TSTP Solution File: SEU664^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU664^2 : 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 : 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 03:50:26 EDT 2024
% Result : Theorem 0.26s 0.43s
% Output : Refutation 0.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU664^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15 % 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
% 0.16/0.40 % Computer : n005.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8042.1875MB
% 0.16/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Sun May 19 16:00:23 EDT 2024
% 0.16/0.40 % CPUTime :
% 0.16/0.40 This is a TH0_THM_EQU_NAR problem
% 0.26/0.40 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
% 0.26/0.42 % (18897)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)
% 0.26/0.42 % (18896)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.26/0.42 % (18893)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.26/0.42 % (18894)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)
% 0.26/0.42 % (18899)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.26/0.42 % (18898)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)
% 0.26/0.42 % (18900)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)
% 0.26/0.42 % (18895)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)
% 0.26/0.42 % (18896)Instruction limit reached!
% 0.26/0.42 % (18896)------------------------------
% 0.26/0.42 % (18896)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.42 % (18896)Termination reason: Unknown
% 0.26/0.42 % (18896)Termination phase: Property scanning
% 0.26/0.42 % (18897)Instruction limit reached!
% 0.26/0.42 % (18897)------------------------------
% 0.26/0.42 % (18897)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.42 % (18897)Termination reason: Unknown
% 0.26/0.42 % (18897)Termination phase: Property scanning
% 0.26/0.42
% 0.26/0.42 % (18897)Memory used [KB]: 895
% 0.26/0.42 % (18897)Time elapsed: 0.003 s
% 0.26/0.42 % (18897)Instructions burned: 2 (million)
% 0.26/0.42 % (18897)------------------------------
% 0.26/0.42 % (18897)------------------------------
% 0.26/0.42
% 0.26/0.42 % (18896)Memory used [KB]: 895
% 0.26/0.42 % (18896)Time elapsed: 0.003 s
% 0.26/0.42 % (18896)Instructions burned: 2 (million)
% 0.26/0.42 % (18896)------------------------------
% 0.26/0.42 % (18896)------------------------------
% 0.26/0.42 % (18900)Instruction limit reached!
% 0.26/0.42 % (18900)------------------------------
% 0.26/0.42 % (18900)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.42 % (18900)Termination reason: Unknown
% 0.26/0.42 % (18900)Termination phase: Saturation
% 0.26/0.42
% 0.26/0.42 % (18900)Memory used [KB]: 5500
% 0.26/0.42 % (18900)Time elapsed: 0.004 s
% 0.26/0.42 % (18900)Instructions burned: 4 (million)
% 0.26/0.42 % (18900)------------------------------
% 0.26/0.42 % (18900)------------------------------
% 0.26/0.42 % (18894)Instruction limit reached!
% 0.26/0.42 % (18894)------------------------------
% 0.26/0.42 % (18894)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.42 % (18894)Termination reason: Unknown
% 0.26/0.42 % (18894)Termination phase: Saturation
% 0.26/0.42
% 0.26/0.42 % (18894)Memory used [KB]: 5500
% 0.26/0.42 % (18894)Time elapsed: 0.005 s
% 0.26/0.42 % (18894)Instructions burned: 5 (million)
% 0.26/0.42 % (18894)------------------------------
% 0.26/0.42 % (18894)------------------------------
% 0.26/0.43 % (18898)First to succeed.
% 0.26/0.43 % (18899)Instruction limit reached!
% 0.26/0.43 % (18899)------------------------------
% 0.26/0.43 % (18899)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.43 % (18899)Termination reason: Unknown
% 0.26/0.43 % (18899)Termination phase: Saturation
% 0.26/0.43
% 0.26/0.43 % (18899)Memory used [KB]: 5628
% 0.26/0.43 % (18899)Time elapsed: 0.013 s
% 0.26/0.43 % (18899)Instructions burned: 18 (million)
% 0.26/0.43 % (18899)------------------------------
% 0.26/0.43 % (18899)------------------------------
% 0.26/0.43 % (18898)Refutation found. Thanks to Tanya!
% 0.26/0.43 % SZS status Theorem for theBenchmark
% 0.26/0.43 % SZS output start Proof for theBenchmark
% 0.26/0.43 thf(func_def_0, type, in: $i > $i > $o).
% 0.26/0.43 thf(func_def_1, type, kpair: $i > $i > $i).
