instructions burned: 4 (million)
% 0.20/0.37 % (14810)------------------------------
% 0.20/0.37 % (14810)------------------------------
% 0.20/0.37 % (14814)Refutation not found, incomplete strategy
% 0.20/0.37 % (14814)------------------------------
% 0.20/0.37 % (14814)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.37 % (14814)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.37
% 0.20/0.37
% 0.20/0.37 % (14814)Memory used [KB]: 5500
% 0.20/0.37 % (14814)Time elapsed: 0.005 s
% 0.20/0.37 % (14814)Instructions burned: 3 (million)
% 0.20/0.37 % (14814)------------------------------
% 0.20/0.37 % (14814)------------------------------
% 0.20/0.38 % (14815)First to succeed.
% 0.20/0.38 % (14809)Also succeeded, but the first one will report.
% 0.20/0.38 % (14815)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% 0.20/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.20/0.38 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.38 thf(func_def_4, type, kpair: $i > $i > $i).
% 0.20/0.38 thf(func_def_5, type, cartprod: $i > $i > $i).
% 0.20/0.38 thf(func_def_8, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.20/0.38 thf(func_def_25, type, sK5: $i > $o).
% 0.20/0.38 thf(func_def_32, type, sK12: $i > $i > $o).
% 0.20/0.38 thf(func_def_38, type, ph17: !>[X0: $tType]:(X0)).
% 0.20/0.38 thf(f102,plain,(
% 0.20/0.38 $false),
% 0.20/0.38 inference(subsumption_resolution,[],[f99,f50])).
% 0.20/0.38 thf(f50,plain,(
% 0.20/0.38 ((sK12 @ sK13 @ sK15) != $true)),
% 0.20/0.38 inference(cnf_transformation,[],[f36])).
% 0.20/0.38 thf(f36,plain,(
% 0.20/0.38 (setukpairinjL = $true) & (((sK12 @ sK13 @ sK15) != $true) & ($true = (in @ (kpair @ sK13 @ sK15) @ (dpsetconstr @ sK14 @ sK11 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK12 @ Y0 @ Y1)))))))) & (setukpairinjR = $true) & (dsetconstrER = $true)),
% 0.20/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15])],[f22,f35])).
% 0.20/0.38 thf(f35,plain,(
% 0.20/0.38 ? [X0,X1 : $i > $i > $o,X2,X3,X4] : (((X1 @ X2 @ X4) != $true) & ((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) = $true)) => (((sK12 @ sK13 @ sK15) != $true) & ($true = (in @ (kpair @ sK13 @ sK15) @ (dpsetconstr @ sK14 @ sK11 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK12 @ Y0 @ Y1))))))))),
% 0.20/0.38 introduced(choice_axiom,[])).
% 0.20/0.38 thf(f22,plain,(
% 0.20/0.38 (setukpairinjL = $true) & ? [X0,X1 : $i > $i > $o,X2,X3,X4] : (((X1 @ X2 @ X4) != $true) & ((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) = $true)) & (setukpairinjR = $true) & (dsetconstrER = $true)),
% 0.20/0.38 inference(flattening,[],[f21])).
% 0.20/0.38 thf(f21,plain,(
% 0.20/0.38 ((? [X0,X1 : $i > $i > $o,X2,X3,X4] : (((X1 @ X2 @ X4) != $true) & ((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) = $true)) & (setukpairinjR = $true)) & (setukpairinjL = $true)) & (dsetconstrER = $true)),
% 0.20/0.38 inference(ennf_transformation,[],[f17])).
% 0.20/0.38 thf(f17,plain,(
% 0.20/0.38 ~((dsetconstrER = $true) => ((setukpairinjL = $true) => ((setukpairinjR = $true) => ! [X0,X1 : $i > $i > $o,X2,X3,X4] : (((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))) = $true) => ((X1 @ X2 @ X4) = $true)))))),
% 0.20/0.38 inference(fool_elimination,[],[f16])).
