TSTP Solution File: SEU681^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU681^2 : 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 : n005.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 03:50:39 EDT 2024
% Result : Theorem 0.11s 0.35s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SEU681^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.12 % 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
% 0.11/0.32 % Computer : n005.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 15:32:22 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/sandbox/benchmark/theBenchmark.p
% 0.11/0.34 % (5814)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.34 % (5818)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)
% 0.11/0.34 % (5816)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)
% 0.11/0.34 % (5817)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.34 % (5815)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)
% 0.11/0.34 % (5819)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)
% 0.11/0.34 % (5820)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.34 % (5818)Instruction limit reached!
% 0.11/0.34 % (5818)------------------------------
% 0.11/0.34 % (5818)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (5818)Termination reason: Unknown
% 0.11/0.34 % (5818)Termination phase: shuffling
% 0.11/0.34
% 0.11/0.34 % (5818)Memory used [KB]: 895
% 0.11/0.34 % (5818)Time elapsed: 0.002 s
% 0.11/0.34 % (5818)Instructions burned: 2 (million)
% 0.11/0.34 % (5818)------------------------------
% 0.11/0.34 % (5818)------------------------------
% 0.11/0.34 % (5821)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)
% 0.11/0.34 % (5817)Instruction limit reached!
% 0.11/0.34 % (5817)------------------------------
% 0.11/0.34 % (5817)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (5817)Termination reason: Unknown
% 0.11/0.34 % (5817)Termination phase: Property scanning
% 0.11/0.34
% 0.11/0.34 % (5817)Memory used [KB]: 1023
% 0.11/0.34 % (5817)Time elapsed: 0.003 s
% 0.11/0.34 % (5817)Instructions burned: 3 (million)
% 0.11/0.34 % (5817)------------------------------
% 0.11/0.34 % (5817)------------------------------
% 0.11/0.34 % (5815)Instruction limit reached!
% 0.11/0.34 % (5815)------------------------------
% 0.11/0.34 % (5815)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (5815)Termination reason: Unknown
% 0.11/0.34 % (5815)Termination phase: Saturation
% 0.11/0.34
% 0.11/0.34 % (5815)Memory used [KB]: 5500
% 0.11/0.34 % (5815)Time elapsed: 0.004 s
% 0.11/0.34 % (5815)Instructions burned: 4 (million)
% 0.11/0.34 % (5815)------------------------------
% 0.11/0.34 % (5815)------------------------------
% 0.11/0.35 % (5821)Instruction limit reached!
% 0.11/0.35 % (5821)------------------------------
% 0.11/0.35 % (5821)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (5821)Termination reason: Unknown
% 0.11/0.35 % (5821)Termination phase: Saturation
% 0.11/0.35
% 0.11/0.35 % (5821)Memory used [KB]: 5500
% 0.11/0.35 % (5821)Time elapsed: 0.003 s
% 0.11/0.35 % (5821)Instructions burned: 4 (million)
% 0.11/0.35 % (5821)------------------------------
% 0.11/0.35 % (5821)------------------------------
% 0.11/0.35 % (5820)First to succeed.
% 0.11/0.35 % (5820)Refutation found. Thanks to Tanya!
% 0.11/0.35 % SZS status Theorem for theBenchmark
% 0.11/0.35 % SZS output start Proof for theBenchmark
% 0.11/0.35 thf(func_def_0, type, in: $i > $i > $o).
% 0.11/0.35 thf(func_def_1, type, subset: $i > $i > $o).
% 0.11/0.35 thf(func_def_4, type, kpair: $i > $i > $i).
% 0.11/0.35 thf(func_def_5, type, cartprod: $i > $i > $i).
% 0.11/0.35 thf(func_def_7, type, breln: $i > $i > $i > $o).
% 0.11/0.35 thf(func_def_20, type, sK6: $i > $o).
% 0.11/0.35 thf(func_def_25, type, sK11: $i > $i > $i > $i).