% 0.26/0.43 thf(func_def_2, type, cartprod: $i > $i > $i).
% 0.26/0.43 thf(func_def_5, type, kfst: $i > $i).
% 0.26/0.43 thf(func_def_6, type, ksnd: $i > $i).
% 0.26/0.43 thf(func_def_18, type, sK7: $i > $i > $i > $i).
% 0.26/0.43 thf(func_def_19, type, sK8: $i > $i > $i > $i).
% 0.26/0.43 thf(f125,plain,(
% 0.26/0.43 $false),
% 0.26/0.43 inference(subsumption_resolution,[],[f124,f50])).
% 0.26/0.43 thf(f50,plain,(
% 0.26/0.43 (sK11 != (kpair @ (kfst @ sK11) @ (ksnd @ sK11)))),
% 0.26/0.43 inference(cnf_transformation,[],[f33])).
% 0.26/0.43 thf(f33,plain,(
% 0.26/0.43 (cartprodmempair1 = $true) & (cartprodfstpairEq = $true) & ((sK11 != (kpair @ (kfst @ sK11) @ (ksnd @ sK11))) & ($true = (in @ sK11 @ (cartprod @ sK9 @ sK10)))) & (cartprodsndpairEq = $true)),
% 0.26/0.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f31,f32])).
% 0.26/0.43 thf(f32,plain,(
% 0.26/0.43 ? [X0,X1,X2] : (((kpair @ (kfst @ X2) @ (ksnd @ X2)) != X2) & ((in @ X2 @ (cartprod @ X0 @ X1)) = $true)) => ((sK11 != (kpair @ (kfst @ sK11) @ (ksnd @ sK11))) & ($true = (in @ sK11 @ (cartprod @ sK9 @ sK10))))),
% 0.26/0.43 introduced(choice_axiom,[])).
% 0.26/0.43 thf(f31,plain,(
% 0.26/0.43 (cartprodmempair1 = $true) & (cartprodfstpairEq = $true) & ? [X0,X1,X2] : (((kpair @ (kfst @ X2) @ (ksnd @ X2)) != X2) & ((in @ X2 @ (cartprod @ X0 @ X1)) = $true)) & (cartprodsndpairEq = $true)),
% 0.26/0.43 inference(rectify,[],[f16])).
% 0.26/0.43 thf(f16,plain,(
% 0.26/0.43 (cartprodmempair1 = $true) & (cartprodfstpairEq = $true) & ? [X2,X1,X0] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) != X0) & ((in @ X0 @ (cartprod @ X2 @ X1)) = $true)) & (cartprodsndpairEq = $true)),
% 0.26/0.43 inference(flattening,[],[f15])).
% 0.26/0.43 thf(f15,plain,(
% 0.26/0.43 ((? [X2,X1,X0] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) != X0) & ((in @ X0 @ (cartprod @ X2 @ X1)) = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempair1 = $true)),
% 0.26/0.43 inference(ennf_transformation,[],[f12])).
% 0.26/0.43 thf(f12,plain,(
% 0.26/0.43 ~((cartprodmempair1 = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ! [X2,X1,X0] : (((in @ X0 @ (cartprod @ X2 @ X1)) = $true) => ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0)))))),
% 0.26/0.43 inference(fool_elimination,[],[f11])).
% 0.26/0.43 thf(f11,plain,(
% 0.26/0.43 ~(cartprodmempair1 => (cartprodfstpairEq => (cartprodsndpairEq => ! [X0,X1,X2] : ((in @ X0 @ (cartprod @ X2 @ X1)) => ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0)))))),
% 0.26/0.43 inference(rectify,[],[f5])).
% 0.26/0.43 thf(f5,negated_conjecture,(
% 0.26/0.43 ~(cartprodmempair1 => (cartprodfstpairEq => (cartprodsndpairEq => ! [X2,X1,X0] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ((kpair @ (kfst @ X2) @ (ksnd @ X2)) = X2)))))),
% 0.26/0.43 inference(negated_conjecture,[],[f4])).
% 0.26/0.43 thf(f4,conjecture,(
% 0.26/0.43 cartprodmempair1 => (cartprodfstpairEq => (cartprodsndpairEq => ! [X2,X1,X0] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ((kpair @ (kfst @ X2) @ (ksnd @ X2)) = X2))))),
% 0.26/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq)).
