TSTP Solution File: SEU668^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU668^2 : 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/sandbox/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 03:50:28 EDT 2024
% Result : Theorem 0.15s 0.42s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SEU668^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.16 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.38 % Computer : n009.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Sun May 19 17:38:08 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.15/0.38 This is a TH0_THM_EQU_NAR problem
% 0.15/0.38 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/sandbox/benchmark/theBenchmark.p
% 0.15/0.39 % (2545)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)
% 0.15/0.40 % (2551)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)
% 0.15/0.40 % (2546)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)
% 0.15/0.40 % (2551)Instruction limit reached!
% 0.15/0.40 % (2551)------------------------------
% 0.15/0.40 % (2551)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (2551)Termination reason: Unknown
% 0.15/0.40 % (2551)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (2551)Memory used [KB]: 1023
% 0.15/0.40 % (2551)Time elapsed: 0.004 s
% 0.15/0.40 % (2551)Instructions burned: 3 (million)
% 0.15/0.40 % (2551)------------------------------
% 0.15/0.40 % (2551)------------------------------
% 0.15/0.40 % (2545)Instruction limit reached!
% 0.15/0.40 % (2545)------------------------------
% 0.15/0.40 % (2545)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (2545)Termination reason: Unknown
% 0.15/0.40 % (2545)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (2545)Memory used [KB]: 1023
% 0.15/0.40 % (2545)Time elapsed: 0.004 s
% 0.15/0.40 % (2545)Instructions burned: 4 (million)
% 0.15/0.40 % (2545)------------------------------
% 0.15/0.40 % (2545)------------------------------
% 0.15/0.41 % (2549)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)
% 0.15/0.41 % (2550)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.41 % (2548)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)
% 0.15/0.41 % (2548)Instruction limit reached!
% 0.15/0.41 % (2548)------------------------------
% 0.15/0.41 % (2548)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (2549)Refutation not found, incomplete strategy
% 0.15/0.41 % (2549)------------------------------
% 0.15/0.41 % (2549)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (2549)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.41
% 0.15/0.41
% 0.15/0.41 % (2549)Memory used [KB]: 5500
% 0.15/0.41 % (2549)Time elapsed: 0.006 s
% 0.15/0.41 % (2549)Instructions burned: 4 (million)
% 0.15/0.41 % (2549)------------------------------
% 0.15/0.41 % (2549)------------------------------
% 0.15/0.41 % (2548)Termination reason: Unknown
% 0.15/0.41 % (2548)Termination phase: Property scanning
% 0.15/0.41
% 0.15/0.41 % (2548)Memory used [KB]: 1023
% 0.15/0.41 % (2548)Time elapsed: 0.002 s
% 0.15/0.41 % (2548)Instructions burned: 2 (million)
% 0.15/0.41 % (2548)------------------------------
% 0.15/0.41 % (2548)------------------------------
% 0.15/0.41 % (2546)First to succeed.
% 0.15/0.41 % (2544)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.41 % (2550)Also succeeded, but the first one will report.
% 0.15/0.42 % (2546)Refutation found. Thanks to Tanya!
% 0.15/0.42 % SZS status Theorem for theBenchmark
% 0.15/0.42 % SZS output start Proof for theBenchmark
% 0.15/0.42 thf(func_def_0, type, in: $i > $i > $o).
% 0.15/0.42 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 0.15/0.42 thf(func_def_4, type, kpair: $i > $i > $i).
% 0.15/0.42 thf(func_def_5, type, cartprod: $i > $i > $i).
% 0.15/0.42 thf(func_def_8, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.15/0.42 thf(func_def_9, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.15/0.42 thf(func_def_23, type, sK0: $i > $i > $o).
% 0.15/0.42 thf(func_def_29, type, ph6: !>[X0: $tType]:(X0)).
% 0.15/0.42 thf(f136,plain,(
% 0.15/0.42 $false),
% 0.15/0.42 inference(trivial_inequality_removal,[],[f135])).