% 0.11/0.35 thf(func_def_26, type, sK12: $i > $i > $i > $i).
% 0.11/0.35 thf(f80,plain,(
% 0.11/0.35 $false),
% 0.11/0.35 inference(subsumption_resolution,[],[f79,f43])).
% 0.11/0.35 thf(f43,plain,(
% 0.11/0.35 ((sK6 @ sK7) != $true)),
% 0.11/0.35 inference(cnf_transformation,[],[f27])).
% 0.11/0.35 thf(f27,plain,(
% 0.11/0.35 ((! [X4] : (! [X5] : (((sK6 @ (kpair @ X4 @ X5)) = $true) | ((in @ X5 @ sK5) != $true) | ((in @ (kpair @ X4 @ X5) @ sK4) != $true)) | ($true != (in @ X4 @ sK3))) & (((sK6 @ sK7) != $true) & ($true = (in @ sK7 @ sK4)))) & ($true = (breln @ sK3 @ sK5 @ sK4))) & (cartprodmempair1 = $true) & (subsetE = $true)),
% 0.11/0.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f16,f26,f25,f24])).
% 0.11/0.35 thf(f24,plain,(
% 0.11/0.35 ? [X0,X1,X2] : (? [X3 : $i > $o] : (! [X4] : (! [X5] : (((X3 @ (kpair @ X4 @ X5)) = $true) | ((in @ X5 @ X2) != $true) | ((in @ (kpair @ X4 @ X5) @ X1) != $true)) | ($true != (in @ X4 @ X0))) & ? [X6] : (((X3 @ X6) != $true) & ($true = (in @ X6 @ X1)))) & ((breln @ X0 @ X2 @ X1) = $true)) => (? [X3 : $i > $o] : (! [X4] : (! [X5] : (((X3 @ (kpair @ X4 @ X5)) = $true) | ((in @ X5 @ sK5) != $true) | ((in @ (kpair @ X4 @ X5) @ sK4) != $true)) | ($true != (in @ X4 @ sK3))) & ? [X6] : (((X3 @ X6) != $true) & ((in @ X6 @ sK4) = $true))) & ($true = (breln @ sK3 @ sK5 @ sK4)))),
% 0.11/0.35 introduced(choice_axiom,[])).
% 0.11/0.35 thf(f25,plain,(
% 0.11/0.35 ? [X3 : $i > $o] : (! [X4] : (! [X5] : (((X3 @ (kpair @ X4 @ X5)) = $true) | ((in @ X5 @ sK5) != $true) | ((in @ (kpair @ X4 @ X5) @ sK4) != $true)) | ($true != (in @ X4 @ sK3))) & ? [X6] : (((X3 @ X6) != $true) & ((in @ X6 @ sK4) = $true))) => (! [X4] : (! [X5] : (((sK6 @ (kpair @ X4 @ X5)) = $true) | ((in @ X5 @ sK5) != $true) | ((in @ (kpair @ X4 @ X5) @ sK4) != $true)) | ($true != (in @ X4 @ sK3))) & ? [X6] : (($true != (sK6 @ X6)) & ((in @ X6 @ sK4) = $true)))),
% 0.11/0.35 introduced(choice_axiom,[])).
% 0.11/0.35 thf(f26,plain,(
% 0.11/0.35 ? [X6] : (($true != (sK6 @ X6)) & ((in @ X6 @ sK4) = $true)) => (((sK6 @ sK7) != $true) & ($true = (in @ sK7 @ sK4)))),
% 0.11/0.35 introduced(choice_axiom,[])).