% 0.26/0.43 thf(f124,plain,(
% 0.26/0.43 (sK11 = (kpair @ (kfst @ sK11) @ (ksnd @ sK11)))),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f119])).
% 0.26/0.43 thf(f119,plain,(
% 0.26/0.43 ($true != $true) | (sK11 = (kpair @ (kfst @ sK11) @ (ksnd @ sK11)))),
% 0.26/0.43 inference(superposition,[],[f118,f49])).
% 0.26/0.43 thf(f49,plain,(
% 0.26/0.43 ($true = (in @ sK11 @ (cartprod @ sK9 @ sK10)))),
% 0.26/0.43 inference(cnf_transformation,[],[f33])).
% 0.26/0.43 thf(f118,plain,(
% 0.26/0.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((kpair @ (kfst @ X2) @ (ksnd @ X2)) = X2)) )),
% 0.26/0.43 inference(duplicate_literal_removal,[],[f116])).
% 0.26/0.43 thf(f116,plain,(
% 0.26/0.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((kpair @ (kfst @ X2) @ (ksnd @ X2)) = X2) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) )),
% 0.26/0.43 inference(superposition,[],[f90,f95])).
% 0.26/0.43 thf(f95,plain,(
% 0.26/0.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((kfst @ X2) = (sK7 @ X0 @ X1 @ X2)) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) )),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f94])).
% 0.26/0.43 thf(f94,plain,(
% 0.26/0.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((kfst @ X2) = (sK7 @ X0 @ X1 @ X2)) | ($true != $true)) )),
% 0.26/0.43 inference(duplicate_literal_removal,[],[f92])).
% 0.26/0.43 thf(f92,plain,(
% 0.26/0.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((kfst @ X2) = (sK7 @ X0 @ X1 @ X2)) | ($true != $true)) )),
% 0.26/0.43 inference(superposition,[],[f85,f70])).
% 0.26/0.43 thf(f70,plain,(
% 0.26/0.43 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((in @ (sK8 @ X7 @ X6 @ X5) @ X6) = $true) | ($true != (in @ X5 @ (cartprod @ X7 @ X6)))) )),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f64])).
% 0.26/0.43 thf(f64,plain,(
% 0.26/0.43 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X5 @ (cartprod @ X7 @ X6))) | ((in @ (sK8 @ X7 @ X6 @ X5) @ X6) = $true) | ($true != $true)) )),
% 0.26/0.43 inference(definition_unfolding,[],[f44,f52])).
% 0.26/0.43 thf(f52,plain,(
% 0.26/0.43 (cartprodmempair1 = $true)),
% 0.26/0.43 inference(cnf_transformation,[],[f33])).
% 0.26/0.43 thf(f44,plain,(
% 0.26/0.43 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X5 @ (cartprod @ X7 @ X6))) | ((in @ (sK8 @ X7 @ X6 @ X5) @ X6) = $true) | (cartprodmempair1 != $true)) )),
% 0.26/0.43 inference(cnf_transformation,[],[f30])).
% 0.26/0.43 thf(f30,plain,(
% 0.26/0.43 ((cartprodmempair1 = $true) | (($true = (in @ sK4 @ (cartprod @ sK6 @ sK5))) & ! [X3] : (! [X4] : (((kpair @ X3 @ X4) != sK4) | ((in @ X4 @ sK5) != $true)) | ($true != (in @ X3 @ sK6))))) & (! [X5,X6,X7] : (($true != (in @ X5 @ (cartprod @ X7 @ X6))) | ((((kpair @ (sK7 @ X7 @ X6 @ X5) @ (sK8 @ X7 @ X6 @ X5)) = X5) & ((in @ (sK8 @ X7 @ X6 @ X5) @ X6) = $true)) & ((in @ (sK7 @ X7 @ X6 @ X5) @ X7) = $true))) | (cartprodmempair1 != $true))),
% 0.26/0.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f26,f29,f28,f27])).
% 0.26/0.43 thf(f27,plain,(
% 0.26/0.43 ? [X0,X1,X2] : (((in @ X0 @ (cartprod @ X2 @ X1)) = $true) & ! [X3] : (! [X4] : (((kpair @ X3 @ X4) != X0) | ((in @ X4 @ X1) != $true)) | ($true != (in @ X3 @ X2)))) => (($true = (in @ sK4 @ (cartprod @ sK6 @ sK5))) & ! [X3] : (! [X4] : (((kpair @ X3 @ X4) != sK4) | ((in @ X4 @ sK5) != $true)) | ($true != (in @ X3 @ sK6))))),
% 0.26/0.43 introduced(choice_axiom,[])).