% 0.15/0.42 thf(f135,plain,(
% 0.15/0.42 ($true != $true)),
% 0.15/0.42 inference(superposition,[],[f29,f133])).
% 0.15/0.42 thf(f133,plain,(
% 0.15/0.42 ((sK0 @ sK2 @ sK4) = $true)),
% 0.15/0.42 inference(backward_demodulation,[],[f114,f130])).
% 0.15/0.42 thf(f130,plain,(
% 0.15/0.42 (sK7 = sK2)),
% 0.15/0.42 inference(equality_resolution,[],[f101])).
% 0.15/0.42 thf(f101,plain,(
% 0.15/0.42 ( ! [X0 : $i,X1 : $i] : (((kpair @ sK2 @ sK4) != (kpair @ X0 @ X1)) | (sK7 = X0)) )),
% 0.15/0.42 inference(superposition,[],[f48,f85])).
% 0.15/0.42 thf(f85,plain,(
% 0.15/0.42 ((kpair @ sK2 @ sK4) = (kpair @ sK7 @ sK8))),
% 0.15/0.42 inference(equality_proxy_clausification,[],[f83])).
% 0.15/0.42 thf(f83,plain,(
% 0.15/0.42 (((kpair @ sK7 @ sK8) = (kpair @ sK2 @ sK4)) = $true)),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f82])).
% 0.15/0.42 thf(f82,plain,(
% 0.15/0.42 ($true = ((in @ sK8 @ sK3) & ((kpair @ sK7 @ sK8) = (kpair @ sK2 @ sK4))))),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f80])).
% 0.15/0.42 thf(f80,plain,(
% 0.15/0.42 ((((in @ sK8 @ sK3) & ((kpair @ sK7 @ sK8) = (kpair @ sK2 @ sK4))) & (sK0 @ sK7 @ sK8)) = $true)),
% 0.15/0.42 inference(beta_eta_normalization,[],[f79])).
% 0.15/0.42 thf(f79,plain,(
% 0.15/0.42 (((^[Y0 : $i]: (((in @ Y0 @ sK3) & ((kpair @ sK7 @ Y0) = (kpair @ sK2 @ sK4))) & (sK0 @ sK7 @ Y0))) @ sK8) = $true)),
% 0.15/0.42 inference(sigma_clausification,[],[f77])).
% 0.15/0.42 thf(f77,plain,(
% 0.15/0.42 ((?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ sK3) & ((kpair @ sK7 @ Y0) = (kpair @ sK2 @ sK4))) & (sK0 @ sK7 @ Y0)))) = $true)),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f76])).
% 0.15/0.42 thf(f76,plain,(
% 0.15/0.42 (((in @ sK7 @ sK1) & (?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ sK3) & ((kpair @ sK7 @ Y0) = (kpair @ sK2 @ sK4))) & (sK0 @ sK7 @ Y0))))) = $true)),
% 0.15/0.42 inference(beta_eta_normalization,[],[f75])).
% 0.15/0.42 thf(f75,plain,(
% 0.15/0.42 ($true = ((^[Y0 : $i]: ((in @ Y0 @ sK1) & (?? @ $i @ (^[Y1 : $i]: (((in @ Y1 @ sK3) & ((kpair @ Y0 @ Y1) = (kpair @ sK2 @ sK4))) & (sK0 @ Y0 @ Y1)))))) @ sK7))),
% 0.15/0.42 inference(sigma_clausification,[],[f74])).
% 0.15/0.42 thf(f74,plain,(
% 0.15/0.42 ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) & (?? @ $i @ (^[Y1 : $i]: (((in @ Y1 @ sK3) & ((kpair @ Y0 @ Y1) = (kpair @ sK2 @ sK4))) & (sK0 @ Y0 @ Y1))))))) = $true)),
% 0.15/0.42 inference(beta_eta_normalization,[],[f73])).