% 0.11/0.35 thf(f16,plain,(
% 0.11/0.35 ? [X0,X1,X2] : (? [X3 : $i > $o] : (! [X4] : (! [X5] : (((X3 @ (kpair @ X4 @ X5)) = $true) | ((in @ X5 @ X2) != $true) | ((in @ (kpair @ X4 @ X5) @ X1) != $true)) | ($true != (in @ X4 @ X0))) & ? [X6] : (((X3 @ X6) != $true) & ($true = (in @ X6 @ X1)))) & ((breln @ X0 @ X2 @ X1) = $true)) & (cartprodmempair1 = $true) & (subsetE = $true)),
% 0.11/0.35 inference(flattening,[],[f15])).
% 0.11/0.35 thf(f15,plain,(
% 0.11/0.35 (? [X0,X1,X2] : (? [X3 : $i > $o] : (? [X6] : (((X3 @ X6) != $true) & ($true = (in @ X6 @ X1))) & ! [X4] : (! [X5] : ((((X3 @ (kpair @ X4 @ X5)) = $true) | ((in @ (kpair @ X4 @ X5) @ X1) != $true)) | ((in @ X5 @ X2) != $true)) | ($true != (in @ X4 @ X0)))) & ((breln @ X0 @ X2 @ X1) = $true)) & (cartprodmempair1 = $true)) & (subsetE = $true)),
% 0.11/0.35 inference(ennf_transformation,[],[f12])).
% 0.11/0.35 thf(f12,plain,(
% 0.11/0.35 ~((subsetE = $true) => ((cartprodmempair1 = $true) => ! [X0,X1,X2] : (((breln @ X0 @ X2 @ X1) = $true) => ! [X3 : $i > $o] : (! [X4] : (($true = (in @ X4 @ X0)) => ! [X5] : (((in @ X5 @ X2) = $true) => (((in @ (kpair @ X4 @ X5) @ X1) = $true) => ((X3 @ (kpair @ X4 @ X5)) = $true)))) => ! [X6] : (($true = (in @ X6 @ X1)) => ((X3 @ X6) = $true))))))),
% 0.11/0.35 inference(fool_elimination,[],[f11])).
% 0.11/0.35 thf(f11,plain,(
% 0.11/0.35 ~(subsetE => (cartprodmempair1 => ! [X0,X1,X2] : ((breln @ X0 @ X2 @ X1) => ! [X3 : $i > $o] : (! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X1) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6] : ((in @ X6 @ X1) => (X3 @ X6))))))),
% 0.11/0.35 inference(rectify,[],[f5])).
% 0.11/0.35 thf(f5,negated_conjecture,(
% 0.11/0.35 ~(subsetE => (cartprodmempair1 => ! [X0,X6,X1] : ((breln @ X0 @ X1 @ X6) => ! [X7 : $i > $o] : (! [X2] : ((in @ X2 @ X0) => ! [X4] : ((in @ X4 @ X1) => ((in @ (kpair @ X2 @ X4) @ X6) => (X7 @ (kpair @ X2 @ X4))))) => ! [X2] : ((in @ X2 @ X6) => (X7 @ X2))))))),
% 0.11/0.35 inference(negated_conjecture,[],[f4])).
% 0.11/0.35 thf(f4,conjecture,(
% 0.11/0.35 subsetE => (cartprodmempair1 => ! [X0,X6,X1] : ((breln @ X0 @ X1 @ X6) => ! [X7 : $i > $o] : (! [X2] : ((in @ X2 @ X0) => ! [X4] : ((in @ X4 @ X1) => ((in @ (kpair @ X2 @ X4) @ X6) => (X7 @ (kpair @ X2 @ X4))))) => ! [X2] : ((in @ X2 @ X6) => (X7 @ X2)))))),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1)).
% 0.11/0.35 thf(f79,plain,(
% 0.11/0.35 ((sK6 @ sK7) = $true)),
% 0.11/0.35 inference(subsumption_resolution,[],[f78,f42])).
% 0.11/0.35 thf(f42,plain,(
% 0.11/0.35 ($true = (in @ sK7 @ sK4))),
% 0.11/0.35 inference(cnf_transformation,[],[f27])).