% 0.20/0.38 thf(f16,plain,(
% 0.20/0.38 ~(dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X0,X1 : $i > $i > $o,X2,X3,X4] : ((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X0 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6)))) => (X1 @ X2 @ X4)))))),
% 0.20/0.38 inference(rectify,[],[f6])).
% 0.20/0.38 thf(f6,negated_conjecture,(
% 0.20/0.38 ~(dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X6,X1 : $i > $i > $o,X2,X0,X3] : ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X6 @ (^[X4 : $i, X5 : $i] : (X1 @ X4 @ X5)))) => (X1 @ X2 @ X3)))))),
% 0.20/0.38 inference(negated_conjecture,[],[f5])).
% 0.20/0.38 thf(f5,conjecture,(
% 0.20/0.38 dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X6,X1 : $i > $i > $o,X2,X0,X3] : ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X6 @ (^[X4 : $i, X5 : $i] : (X1 @ X4 @ X5)))) => (X1 @ X2 @ X3))))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrER)).
% 0.20/0.38 thf(f99,plain,(
% 0.20/0.38 ((sK12 @ sK13 @ sK15) = $true)),
% 0.20/0.38 inference(backward_demodulation,[],[f91,f98])).
% 0.20/0.38 thf(f98,plain,(
% 0.20/0.38 (sK18 = sK13)),
% 0.20/0.38 inference(equality_resolution,[],[f86])).
% 0.20/0.38 thf(f86,plain,(
% 0.20/0.38 ( ! [X0 : $i,X1 : $i] : (((kpair @ X0 @ X1) != (kpair @ sK13 @ sK15)) | (sK18 = X0)) )),
% 0.20/0.38 inference(superposition,[],[f62,f82])).
% 0.20/0.38 thf(f82,plain,(
% 0.20/0.38 ((kpair @ sK13 @ sK15) = (kpair @ sK18 @ sK19))),
% 0.20/0.38 inference(equality_proxy_clausification,[],[f78])).
% 0.20/0.38 thf(f78,plain,(
% 0.20/0.38 ($true = ((kpair @ sK18 @ sK19) = (kpair @ sK13 @ sK15)))),
% 0.20/0.38 inference(binary_proxy_clausification,[],[f77])).
% 0.20/0.38 thf(f77,plain,(
% 0.20/0.38 ($true = (((in @ sK19 @ sK11) & (sK12 @ sK18 @ sK19)) & ((kpair @ sK18 @ sK19) = (kpair @ sK13 @ sK15))))),
% 0.20/0.38 inference(beta_eta_normalization,[],[f76])).
% 0.20/0.38 thf(f76,plain,(
% 0.20/0.38 (((^[Y0 : $i]: (((in @ Y0 @ sK11) & (sK12 @ sK18 @ Y0)) & ((kpair @ sK18 @ Y0) = (kpair @ sK13 @ sK15)))) @ sK19) = $true)),
% 0.20/0.38 inference(sigma_clausification,[],[f74])).
% 0.20/0.38 thf(f74,plain,(
% 0.20/0.38 ((?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ sK11) & (sK12 @ sK18 @ Y0)) & ((kpair @ sK18 @ Y0) = (kpair @ sK13 @ sK15))))) = $true)),
% 0.20/0.38 inference(binary_proxy_clausification,[],[f73])).
% 0.20/0.38 thf(f73,plain,(
% 0.20/0.38 (((in @ sK18 @ sK14) & (?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ sK11) & (sK12 @ sK18 @ Y0)) & ((kpair @ sK18 @ Y0) = (kpair @ sK13 @ sK15)))))) = $true)),
% 0.20/0.38 inference(beta_eta_normalization,[],[f72])).
% 0.20/0.38 thf(f72,plain,(
% 0.20/0.38 (((^[Y0 : $i]: ((in @ Y0 @ sK14) & (?? @ $i @ (^[Y1 : $i]: (((in @ Y1 @ sK11) & (sK12 @ Y0 @ Y1)) & ((kpair @ Y0 @ Y1) = (kpair @ sK13 @ sK15))))))) @ sK18) = $true)),
% 0.20/0.38 inference(sigma_clausification,[],[f71])).