% 0.15/0.42 thf(f73,plain,(
% 0.15/0.42 ($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK1) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK3) & ((kpair @ Y1 @ Y2) = Y0)) & (sK0 @ Y1 @ Y2)))))))) @ (kpair @ sK2 @ sK4)))),
% 0.15/0.42 inference(trivial_inequality_removal,[],[f71])).
% 0.15/0.42 thf(f71,plain,(
% 0.15/0.42 ($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK1) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK3) & ((kpair @ Y1 @ Y2) = Y0)) & (sK0 @ Y1 @ Y2)))))))) @ (kpair @ sK2 @ sK4))) | ($false = $true)),
% 0.15/0.42 inference(superposition,[],[f68,f67])).
% 0.15/0.42 thf(f67,plain,(
% 0.15/0.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((in @ X1 @ (dsetconstr @ X3 @ X2)) = $false) | ((X2 @ X1) = $true)) )),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f66])).
% 0.15/0.42 thf(f66,plain,(
% 0.15/0.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((in @ X1 @ (dsetconstr @ X3 @ X2)) => (X2 @ X1)) = $true)) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f65])).
% 0.15/0.42 thf(f65,plain,(
% 0.15/0.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X1 @ (dsetconstr @ Y0 @ X2)) => (X2 @ X1))) @ X3))) )),
% 0.15/0.42 inference(pi_clausification,[],[f64])).
% 0.15/0.42 thf(f64,plain,(
% 0.15/0.42 ( ! [X2 : $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (dsetconstr @ Y0 @ X2)) => (X2 @ X1)))) = $true)) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f63])).
% 0.15/0.42 thf(f63,plain,(
% 0.15/0.42 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ X1))))) @ X2) = $true)) )),
% 0.15/0.42 inference(pi_clausification,[],[f62])).
% 0.15/0.42 thf(f62,plain,(
% 0.15/0.42 ( ! [X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ X1)))))) = $true)) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f61])).
% 0.15/0.42 thf(f61,plain,(
% 0.15/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0))))))) @ X1) = $true)) )),
% 0.15/0.42 inference(pi_clausification,[],[f60])).
% 0.15/0.42 thf(f60,plain,(
% 0.15/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))))),
% 0.15/0.42 inference(beta_eta_normalization,[],[f34])).
% 0.15/0.42 thf(f34,plain,(
% 0.15/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y0)))))))) = $true)),
% 0.15/0.42 inference(definition_unfolding,[],[f33,f26])).
% 0.15/0.42 thf(f26,plain,(
% 0.15/0.42 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y0)))))))))),
% 0.15/0.42 inference(cnf_transformation,[],[f17])).
% 0.15/0.42 thf(f17,plain,(
% 0.15/0.42 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y0)))))))))),
% 0.15/0.42 inference(fool_elimination,[],[f16])).
% 0.15/0.42 thf(f16,plain,(
% 0.15/0.42 (dsetconstrER = ! [X0,X1 : $i > $o,X2] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)))),
% 0.15/0.42 inference(rectify,[],[f1])).
% 0.15/0.42 thf(f1,axiom,(
% 0.15/0.42 (dsetconstrER = ! [X0,X1 : $i > $o,X2] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)))),
% 0.15/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER)).
% 0.15/0.42 thf(f33,plain,(
% 0.15/0.42 (dsetconstrER = $true)),
% 0.15/0.42 inference(cnf_transformation,[],[f22])).
% 0.15/0.42 thf(f22,plain,(
% 0.15/0.42 (dsetconstrER = $true) & (setukpairinjL = $true) & ((((in @ (kpair @ sK2 @ sK4) @ (dpsetconstr @ sK1 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))) = $true) & ((in @ sK4 @ sK3) = $true) & ((sK0 @ sK2 @ sK4) != $true)) & ((in @ sK2 @ sK1) = $true)) & (setukpairinjR = $true)),
% 0.15/0.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f19,f21,f20])).