% 0.11/0.35 thf(f78,plain,(
% 0.11/0.35 ($true != (in @ sK7 @ sK4)) | ((sK6 @ sK7) = $true)),
% 0.11/0.35 inference(subsumption_resolution,[],[f77,f72])).
% 0.11/0.35 thf(f72,plain,(
% 0.11/0.35 ((in @ (sK12 @ sK7 @ sK3 @ sK5) @ sK5) = $true)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f71])).
% 0.11/0.35 thf(f71,plain,(
% 0.11/0.35 ($true != $true) | ((in @ (sK12 @ sK7 @ sK3 @ sK5) @ sK5) = $true)),
% 0.11/0.35 inference(superposition,[],[f63,f68])).
% 0.11/0.35 thf(f68,plain,(
% 0.11/0.35 ((in @ sK7 @ (cartprod @ sK3 @ sK5)) = $true)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f67])).
% 0.11/0.35 thf(f67,plain,(
% 0.11/0.35 ($true != $true) | ((in @ sK7 @ (cartprod @ sK3 @ sK5)) = $true)),
% 0.11/0.35 inference(superposition,[],[f66,f42])).
% 0.11/0.35 thf(f66,plain,(
% 0.11/0.35 ( ! [X0 : $i] : (((in @ X0 @ sK4) != $true) | ((in @ X0 @ (cartprod @ sK3 @ sK5)) = $true)) )),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f65])).
% 0.11/0.35 thf(f65,plain,(
% 0.11/0.35 ( ! [X0 : $i] : (((in @ X0 @ (cartprod @ sK3 @ sK5)) = $true) | ((in @ X0 @ sK4) != $true) | ($true != $true)) )),
% 0.11/0.35 inference(superposition,[],[f64,f62])).
% 0.11/0.35 thf(f62,plain,(
% 0.11/0.35 ((subset @ sK4 @ (cartprod @ sK3 @ sK5)) = $true)),
% 0.11/0.35 inference(beta_eta_normalization,[],[f54])).
% 0.11/0.35 thf(f54,plain,(
% 0.11/0.35 (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ sK3 @ sK5 @ sK4) = $true)),
% 0.11/0.35 inference(definition_unfolding,[],[f41,f34])).
% 0.11/0.35 thf(f34,plain,(
% 0.11/0.35 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.11/0.35 inference(cnf_transformation,[],[f10])).
% 0.11/0.35 thf(f10,plain,(
% 0.11/0.35 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.11/0.35 inference(fool_elimination,[],[f9])).
% 0.11/0.35 thf(f9,plain,(
% 0.11/0.35 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 0.11/0.35 inference(rectify,[],[f3])).
% 0.11/0.35 thf(f3,axiom,(
% 0.11/0.35 (breln = (^[X0 : $i, X1 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X0 @ X1))))),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln)).
% 0.11/0.35 thf(f41,plain,(
% 0.11/0.35 ($true = (breln @ sK3 @ sK5 @ sK4))),
% 0.11/0.35 inference(cnf_transformation,[],[f27])).
% 0.11/0.35 thf(f64,plain,(
% 0.11/0.35 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X3 @ X4) != $true) | ((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true)) )),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f53])).
% 0.11/0.35 thf(f53,plain,(
% 0.11/0.35 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ($true != $true) | ((subset @ X3 @ X4) != $true) | ((in @ X5 @ X4) = $true)) )),
% 0.11/0.35 inference(definition_unfolding,[],[f35,f39])).
% 0.11/0.35 thf(f39,plain,(
% 0.11/0.35 (subsetE = $true)),
% 0.11/0.35 inference(cnf_transformation,[],[f27])).
% 0.11/0.35 thf(f35,plain,(
% 0.11/0.35 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X3 @ X4) != $true) | ((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true) | (subsetE != $true)) )),
% 0.11/0.35 inference(cnf_transformation,[],[f23])).