% 0.26/0.43 thf(f28,plain,(
% 0.26/0.43 ! [X5,X6,X7] : (? [X8] : (? [X9] : (((kpair @ X8 @ X9) = X5) & ((in @ X9 @ X6) = $true)) & ((in @ X8 @ X7) = $true)) => (? [X9] : (((kpair @ (sK7 @ X7 @ X6 @ X5) @ X9) = X5) & ((in @ X9 @ X6) = $true)) & ((in @ (sK7 @ X7 @ X6 @ X5) @ X7) = $true)))),
% 0.26/0.43 introduced(choice_axiom,[])).
% 0.26/0.43 thf(f29,plain,(
% 0.26/0.43 ! [X5,X6,X7] : (? [X9] : (((kpair @ (sK7 @ X7 @ X6 @ X5) @ X9) = X5) & ((in @ X9 @ X6) = $true)) => (((kpair @ (sK7 @ X7 @ X6 @ X5) @ (sK8 @ X7 @ X6 @ X5)) = X5) & ((in @ (sK8 @ X7 @ X6 @ X5) @ X6) = $true)))),
% 0.26/0.43 introduced(choice_axiom,[])).
% 0.26/0.43 thf(f26,plain,(
% 0.26/0.43 ((cartprodmempair1 = $true) | ? [X0,X1,X2] : (((in @ X0 @ (cartprod @ X2 @ X1)) = $true) & ! [X3] : (! [X4] : (((kpair @ X3 @ X4) != X0) | ((in @ X4 @ X1) != $true)) | ($true != (in @ X3 @ X2))))) & (! [X5,X6,X7] : (($true != (in @ X5 @ (cartprod @ X7 @ X6))) | ? [X8] : (? [X9] : (((kpair @ X8 @ X9) = X5) & ((in @ X9 @ X6) = $true)) & ((in @ X8 @ X7) = $true))) | (cartprodmempair1 != $true))),
% 0.26/0.43 inference(rectify,[],[f25])).
% 0.26/0.43 thf(f25,plain,(
% 0.26/0.43 ((cartprodmempair1 = $true) | ? [X0,X2,X1] : (($true = (in @ X0 @ (cartprod @ X1 @ X2))) & ! [X3] : (! [X4] : (((kpair @ X3 @ X4) != X0) | ($true != (in @ X4 @ X2))) | ($true != (in @ X3 @ X1))))) & (! [X0,X2,X1] : (($true != (in @ X0 @ (cartprod @ X1 @ X2))) | ? [X3] : (? [X4] : (((kpair @ X3 @ X4) = X0) & ($true = (in @ X4 @ X2))) & ($true = (in @ X3 @ X1)))) | (cartprodmempair1 != $true))),
% 0.26/0.43 inference(nnf_transformation,[],[f18])).
% 0.26/0.43 thf(f18,plain,(
% 0.26/0.43 (cartprodmempair1 = $true) <=> ! [X0,X2,X1] : (($true != (in @ X0 @ (cartprod @ X1 @ X2))) | ? [X3] : (? [X4] : (((kpair @ X3 @ X4) = X0) & ($true = (in @ X4 @ X2))) & ($true = (in @ X3 @ X1))))),
% 0.26/0.43 inference(ennf_transformation,[],[f10])).
% 0.26/0.43 thf(f10,plain,(
% 0.26/0.43 ! [X1,X2,X0] : (($true = (in @ X0 @ (cartprod @ X1 @ X2))) => ? [X3] : (? [X4] : (((kpair @ X3 @ X4) = X0) & ($true = (in @ X4 @ X2))) & ($true = (in @ X3 @ X1)))) <=> (cartprodmempair1 = $true)),
% 0.26/0.43 inference(fool_elimination,[],[f9])).
% 0.26/0.43 thf(f9,plain,(
% 0.26/0.43 (! [X0,X1,X2] : ((in @ X0 @ (cartprod @ X1 @ X2)) => ? [X3] : ((in @ X3 @ X1) & ? [X4] : (((kpair @ X3 @ X4) = X0) & (in @ X4 @ X2)))) = cartprodmempair1)),
% 0.26/0.43 inference(rectify,[],[f1])).