% 0.15/0.42 thf(f20,plain,(
% 0.15/0.42 ? [X0 : $i > $i > $o,X1,X2,X3] : (? [X4] : (((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) = $true) & ((in @ X4 @ X3) = $true) & ((X0 @ X2 @ X4) != $true)) & ((in @ X2 @ X1) = $true)) => (? [X4] : (((in @ (kpair @ sK2 @ X4) @ (dpsetconstr @ sK1 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))) = $true) & ((in @ X4 @ sK3) = $true) & ((sK0 @ sK2 @ X4) != $true)) & ((in @ sK2 @ sK1) = $true))),
% 0.15/0.42 introduced(choice_axiom,[])).
% 0.15/0.42 thf(f21,plain,(
% 0.15/0.42 ? [X4] : (((in @ (kpair @ sK2 @ X4) @ (dpsetconstr @ sK1 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))) = $true) & ((in @ X4 @ sK3) = $true) & ((sK0 @ sK2 @ X4) != $true)) => (((in @ (kpair @ sK2 @ sK4) @ (dpsetconstr @ sK1 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))) = $true) & ((in @ sK4 @ sK3) = $true) & ((sK0 @ sK2 @ sK4) != $true))),
% 0.15/0.42 introduced(choice_axiom,[])).
% 0.15/0.42 thf(f19,plain,(
% 0.15/0.42 (dsetconstrER = $true) & (setukpairinjL = $true) & ? [X0 : $i > $i > $o,X1,X2,X3] : (? [X4] : (((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) = $true) & ((in @ X4 @ X3) = $true) & ((X0 @ X2 @ X4) != $true)) & ((in @ X2 @ X1) = $true)) & (setukpairinjR = $true)),
% 0.15/0.42 inference(flattening,[],[f18])).
% 0.15/0.42 thf(f18,plain,(
% 0.15/0.42 ((? [X0 : $i > $i > $o,X1,X2,X3] : (? [X4] : ((((X0 @ X2 @ X4) != $true) & ((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) = $true)) & ((in @ X4 @ X3) = $true)) & ((in @ X2 @ X1) = $true)) & (setukpairinjR = $true)) & (setukpairinjL = $true)) & (dsetconstrER = $true)),
% 0.15/0.42 inference(ennf_transformation,[],[f9])).
% 0.15/0.42 thf(f9,plain,(
% 0.15/0.42 ~((dsetconstrER = $true) => ((setukpairinjL = $true) => ((setukpairinjR = $true) => ! [X0 : $i > $i > $o,X1,X2,X3] : (((in @ X2 @ X1) = $true) => ! [X4] : (((in @ X4 @ X3) = $true) => (((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) = $true) => ((X0 @ X2 @ X4) = $true)))))))),
% 0.15/0.42 inference(fool_elimination,[],[f8])).
% 0.15/0.42 thf(f8,plain,(
% 0.15/0.42 ~(dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X0 : $i > $i > $o,X1,X2,X3] : ((in @ X2 @ X1) => ! [X4] : ((in @ X4 @ X3) => ((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X3 @ (^[X5 : $i, X6 : $i] : (X0 @ X5 @ X6)))) => (X0 @ X2 @ X4)))))))),
% 0.15/0.42 inference(rectify,[],[f6])).
% 0.15/0.42 thf(f6,negated_conjecture,(
% 0.15/0.42 ~(dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X1 : $i > $i > $o,X0,X2,X6] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X6) => ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X6 @ (^[X4 : $i, X5 : $i] : (X1 @ X4 @ X5)))) => (X1 @ X2 @ X3)))))))),
% 0.15/0.42 inference(negated_conjecture,[],[f5])).
% 0.15/0.42 thf(f5,conjecture,(
% 0.15/0.42 dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X1 : $i > $i > $o,X0,X2,X6] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X6) => ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X6 @ (^[X4 : $i, X5 : $i] : (X1 @ X4 @ X5)))) => (X1 @ X2 @ X3))))))),
% 0.15/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa)).