% 0.11/0.35 thf(f23,plain,(
% 0.11/0.35 ((subsetE = $true) | (((subset @ sK0 @ sK1) = $true) & ((in @ sK2 @ sK1) != $true) & ((in @ sK2 @ sK0) = $true))) & (! [X3,X4,X5] : (((subset @ X3 @ X4) != $true) | ((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true)) | (subsetE != $true))),
% 0.11/0.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f21,f22])).
% 0.11/0.35 thf(f22,plain,(
% 0.11/0.35 ? [X0,X1,X2] : (((subset @ X0 @ X1) = $true) & ((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) => (((subset @ sK0 @ sK1) = $true) & ((in @ sK2 @ sK1) != $true) & ((in @ sK2 @ sK0) = $true))),
% 0.11/0.35 introduced(choice_axiom,[])).
% 0.11/0.35 thf(f21,plain,(
% 0.11/0.35 ((subsetE = $true) | ? [X0,X1,X2] : (((subset @ X0 @ X1) = $true) & ((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) & (! [X3,X4,X5] : (((subset @ X3 @ X4) != $true) | ((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true)) | (subsetE != $true))),
% 0.11/0.35 inference(rectify,[],[f20])).
% 0.11/0.35 thf(f20,plain,(
% 0.11/0.35 ((subsetE = $true) | ? [X0,X1,X2] : (((subset @ X0 @ X1) = $true) & ((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) & (! [X0,X1,X2] : (((subset @ X0 @ X1) != $true) | ((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) | (subsetE != $true))),
% 0.11/0.35 inference(nnf_transformation,[],[f18])).
% 0.11/0.35 thf(f18,plain,(
% 0.11/0.35 (subsetE = $true) <=> ! [X0,X1,X2] : (((subset @ X0 @ X1) != $true) | ((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true))),
% 0.11/0.35 inference(flattening,[],[f17])).
% 0.11/0.35 thf(f17,plain,(
% 0.11/0.35 (subsetE = $true) <=> ! [X0,X1,X2] : ((((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) | ((subset @ X0 @ X1) != $true))),
% 0.11/0.35 inference(ennf_transformation,[],[f8])).
% 0.11/0.35 thf(f8,plain,(
% 0.11/0.35 (subsetE = $true) <=> ! [X0,X1,X2] : (((subset @ X0 @ X1) = $true) => (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)))),
% 0.11/0.35 inference(fool_elimination,[],[f7])).
% 0.11/0.35 thf(f7,plain,(
% 0.11/0.35 (subsetE = ! [X0,X1,X2] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 0.11/0.35 inference(rectify,[],[f1])).
% 0.11/0.35 thf(f1,axiom,(
% 0.11/0.35 (subsetE = ! [X0,X1,X2] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE)).
% 0.11/0.35 thf(f63,plain,(
% 0.11/0.35 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((in @ X7 @ (cartprod @ X6 @ X5)) != $true) | ((in @ (sK12 @ X7 @ X6 @ X5) @ X5) = $true)) )),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f58])).
% 0.11/0.35 thf(f58,plain,(
% 0.11/0.35 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != $true) | ((in @ (sK12 @ X7 @ X6 @ X5) @ X5) = $true) | ((in @ X7 @ (cartprod @ X6 @ X5)) != $true)) )),
% 0.11/0.35 inference(definition_unfolding,[],[f46,f40])).
% 0.11/0.35 thf(f40,plain,(
% 0.11/0.35 (cartprodmempair1 = $true)),
% 0.11/0.35 inference(cnf_transformation,[],[f27])).
% 0.11/0.35 thf(f46,plain,(
% 0.11/0.35 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((in @ X7 @ (cartprod @ X6 @ X5)) != $true) | ((in @ (sK12 @ X7 @ X6 @ X5) @ X5) = $true) | (cartprodmempair1 != $true)) )),
% 0.11/0.35 inference(cnf_transformation,[],[f33])).