% 0.20/0.38 thf(f71,plain,(
% 0.20/0.38 ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK14) & (?? @ $i @ (^[Y1 : $i]: (((in @ Y1 @ sK11) & (sK12 @ Y0 @ Y1)) & ((kpair @ Y0 @ Y1) = (kpair @ sK13 @ sK15)))))))) = $true)),
% 0.20/0.38 inference(beta_eta_normalization,[],[f70])).
% 0.20/0.38 thf(f70,plain,(
% 0.20/0.38 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK14) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK11) & (sK12 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))))))) @ (kpair @ sK13 @ sK15)) = $true)),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f69])).
% 0.20/0.38 thf(f69,plain,(
% 0.20/0.38 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK14) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK11) & (sK12 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))))))) @ (kpair @ sK13 @ sK15)) = $true) | ($true != $true)),
% 0.20/0.38 inference(superposition,[],[f66,f63])).
% 0.20/0.38 thf(f63,plain,(
% 0.20/0.38 ($true = (in @ (kpair @ sK13 @ sK15) @ (dsetconstr @ (cartprod @ sK14 @ sK11) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK14) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK11) & (sK12 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))))))))))),
% 0.20/0.38 inference(beta_eta_normalization,[],[f61])).
% 0.20/0.38 thf(f61,plain,(
% 0.20/0.38 ($true = (in @ (kpair @ sK13 @ sK15) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))) @ sK14 @ sK11 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK12 @ Y0 @ Y1)))))))),
% 0.20/0.38 inference(definition_unfolding,[],[f49,f37])).
% 0.20/0.38 thf(f37,plain,(
% 0.20/0.38 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f9])).
% 0.20/0.38 thf(f9,plain,(
% 0.20/0.38 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))))),
% 0.20/0.38 inference(fool_elimination,[],[f8])).
% 0.20/0.38 thf(f8,plain,(
% 0.20/0.38 ((^[X0 : $i, X1 : $i, X2 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4] : (? [X5] : (((kpair @ X4 @ X5) = X3) & (X2 @ X4 @ X5) & (in @ X5 @ X1)) & (in @ X4 @ X0)))))) = dpsetconstr)),
% 0.20/0.38 inference(rectify,[],[f4])).
% 0.20/0.38 thf(f4,axiom,(
% 0.20/0.38 ((^[X0 : $i, X6 : $i, X1 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X6) @ (^[X5 : $i] : (? [X2] : (? [X3] : (((kpair @ X2 @ X3) = X5) & (X1 @ X2 @ X3) & (in @ X3 @ X6)) & (in @ X2 @ X0)))))) = dpsetconstr)),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstr)).
% 0.20/0.38 thf(f49,plain,(
% 0.20/0.38 ($true = (in @ (kpair @ sK13 @ sK15) @ (dpsetconstr @ sK14 @ sK11 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK12 @ Y0 @ Y1)))))))),
% 0.20/0.38 inference(cnf_transformation,[],[f36])).
% 0.20/0.38 thf(f66,plain,(
% 0.20/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (($true != (in @ X2 @ (dsetconstr @ X0 @ X1))) | ((X1 @ X2) = $true)) )),
% 0.20/0.38 inference(beta_eta_normalization,[],[f65])).
% 0.20/0.38 thf(f65,plain,(
% 0.20/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((X1 @ X2) = $true) | ($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) )),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f55])).
% 0.20/0.38 thf(f55,plain,(
% 0.20/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (($true != $true) | ((X1 @ X2) = $true) | ($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) )),
% 0.20/0.38 inference(definition_unfolding,[],[f43,f47])).
% 0.20/0.38 thf(f47,plain,(
% 0.20/0.38 (dsetconstrER = $true)),
% 0.20/0.38 inference(cnf_transformation,[],[f36])).
% 0.20/0.38 thf(f43,plain,(
% 0.20/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((X1 @ X2) = $true) | ($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) | (dsetconstrER != $true)) )),
% 0.20/0.38 inference(cnf_transformation,[],[f30])).