% 0.26/0.43 thf(f1,axiom,(
% 0.26/0.43 (! [X2,X0,X1] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ? [X3] : ((in @ X3 @ X0) & ? [X4] : (((kpair @ X3 @ X4) = X2) & (in @ X4 @ X1)))) = cartprodmempair1)),
% 0.26/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1)).
% 0.26/0.43 thf(f85,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK8 @ X0 @ X1 @ X2) @ X3) != $true) | ((kfst @ X2) = (sK7 @ X0 @ X1 @ X2)) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) )),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f84])).
% 0.26/0.43 thf(f84,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kfst @ X2) = (sK7 @ X0 @ X1 @ X2)) | ($true != $true) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((in @ (sK8 @ X0 @ X1 @ X2) @ X3) != $true)) )),
% 0.26/0.43 inference(duplicate_literal_removal,[],[f83])).
% 0.26/0.43 thf(f83,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((kfst @ X2) = (sK7 @ X0 @ X1 @ X2)) | ($true != $true) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((in @ (sK8 @ X0 @ X1 @ X2) @ X3) != $true)) )),
% 0.26/0.43 inference(superposition,[],[f76,f74])).
% 0.26/0.43 thf(f74,plain,(
% 0.26/0.43 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((in @ (sK7 @ X7 @ X6 @ X5) @ X7) = $true) | ($true != (in @ X5 @ (cartprod @ X7 @ X6)))) )),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f65])).
% 0.26/0.43 thf(f65,plain,(
% 0.26/0.43 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X5 @ (cartprod @ X7 @ X6))) | ($true != $true) | ((in @ (sK7 @ X7 @ X6 @ X5) @ X7) = $true)) )),
% 0.26/0.43 inference(definition_unfolding,[],[f43,f52])).
% 0.26/0.43 thf(f43,plain,(
% 0.26/0.43 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X5 @ (cartprod @ X7 @ X6))) | ((in @ (sK7 @ X7 @ X6 @ X5) @ X7) = $true) | (cartprodmempair1 != $true)) )),
% 0.26/0.43 inference(cnf_transformation,[],[f30])).
% 0.26/0.43 thf(f76,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ (sK7 @ X0 @ X1 @ X2) @ X4)) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((in @ (sK8 @ X0 @ X1 @ X2) @ X3) != $true) | ((kfst @ X2) = (sK7 @ X0 @ X1 @ X2))) )),
% 0.26/0.43 inference(superposition,[],[f71,f73])).
% 0.26/0.43 thf(f73,plain,(
% 0.26/0.43 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((kpair @ (sK7 @ X7 @ X6 @ X5) @ (sK8 @ X7 @ X6 @ X5)) = X5) | ($true != (in @ X5 @ (cartprod @ X7 @ X6)))) )),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f63])).
% 0.26/0.43 thf(f63,plain,(
% 0.26/0.43 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != $true) | ($true != (in @ X5 @ (cartprod @ X7 @ X6))) | ((kpair @ (sK7 @ X7 @ X6 @ X5) @ (sK8 @ X7 @ X6 @ X5)) = X5)) )),
% 0.26/0.43 inference(definition_unfolding,[],[f45,f52])).
% 0.26/0.43 thf(f45,plain,(
% 0.26/0.43 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X5 @ (cartprod @ X7 @ X6))) | ((kpair @ (sK7 @ X7 @ X6 @ X5) @ (sK8 @ X7 @ X6 @ X5)) = X5) | (cartprodmempair1 != $true)) )),
% 0.26/0.43 inference(cnf_transformation,[],[f30])).
% 0.26/0.43 thf(f71,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kfst @ (kpair @ X2 @ X3)) = X2) | ((in @ X3 @ X0) != $true) | ((in @ X2 @ X1) != $true)) )),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f66])).
% 0.26/0.43 thf(f66,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) != $true) | ($true != $true) | ((kfst @ (kpair @ X2 @ X3)) = X2) | ((in @ X3 @ X0) != $true)) )),
% 0.26/0.43 inference(definition_unfolding,[],[f56,f51])).
% 0.26/0.43 thf(f51,plain,(
% 0.26/0.43 (cartprodfstpairEq = $true)),
% 0.26/0.43 inference(cnf_transformation,[],[f33])).