% 0.11/0.35 thf(f33,plain,(
% 0.11/0.35 ((cartprodmempair1 = $true) | (($true = (in @ sK10 @ (cartprod @ sK9 @ sK8))) & ! [X3] : (($true != (in @ X3 @ sK9)) | ! [X4] : (((in @ X4 @ sK8) != $true) | (sK10 != (kpair @ X3 @ X4)))))) & (! [X5,X6,X7] : (((in @ X7 @ (cartprod @ X6 @ X5)) != $true) | (((in @ (sK11 @ X7 @ X6 @ X5) @ X6) = $true) & (((in @ (sK12 @ X7 @ X6 @ X5) @ X5) = $true) & ((kpair @ (sK11 @ X7 @ X6 @ X5) @ (sK12 @ X7 @ X6 @ X5)) = X7)))) | (cartprodmempair1 != $true))),
% 0.11/0.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f29,f32,f31,f30])).
% 0.11/0.35 thf(f30,plain,(
% 0.11/0.35 ? [X0,X1,X2] : (((in @ X2 @ (cartprod @ X1 @ X0)) = $true) & ! [X3] : (((in @ X3 @ X1) != $true) | ! [X4] : (($true != (in @ X4 @ X0)) | ((kpair @ X3 @ X4) != X2)))) => (($true = (in @ sK10 @ (cartprod @ sK9 @ sK8))) & ! [X3] : (($true != (in @ X3 @ sK9)) | ! [X4] : (((in @ X4 @ sK8) != $true) | (sK10 != (kpair @ X3 @ X4)))))),
% 0.11/0.35 introduced(choice_axiom,[])).
% 0.11/0.35 thf(f31,plain,(
% 0.11/0.35 ! [X5,X6,X7] : (? [X8] : (((in @ X8 @ X6) = $true) & ? [X9] : (((in @ X9 @ X5) = $true) & ((kpair @ X8 @ X9) = X7))) => (((in @ (sK11 @ X7 @ X6 @ X5) @ X6) = $true) & ? [X9] : (((in @ X9 @ X5) = $true) & ((kpair @ (sK11 @ X7 @ X6 @ X5) @ X9) = X7))))),
% 0.11/0.35 introduced(choice_axiom,[])).
% 0.11/0.35 thf(f32,plain,(
% 0.11/0.35 ! [X5,X6,X7] : (? [X9] : (((in @ X9 @ X5) = $true) & ((kpair @ (sK11 @ X7 @ X6 @ X5) @ X9) = X7)) => (((in @ (sK12 @ X7 @ X6 @ X5) @ X5) = $true) & ((kpair @ (sK11 @ X7 @ X6 @ X5) @ (sK12 @ X7 @ X6 @ X5)) = X7)))),
% 0.11/0.35 introduced(choice_axiom,[])).
% 0.11/0.35 thf(f29,plain,(
% 0.11/0.35 ((cartprodmempair1 = $true) | ? [X0,X1,X2] : (((in @ X2 @ (cartprod @ X1 @ X0)) = $true) & ! [X3] : (((in @ X3 @ X1) != $true) | ! [X4] : (($true != (in @ X4 @ X0)) | ((kpair @ X3 @ X4) != X2))))) & (! [X5,X6,X7] : (((in @ X7 @ (cartprod @ X6 @ X5)) != $true) | ? [X8] : (((in @ X8 @ X6) = $true) & ? [X9] : (((in @ X9 @ X5) = $true) & ((kpair @ X8 @ X9) = X7)))) | (cartprodmempair1 != $true))),
% 0.11/0.35 inference(rectify,[],[f28])).