% 0.15/0.42 thf(f68,plain,(
% 0.15/0.42 ((in @ (kpair @ sK2 @ sK4) @ (dsetconstr @ (cartprod @ sK1 @ sK3) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK1) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK3) & ((kpair @ Y1 @ Y2) = Y0)) & (sK0 @ Y1 @ Y2)))))))))) = $true)),
% 0.15/0.42 inference(beta_eta_normalization,[],[f36])).
% 0.15/0.42 thf(f36,plain,(
% 0.15/0.42 ((in @ (kpair @ sK2 @ sK4) @ ((^[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) & ((kpair @ Y4 @ Y5) = Y3)) & (Y2 @ Y4 @ Y5)))))))))))))) @ sK1 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))) = $true)),
% 0.15/0.42 inference(definition_unfolding,[],[f31,f25])).
% 0.15/0.42 thf(f25,plain,(
% 0.15/0.42 (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) & ((kpair @ Y4 @ Y5) = Y3)) & (Y2 @ Y4 @ Y5)))))))))))))))),
% 0.15/0.42 inference(cnf_transformation,[],[f11])).
% 0.15/0.42 thf(f11,plain,(
% 0.15/0.42 (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) & ((kpair @ Y4 @ Y5) = Y3)) & (Y2 @ Y4 @ Y5)))))))))))))))),
% 0.15/0.42 inference(fool_elimination,[],[f10])).
% 0.15/0.42 thf(f10,plain,(
% 0.15/0.42 (dpsetconstr = (^[X0 : $i, X1 : $i, X2 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4] : (? [X5] : ((X2 @ X4 @ X5) & ((kpair @ X4 @ X5) = X3) & (in @ X5 @ X1)) & (in @ X4 @ X0)))))))),
% 0.15/0.42 inference(rectify,[],[f4])).
% 0.15/0.42 thf(f4,axiom,(
% 0.15/0.42 (dpsetconstr = (^[X0 : $i, X6 : $i, X1 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X6) @ (^[X5 : $i] : (? [X2] : (? [X3] : ((X1 @ X2 @ X3) & ((kpair @ X2 @ X3) = X5) & (in @ X3 @ X6)) & (in @ X2 @ X0)))))))),
% 0.15/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstr)).
% 0.15/0.42 thf(f31,plain,(
% 0.15/0.42 ((in @ (kpair @ sK2 @ sK4) @ (dpsetconstr @ sK1 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK0 @ Y0 @ Y1)))))) = $true)),
% 0.15/0.42 inference(cnf_transformation,[],[f22])).
% 0.15/0.42 thf(f48,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((kpair @ X4 @ X1) != (kpair @ X3 @ X2)) | (X3 = X4)) )),
% 0.15/0.42 inference(equality_proxy_clausification,[],[f47])).
% 0.15/0.42 thf(f47,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((X4 = X3) = $true) | ((kpair @ X4 @ X1) != (kpair @ X3 @ X2))) )),
% 0.15/0.42 inference(equality_proxy_clausification,[],[f46])).
% 0.15/0.42 thf(f46,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((kpair @ X3 @ X2) = (kpair @ X4 @ X1))) | ((X4 = X3) = $true)) )),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f45])).
% 0.15/0.42 thf(f45,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((kpair @ X3 @ X2) = (kpair @ X4 @ X1)) => (X4 = X3)) = $true)) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f44])).
% 0.15/0.42 thf(f44,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((^[Y0 : $i]: (((kpair @ X3 @ X2) = (kpair @ Y0 @ X1)) => (Y0 = X3))) @ X4))) )),
% 0.15/0.42 inference(pi_clausification,[],[f43])).
% 0.15/0.42 thf(f43,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((kpair @ X3 @ X2) = (kpair @ Y0 @ X1)) => (Y0 = X3)))))) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f42])).
% 0.15/0.42 thf(f42,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((kpair @ Y0 @ X2) = (kpair @ Y1 @ X1)) => (Y1 = Y0))))) @ X3) = $true)) )),
% 0.15/0.42 inference(pi_clausification,[],[f41])).
% 0.15/0.42 thf(f41,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((kpair @ Y0 @ X2) = (kpair @ Y1 @ X1)) => (Y1 = Y0)))))) = $true)) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f40])).