% 0.26/0.43 thf(f56,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kfst @ (kpair @ X2 @ X3)) = X2) | ((in @ X3 @ X0) != $true) | ((in @ X2 @ X1) != $true) | (cartprodfstpairEq != $true)) )),
% 0.26/0.43 inference(cnf_transformation,[],[f38])).
% 0.26/0.43 thf(f38,plain,(
% 0.26/0.43 (! [X0,X1,X2] : (! [X3] : (((kfst @ (kpair @ X2 @ X3)) = X2) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ X1) != $true)) | (cartprodfstpairEq != $true)) & ((cartprodfstpairEq = $true) | ((((kfst @ (kpair @ sK14 @ sK15)) != sK14) & ((in @ sK15 @ sK12) = $true)) & ($true = (in @ sK14 @ sK13))))),
% 0.26/0.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f35,f37,f36])).
% 0.26/0.43 thf(f36,plain,(
% 0.26/0.43 ? [X4,X5,X6] : (? [X7] : (((kfst @ (kpair @ X6 @ X7)) != X6) & ((in @ X7 @ X4) = $true)) & ($true = (in @ X6 @ X5))) => (? [X7] : (((kfst @ (kpair @ sK14 @ X7)) != sK14) & ($true = (in @ X7 @ sK12))) & ($true = (in @ sK14 @ sK13)))),
% 0.26/0.43 introduced(choice_axiom,[])).
% 0.26/0.43 thf(f37,plain,(
% 0.26/0.43 ? [X7] : (((kfst @ (kpair @ sK14 @ X7)) != sK14) & ($true = (in @ X7 @ sK12))) => (((kfst @ (kpair @ sK14 @ sK15)) != sK14) & ((in @ sK15 @ sK12) = $true))),
% 0.26/0.43 introduced(choice_axiom,[])).
% 0.26/0.43 thf(f35,plain,(
% 0.26/0.43 (! [X0,X1,X2] : (! [X3] : (((kfst @ (kpair @ X2 @ X3)) = X2) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ X1) != $true)) | (cartprodfstpairEq != $true)) & ((cartprodfstpairEq = $true) | ? [X4,X5,X6] : (? [X7] : (((kfst @ (kpair @ X6 @ X7)) != X6) & ((in @ X7 @ X4) = $true)) & ($true = (in @ X6 @ X5))))),
% 0.26/0.43 inference(rectify,[],[f34])).
% 0.26/0.43 thf(f34,plain,(
% 0.26/0.43 (! [X2,X0,X1] : (! [X3] : (((kfst @ (kpair @ X1 @ X3)) = X1) | ($true != (in @ X3 @ X2))) | ($true != (in @ X1 @ X0))) | (cartprodfstpairEq != $true)) & ((cartprodfstpairEq = $true) | ? [X2,X0,X1] : (? [X3] : (((kfst @ (kpair @ X1 @ X3)) != X1) & ($true = (in @ X3 @ X2))) & ($true = (in @ X1 @ X0))))),
% 0.26/0.43 inference(nnf_transformation,[],[f17])).
% 0.26/0.43 thf(f17,plain,(
% 0.26/0.43 ! [X2,X0,X1] : (! [X3] : (((kfst @ (kpair @ X1 @ X3)) = X1) | ($true != (in @ X3 @ X2))) | ($true != (in @ X1 @ X0))) <=> (cartprodfstpairEq = $true)),
% 0.26/0.43 inference(ennf_transformation,[],[f8])).
% 0.26/0.43 thf(f8,plain,(
% 0.26/0.43 ! [X1,X0,X2] : (($true = (in @ X1 @ X0)) => ! [X3] : (($true = (in @ X3 @ X2)) => ((kfst @ (kpair @ X1 @ X3)) = X1))) <=> (cartprodfstpairEq = $true)),
% 0.26/0.43 inference(fool_elimination,[],[f7])).
% 0.26/0.43 thf(f7,plain,(
% 0.26/0.43 (cartprodfstpairEq = ! [X0,X1,X2] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => ((kfst @ (kpair @ X1 @ X3)) = X1))))),
% 0.26/0.43 inference(rectify,[],[f2])).