% 0.11/0.35 thf(f28,plain,(
% 0.11/0.35 ((cartprodmempair1 = $true) | ? [X0,X1,X2] : (((in @ X2 @ (cartprod @ X1 @ X0)) = $true) & ! [X3] : (((in @ X3 @ X1) != $true) | ! [X4] : (($true != (in @ X4 @ X0)) | ((kpair @ X3 @ X4) != X2))))) & (! [X0,X1,X2] : (((in @ X2 @ (cartprod @ X1 @ X0)) != $true) | ? [X3] : (((in @ X3 @ X1) = $true) & ? [X4] : (($true = (in @ X4 @ X0)) & ((kpair @ X3 @ X4) = X2)))) | (cartprodmempair1 != $true))),
% 0.11/0.35 inference(nnf_transformation,[],[f19])).
% 0.11/0.35 thf(f19,plain,(
% 0.11/0.35 (cartprodmempair1 = $true) <=> ! [X0,X1,X2] : (((in @ X2 @ (cartprod @ X1 @ X0)) != $true) | ? [X3] : (((in @ X3 @ X1) = $true) & ? [X4] : (($true = (in @ X4 @ X0)) & ((kpair @ X3 @ X4) = X2))))),
% 0.11/0.35 inference(ennf_transformation,[],[f14])).
% 0.11/0.35 thf(f14,plain,(
% 0.11/0.35 ! [X0,X1,X2] : (((in @ X2 @ (cartprod @ X1 @ X0)) = $true) => ? [X3] : (((in @ X3 @ X1) = $true) & ? [X4] : (($true = (in @ X4 @ X0)) & ((kpair @ X3 @ X4) = X2)))) <=> (cartprodmempair1 = $true)),
% 0.11/0.35 inference(fool_elimination,[],[f13])).
% 0.11/0.35 thf(f13,plain,(
% 0.11/0.35 (cartprodmempair1 = ! [X0,X1,X2] : ((in @ X2 @ (cartprod @ X1 @ X0)) => ? [X3] : ((in @ X3 @ X1) & ? [X4] : ((in @ X4 @ X0) & ((kpair @ X3 @ X4) = X2)))))),
% 0.11/0.35 inference(rectify,[],[f2])).
% 0.11/0.35 thf(f2,axiom,(
% 0.11/0.35 (cartprodmempair1 = ! [X1,X0,X3] : ((in @ X3 @ (cartprod @ X0 @ X1)) => ? [X2] : ((in @ X2 @ X0) & ? [X4] : ((in @ X4 @ X1) & ((kpair @ X2 @ X4) = X3)))))),
% 0.11/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1)).
% 0.11/0.35 thf(f77,plain,(
% 0.11/0.35 ((in @ (sK12 @ sK7 @ sK3 @ sK5) @ sK5) != $true) | ((sK6 @ sK7) = $true) | ($true != (in @ sK7 @ sK4))),
% 0.11/0.35 inference(superposition,[],[f74,f76])).
% 0.11/0.35 thf(f76,plain,(
% 0.11/0.35 ((kpair @ (sK11 @ sK7 @ sK3 @ sK5) @ (sK12 @ sK7 @ sK3 @ sK5)) = sK7)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f75])).
% 0.11/0.35 thf(f75,plain,(
% 0.11/0.35 ($true != $true) | ((kpair @ (sK11 @ sK7 @ sK3 @ sK5) @ (sK12 @ sK7 @ sK3 @ sK5)) = sK7)),
% 0.11/0.35 inference(superposition,[],[f60,f68])).
% 0.11/0.35 thf(f60,plain,(
% 0.11/0.35 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((in @ X7 @ (cartprod @ X6 @ X5)) != $true) | ((kpair @ (sK11 @ X7 @ X6 @ X5) @ (sK12 @ X7 @ X6 @ X5)) = X7)) )),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f59])).
% 0.11/0.35 thf(f59,plain,(
% 0.11/0.35 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((kpair @ (sK11 @ X7 @ X6 @ X5) @ (sK12 @ X7 @ X6 @ X5)) = X7) | ((in @ X7 @ (cartprod @ X6 @ X5)) != $true) | ($true != $true)) )),
% 0.11/0.35 inference(definition_unfolding,[],[f45,f40])).