% 0.15/0.42 thf(f40,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((kpair @ Y1 @ Y0) = (kpair @ Y2 @ X1)) => (Y2 = Y1))))))) @ X2) = $true)) )),
% 0.15/0.42 inference(pi_clausification,[],[f39])).
% 0.15/0.42 thf(f39,plain,(
% 0.15/0.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((kpair @ Y1 @ Y0) = (kpair @ Y2 @ X1)) => (Y2 = Y1)))))))))) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f38])).
% 0.15/0.42 thf(f38,plain,(
% 0.15/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y3 = Y2))))))))) @ X1) = $true)) )),
% 0.15/0.42 inference(pi_clausification,[],[f35])).
% 0.15/0.42 thf(f35,plain,(
% 0.15/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y3 = Y2)))))))))) = $true)),
% 0.15/0.42 inference(definition_unfolding,[],[f32,f24])).
% 0.15/0.42 thf(f24,plain,(
% 0.15/0.42 (setukpairinjL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y3 = Y2)))))))))))),
% 0.15/0.42 inference(cnf_transformation,[],[f15])).
% 0.15/0.42 thf(f15,plain,(
% 0.15/0.42 (setukpairinjL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y3 = Y2)))))))))))),
% 0.15/0.42 inference(fool_elimination,[],[f14])).
% 0.15/0.42 thf(f14,plain,(
% 0.15/0.42 (setukpairinjL = ! [X0,X1,X2,X3] : (((kpair @ X1 @ X2) = (kpair @ X0 @ X3)) => (X0 = X1)))),
% 0.15/0.42 inference(rectify,[],[f2])).
% 0.15/0.42 thf(f2,axiom,(
% 0.15/0.42 (setukpairinjL = ! [X2,X4,X5,X3] : (((kpair @ X2 @ X3) = (kpair @ X4 @ X5)) => (X2 = X4)))),
% 0.15/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL)).
% 0.15/0.42 thf(f32,plain,(
% 0.15/0.42 (setukpairinjL = $true)),
% 0.15/0.42 inference(cnf_transformation,[],[f22])).
% 0.15/0.42 thf(f114,plain,(
% 0.15/0.42 ((sK0 @ sK7 @ sK4) = $true)),
% 0.15/0.42 inference(backward_demodulation,[],[f81,f109])).
% 0.15/0.42 thf(f109,plain,(
% 0.15/0.42 (sK8 = sK4)),
% 0.15/0.42 inference(equality_resolution,[],[f99])).
% 0.15/0.42 thf(f99,plain,(
% 0.15/0.42 ( ! [X0 : $i,X1 : $i] : (((kpair @ sK2 @ sK4) != (kpair @ X0 @ X1)) | (sK8 = X1)) )),
% 0.15/0.42 inference(superposition,[],[f59,f85])).
% 0.15/0.42 thf(f59,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((kpair @ X1 @ X2) != (kpair @ X3 @ X4)) | (X2 = X4)) )),
% 0.15/0.42 inference(equality_proxy_clausification,[],[f58])).
% 0.15/0.42 thf(f58,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((kpair @ X1 @ X2) = (kpair @ X3 @ X4)) = $false) | (X2 = X4)) )),
% 0.15/0.42 inference(equality_proxy_clausification,[],[f57])).
% 0.15/0.42 thf(f57,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((X4 = X2) = $true) | (((kpair @ X1 @ X2) = (kpair @ X3 @ X4)) = $false)) )),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f56])).
% 0.15/0.42 thf(f56,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((kpair @ X1 @ X2) = (kpair @ X3 @ X4)) => (X4 = X2)) = $true)) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f55])).
% 0.15/0.42 thf(f55,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: (((kpair @ X1 @ X2) = (kpair @ X3 @ Y0)) => (Y0 = X2))) @ X4) = $true)) )),
% 0.15/0.42 inference(pi_clausification,[],[f54])).