% 0.20/0.38 thf(f30,plain,(
% 0.20/0.38 (! [X0,X1 : $i > $o,X2] : (((X1 @ X2) = $true) | ($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | (((sK5 @ sK6) != $true) & ($true = (in @ sK6 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK5 @ Y0)))))))),
% 0.20/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f28,f29])).
% 0.20/0.38 thf(f29,plain,(
% 0.20/0.38 ? [X3,X4 : $i > $o,X5] : (($true != (X4 @ X5)) & ($true = (in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))))) => (((sK5 @ sK6) != $true) & ($true = (in @ sK6 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: (sK5 @ Y0))))))),
% 0.20/0.38 introduced(choice_axiom,[])).
% 0.20/0.38 thf(f28,plain,(
% 0.20/0.38 (! [X0,X1 : $i > $o,X2] : (((X1 @ X2) = $true) | ($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X3,X4 : $i > $o,X5] : (($true != (X4 @ X5)) & ($true = (in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))))))),
% 0.20/0.38 inference(rectify,[],[f27])).
% 0.20/0.38 thf(f27,plain,(
% 0.20/0.38 (! [X0,X1 : $i > $o,X2] : (((X1 @ X2) = $true) | ($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X0,X1 : $i > $o,X2] : (((X1 @ X2) != $true) & ($true = (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))))),
% 0.20/0.38 inference(nnf_transformation,[],[f20])).
% 0.20/0.38 thf(f20,plain,(
% 0.20/0.38 ! [X0,X1 : $i > $o,X2] : (((X1 @ X2) = $true) | ($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) <=> (dsetconstrER = $true)),
% 0.20/0.38 inference(ennf_transformation,[],[f11])).
% 0.20/0.38 thf(f11,plain,(
% 0.20/0.38 (dsetconstrER = $true) <=> ! [X0,X1 : $i > $o,X2] : (($true = (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) => ((X1 @ X2) = $true))),
% 0.20/0.38 inference(fool_elimination,[],[f10])).
% 0.20/0.38 thf(f10,plain,(
% 0.20/0.38 (! [X0,X1 : $i > $o,X2] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 0.20/0.38 inference(rectify,[],[f1])).
% 0.20/0.38 thf(f1,axiom,(
% 0.20/0.38 (! [X0,X1 : $i > $o,X2] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER)).
% 0.20/0.38 thf(f62,plain,(
% 0.20/0.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ X2 @ X3) != (kpair @ X1 @ X0)) | (X1 = X2)) )),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f58])).
% 0.20/0.38 thf(f58,plain,(
% 0.20/0.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X1 = X2) | ($true != $true) | ((kpair @ X2 @ X3) != (kpair @ X1 @ X0))) )),
% 0.20/0.38 inference(definition_unfolding,[],[f46,f51])).
% 0.20/0.38 thf(f51,plain,(
% 0.20/0.38 (setukpairinjL = $true)),
% 0.20/0.38 inference(cnf_transformation,[],[f36])).
% 0.20/0.38 thf(f46,plain,(
% 0.20/0.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X1 = X2) | ((kpair @ X2 @ X3) != (kpair @ X1 @ X0)) | (setukpairinjL != $true)) )),
% 0.20/0.38 inference(cnf_transformation,[],[f34])).
% 0.20/0.38 thf(f34,plain,(
% 0.20/0.38 (! [X0,X1,X2,X3] : ((X1 = X2) | ((kpair @ X2 @ X3) != (kpair @ X1 @ X0))) | (setukpairinjL != $true)) & ((setukpairinjL = $true) | ((sK9 != sK8) & ((kpair @ sK8 @ sK7) = (kpair @ sK9 @ sK10))))),
% 0.20/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f32,f33])).
% 0.20/0.38 thf(f33,plain,(
% 0.20/0.38 ? [X4,X5,X6,X7] : ((X5 != X6) & ((kpair @ X5 @ X4) = (kpair @ X6 @ X7))) => ((sK9 != sK8) & ((kpair @ sK8 @ sK7) = (kpair @ sK9 @ sK10)))),
% 0.20/0.38 introduced(choice_axiom,[])).