% 0.11/0.35 thf(f45,plain,(
% 0.11/0.35 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((in @ X7 @ (cartprod @ X6 @ X5)) != $true) | ((kpair @ (sK11 @ X7 @ X6 @ X5) @ (sK12 @ X7 @ X6 @ X5)) = X7) | (cartprodmempair1 != $true)) )),
% 0.11/0.35 inference(cnf_transformation,[],[f33])).
% 0.11/0.35 thf(f74,plain,(
% 0.11/0.35 ( ! [X0 : $i] : (((in @ (kpair @ (sK11 @ sK7 @ sK3 @ sK5) @ X0) @ sK4) != $true) | ($true != (in @ X0 @ sK5)) | ((sK6 @ (kpair @ (sK11 @ sK7 @ sK3 @ sK5) @ X0)) = $true)) )),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f73])).
% 0.11/0.35 thf(f73,plain,(
% 0.11/0.35 ( ! [X0 : $i] : (((sK6 @ (kpair @ (sK11 @ sK7 @ sK3 @ sK5) @ X0)) = $true) | ($true != $true) | ((in @ (kpair @ (sK11 @ sK7 @ sK3 @ sK5) @ X0) @ sK4) != $true) | ($true != (in @ X0 @ sK5))) )),
% 0.11/0.35 inference(superposition,[],[f44,f70])).
% 0.11/0.35 thf(f70,plain,(
% 0.11/0.35 ((in @ (sK11 @ sK7 @ sK3 @ sK5) @ sK3) = $true)),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f69])).
% 0.11/0.35 thf(f69,plain,(
% 0.11/0.35 ((in @ (sK11 @ sK7 @ sK3 @ sK5) @ sK3) = $true) | ($true != $true)),
% 0.11/0.35 inference(superposition,[],[f61,f68])).
% 0.11/0.35 thf(f61,plain,(
% 0.11/0.35 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((in @ X7 @ (cartprod @ X6 @ X5)) != $true) | ((in @ (sK11 @ X7 @ X6 @ X5) @ X6) = $true)) )),
% 0.11/0.35 inference(trivial_inequality_removal,[],[f57])).
% 0.11/0.35 thf(f57,plain,(
% 0.11/0.35 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((in @ X7 @ (cartprod @ X6 @ X5)) != $true) | ($true != $true) | ((in @ (sK11 @ X7 @ X6 @ X5) @ X6) = $true)) )),
% 0.11/0.35 inference(definition_unfolding,[],[f47,f40])).
% 0.11/0.35 thf(f47,plain,(
% 0.11/0.35 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((in @ X7 @ (cartprod @ X6 @ X5)) != $true) | ((in @ (sK11 @ X7 @ X6 @ X5) @ X6) = $true) | (cartprodmempair1 != $true)) )),
% 0.11/0.35 inference(cnf_transformation,[],[f33])).
% 0.11/0.35 thf(f44,plain,(
% 0.11/0.35 ( ! [X4 : $i,X5 : $i] : (($true != (in @ X4 @ sK3)) | ((in @ (kpair @ X4 @ X5) @ sK4) != $true) | ((in @ X5 @ sK5) != $true) | ((sK6 @ (kpair @ X4 @ X5)) = $true)) )),
% 0.11/0.35 inference(cnf_transformation,[],[f27])).
% 0.11/0.35 % SZS output end Proof for theBenchmark
% 0.11/0.35 % (5820)------------------------------
% 0.11/0.35 % (5820)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.35 % (5820)Termination reason: Refutation
% 0.11/0.35
% 0.11/0.35 % (5820)Memory used [KB]: 5628
% 0.11/0.35 % (5820)Time elapsed: 0.009 s
% 0.11/0.35 % (5820)Instructions burned: 7 (million)
% 0.11/0.35 % (5820)------------------------------
% 0.11/0.35 % (5820)------------------------------
% 0.11/0.35 % (5813)Success in time 0.019 s
% 0.11/0.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------