% 0.15/0.42 thf(f54,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((kpair @ X1 @ X2) = (kpair @ X3 @ Y0)) => (Y0 = X2)))) = $true)) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f53])).
% 0.15/0.42 thf(f53,plain,(
% 0.15/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((kpair @ X1 @ X2) = (kpair @ Y0 @ Y1)) => (Y1 = X2))))) @ X3) = $true)) )),
% 0.15/0.42 inference(pi_clausification,[],[f52])).
% 0.15/0.42 thf(f52,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((kpair @ X1 @ X2) = (kpair @ Y0 @ Y1)) => (Y1 = X2)))))) = $true)) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f51])).
% 0.15/0.42 thf(f51,plain,(
% 0.15/0.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((kpair @ X1 @ Y0) = (kpair @ Y1 @ Y2)) => (Y2 = Y0))))))) @ X2) = $true)) )),
% 0.15/0.42 inference(pi_clausification,[],[f50])).
% 0.15/0.42 thf(f50,plain,(
% 0.15/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((kpair @ X1 @ Y0) = (kpair @ Y1 @ Y2)) => (Y2 = Y0)))))))) = $true)) )),
% 0.15/0.42 inference(beta_eta_normalization,[],[f49])).
% 0.15/0.42 thf(f49,plain,(
% 0.15/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y2 @ Y3)) => (Y3 = Y1))))))))) @ X1) = $true)) )),
% 0.15/0.42 inference(pi_clausification,[],[f37])).
% 0.15/0.42 thf(f37,plain,(
% 0.15/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y2 @ Y3)) => (Y3 = Y1)))))))))) = $true)),
% 0.15/0.42 inference(definition_unfolding,[],[f27,f23])).
% 0.15/0.42 thf(f23,plain,(
% 0.15/0.42 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y2 @ Y3)) => (Y3 = Y1)))))))))))),
% 0.15/0.42 inference(cnf_transformation,[],[f13])).
% 0.15/0.42 thf(f13,plain,(
% 0.15/0.42 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y2 @ Y3)) => (Y3 = Y1)))))))))))),
% 0.15/0.42 inference(fool_elimination,[],[f12])).
% 0.15/0.42 thf(f12,plain,(
% 0.15/0.42 (! [X0,X1,X2,X3] : (((kpair @ X3 @ X2) = (kpair @ X1 @ X0)) => (X0 = X2)) = setukpairinjR)),
% 0.15/0.42 inference(rectify,[],[f3])).
% 0.15/0.42 thf(f3,axiom,(
% 0.15/0.42 (! [X5,X4,X3,X2] : (((kpair @ X2 @ X3) = (kpair @ X4 @ X5)) => (X3 = X5)) = setukpairinjR)),
% 0.15/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR)).
% 0.15/0.42 thf(f27,plain,(
% 0.15/0.42 (setukpairinjR = $true)),
% 0.15/0.42 inference(cnf_transformation,[],[f22])).
% 0.15/0.42 thf(f81,plain,(
% 0.15/0.42 ((sK0 @ sK7 @ sK8) = $true)),
% 0.15/0.42 inference(binary_proxy_clausification,[],[f80])).
% 0.15/0.42 thf(f29,plain,(
% 0.15/0.42 ((sK0 @ sK2 @ sK4) != $true)),
% 0.15/0.42 inference(cnf_transformation,[],[f22])).
% 0.15/0.42 % SZS output end Proof for theBenchmark
% 0.15/0.42 % (2546)------------------------------
% 0.15/0.42 % (2546)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (2546)Termination reason: Refutation
% 0.15/0.42
% 0.15/0.42 % (2546)Memory used [KB]: 5628
% 0.15/0.42 % (2546)Time elapsed: 0.013 s
% 0.15/0.42 % (2546)Instructions burned: 16 (million)
% 0.15/0.42 % (2546)------------------------------
% 0.15/0.42 % (2546)------------------------------
% 0.15/0.42 % (2543)Success in time 0.029 s
% 0.15/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------