% 0.20/0.38 thf(f32,plain,(
% 0.20/0.38 (! [X0,X1,X2,X3] : ((X1 = X2) | ((kpair @ X2 @ X3) != (kpair @ X1 @ X0))) | (setukpairinjL != $true)) & ((setukpairinjL = $true) | ? [X4,X5,X6,X7] : ((X5 != X6) & ((kpair @ X5 @ X4) = (kpair @ X6 @ X7))))),
% 0.20/0.38 inference(rectify,[],[f31])).
% 0.20/0.38 thf(f31,plain,(
% 0.20/0.38 (! [X0,X1,X2,X3] : ((X1 = X2) | ((kpair @ X2 @ X3) != (kpair @ X1 @ X0))) | (setukpairinjL != $true)) & ((setukpairinjL = $true) | ? [X0,X1,X2,X3] : ((X1 != X2) & ((kpair @ X2 @ X3) = (kpair @ X1 @ X0))))),
% 0.20/0.38 inference(nnf_transformation,[],[f18])).
% 0.20/0.38 thf(f18,plain,(
% 0.20/0.38 ! [X0,X1,X2,X3] : ((X1 = X2) | ((kpair @ X2 @ X3) != (kpair @ X1 @ X0))) <=> (setukpairinjL = $true)),
% 0.20/0.38 inference(ennf_transformation,[],[f13])).
% 0.20/0.38 thf(f13,plain,(
% 0.20/0.38 ! [X0,X1,X2,X3] : (((kpair @ X2 @ X3) = (kpair @ X1 @ X0)) => (X1 = X2)) <=> (setukpairinjL = $true)),
% 0.20/0.38 inference(fool_elimination,[],[f12])).
% 0.20/0.38 thf(f12,plain,(
% 0.20/0.38 (setukpairinjL = ! [X0,X1,X2,X3] : (((kpair @ X2 @ X3) = (kpair @ X1 @ X0)) => (X1 = X2)))),
% 0.20/0.38 inference(rectify,[],[f2])).
% 0.20/0.38 thf(f2,axiom,(
% 0.20/0.38 (setukpairinjL = ! [X3,X2,X4,X5] : (((kpair @ X2 @ X3) = (kpair @ X4 @ X5)) => (X2 = X4)))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL)).
% 0.20/0.38 thf(f91,plain,(
% 0.20/0.38 ((sK12 @ sK18 @ sK15) = $true)),
% 0.20/0.38 inference(backward_demodulation,[],[f80,f88])).
% 0.20/0.38 thf(f88,plain,(
% 0.20/0.38 (sK15 = sK19)),
% 0.20/0.38 inference(equality_resolution,[],[f83])).
% 0.20/0.38 thf(f83,plain,(
% 0.20/0.38 ( ! [X0 : $i,X1 : $i] : (((kpair @ X0 @ X1) != (kpair @ sK13 @ sK15)) | (sK19 = X1)) )),
% 0.20/0.38 inference(superposition,[],[f64,f82])).
% 0.20/0.38 thf(f64,plain,(
% 0.20/0.38 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((kpair @ X5 @ X4) != (kpair @ X7 @ X6)) | (X4 = X6)) )),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f54])).
% 0.20/0.38 thf(f54,plain,(
% 0.20/0.38 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((X4 = X6) | ($true != $true) | ((kpair @ X5 @ X4) != (kpair @ X7 @ X6))) )),
% 0.20/0.38 inference(definition_unfolding,[],[f38,f48])).
% 0.20/0.38 thf(f48,plain,(
% 0.20/0.38 (setukpairinjR = $true)),
% 0.20/0.38 inference(cnf_transformation,[],[f36])).
% 0.20/0.38 thf(f38,plain,(
% 0.20/0.38 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((kpair @ X5 @ X4) != (kpair @ X7 @ X6)) | (X4 = X6) | (setukpairinjR != $true)) )),
% 0.20/0.38 inference(cnf_transformation,[],[f26])).
% 0.20/0.38 thf(f26,plain,(
% 0.20/0.38 ((setukpairinjR = $true) | (((kpair @ sK1 @ sK0) = (kpair @ sK3 @ sK2)) & (sK0 != sK2))) & (! [X4,X5,X6,X7] : (((kpair @ X5 @ X4) != (kpair @ X7 @ X6)) | (X4 = X6)) | (setukpairinjR != $true))),
% 0.20/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f24,f25])).
% 0.20/0.38 thf(f25,plain,(
% 0.20/0.38 ? [X0,X1,X2,X3] : (((kpair @ X3 @ X2) = (kpair @ X1 @ X0)) & (X0 != X2)) => (((kpair @ sK1 @ sK0) = (kpair @ sK3 @ sK2)) & (sK0 != sK2))),
% 0.20/0.38 introduced(choice_axiom,[])).
% 0.20/0.38 thf(f24,plain,(
% 0.20/0.38 ((setukpairinjR = $true) | ? [X0,X1,X2,X3] : (((kpair @ X3 @ X2) = (kpair @ X1 @ X0)) & (X0 != X2))) & (! [X4,X5,X6,X7] : (((kpair @ X5 @ X4) != (kpair @ X7 @ X6)) | (X4 = X6)) | (setukpairinjR != $true))),
% 0.20/0.38 inference(rectify,[],[f23])).
% 0.20/0.38 thf(f23,plain,(
% 0.20/0.38 ((setukpairinjR = $true) | ? [X0,X1,X2,X3] : (((kpair @ X3 @ X2) = (kpair @ X1 @ X0)) & (X0 != X2))) & (! [X0,X1,X2,X3] : (((kpair @ X3 @ X2) != (kpair @ X1 @ X0)) | (X0 = X2)) | (setukpairinjR != $true))),
% 0.20/0.38 inference(nnf_transformation,[],[f19])).
% 0.20/0.38 thf(f19,plain,(
% 0.20/0.38 (setukpairinjR = $true) <=> ! [X0,X1,X2,X3] : (((kpair @ X3 @ X2) != (kpair @ X1 @ X0)) | (X0 = X2))),
% 0.20/0.38 inference(ennf_transformation,[],[f15])).
% 0.20/0.38 thf(f15,plain,(
% 0.20/0.38 (setukpairinjR = $true) <=> ! [X0,X1,X2,X3] : (((kpair @ X3 @ X2) = (kpair @ X1 @ X0)) => (X0 = X2))),
% 0.20/0.38 inference(fool_elimination,[],[f14])).
% 0.20/0.38 thf(f14,plain,(
% 0.20/0.38 (setukpairinjR = ! [X0,X1,X2,X3] : (((kpair @ X3 @ X2) = (kpair @ X1 @ X0)) => (X0 = X2)))),
% 0.20/0.38 inference(rectify,[],[f3])).
% 0.20/0.38 thf(f3,axiom,(
% 0.20/0.38 (setukpairinjR = ! [X5,X4,X3,X2] : (((kpair @ X2 @ X3) = (kpair @ X4 @ X5)) => (X3 = X5)))),
% 0.20/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR)).
% 0.20/0.38 thf(f80,plain,(
% 0.20/0.38 ((sK12 @ sK18 @ sK19) = $true)),
% 0.20/0.38 inference(binary_proxy_clausification,[],[f79])).
% 0.20/0.38 thf(f79,plain,(
% 0.20/0.38 (((in @ sK19 @ sK11) & (sK12 @ sK18 @ sK19)) = $true)),
% 0.20/0.38 inference(binary_proxy_clausification,[],[f77])).
% 0.20/0.38 % SZS output end Proof for theBenchmark
% 0.20/0.38 % (14815)------------------------------
% 0.20/0.38 % (14815)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (14815)Termination reason: Refutation
% 0.20/0.38
% 0.20/0.38 % (14815)Memory used [KB]: 5628
% 0.20/0.38 % (14815)Time elapsed: 0.011 s
% 0.20/0.38 % (14815)Instructions burned: 9 (million)
% 0.20/0.38 % (14815)------------------------------
% 0.20/0.38 % (14815)------------------------------
% 0.20/0.38 % (14808)Success in time 0.023 s
%------------------------------------------------------------------------------