% 0.26/0.43 thf(f2,axiom,(
% 0.26/0.43 (cartprodfstpairEq = ! [X0,X3,X1] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X1) => ((kfst @ (kpair @ X3 @ X4)) = X3))))),
% 0.26/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq)).
% 0.26/0.43 thf(f90,plain,(
% 0.26/0.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((kpair @ (sK7 @ X0 @ X1 @ X2) @ (ksnd @ X2)) = X2) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) )),
% 0.26/0.43 inference(duplicate_literal_removal,[],[f87])).
% 0.26/0.43 thf(f87,plain,(
% 0.26/0.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((kpair @ (sK7 @ X0 @ X1 @ X2) @ (ksnd @ X2)) = X2) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) )),
% 0.26/0.43 inference(superposition,[],[f73,f82])).
% 0.26/0.43 thf(f82,plain,(
% 0.26/0.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((ksnd @ X2) = (sK8 @ X0 @ X1 @ X2)) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) )),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f81])).
% 0.26/0.43 thf(f81,plain,(
% 0.26/0.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((ksnd @ X2) = (sK8 @ X0 @ X1 @ X2)) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) )),
% 0.26/0.43 inference(duplicate_literal_removal,[],[f80])).
% 0.26/0.43 thf(f80,plain,(
% 0.26/0.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((ksnd @ X2) = (sK8 @ X0 @ X1 @ X2)) | ($true != $true) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) )),
% 0.26/0.43 inference(superposition,[],[f79,f70])).
% 0.26/0.43 thf(f79,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK8 @ X0 @ X1 @ X2) @ X3) != $true) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((ksnd @ X2) = (sK8 @ X0 @ X1 @ X2))) )),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f78])).
% 0.26/0.43 thf(f78,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((ksnd @ X2) = (sK8 @ X0 @ X1 @ X2)) | ((in @ (sK8 @ X0 @ X1 @ X2) @ X3) != $true) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ($true != $true)) )),
% 0.26/0.43 inference(duplicate_literal_removal,[],[f77])).
% 0.26/0.43 thf(f77,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK8 @ X0 @ X1 @ X2) @ X3) != $true) | ($true != $true) | ((ksnd @ X2) = (sK8 @ X0 @ X1 @ X2)) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) )),
% 0.26/0.43 inference(superposition,[],[f75,f74])).
% 0.26/0.43 thf(f75,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ (sK7 @ X0 @ X1 @ X2) @ X4)) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ((in @ (sK8 @ X0 @ X1 @ X2) @ X3) != $true) | ((ksnd @ X2) = (sK8 @ X0 @ X1 @ X2))) )),
% 0.26/0.43 inference(superposition,[],[f72,f73])).
% 0.26/0.43 thf(f72,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X2 @ X3)) = X3) | ($true != (in @ X3 @ X1)) | ((in @ X2 @ X0) != $true)) )),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f57])).
% 0.26/0.43 thf(f57,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X3 @ X1)) | ($true != $true) | ((ksnd @ (kpair @ X2 @ X3)) = X3) | ((in @ X2 @ X0) != $true)) )),
% 0.26/0.43 inference(definition_unfolding,[],[f42,f48])).
% 0.26/0.43 thf(f48,plain,(
% 0.26/0.43 (cartprodsndpairEq = $true)),
% 0.26/0.43 inference(cnf_transformation,[],[f33])).
% 0.26/0.43 thf(f42,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) != $true) | ((ksnd @ (kpair @ X2 @ X3)) = X3) | ($true != (in @ X3 @ X1)) | (cartprodsndpairEq != $true)) )),
% 0.26/0.43 inference(cnf_transformation,[],[f24])).
% 0.26/0.43 thf(f24,plain,(
% 0.26/0.43 (! [X0,X1,X2] : (((in @ X2 @ X0) != $true) | ! [X3] : (((ksnd @ (kpair @ X2 @ X3)) = X3) | ($true != (in @ X3 @ X1)))) | (cartprodsndpairEq != $true)) & ((cartprodsndpairEq = $true) | (($true = (in @ sK2 @ sK0)) & (((ksnd @ (kpair @ sK2 @ sK3)) != sK3) & ($true = (in @ sK3 @ sK1)))))),
% 0.26/0.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f23,f22])).
% 0.26/0.43 thf(f22,plain,(
% 0.26/0.43 ? [X4,X5,X6] : (((in @ X6 @ X4) = $true) & ? [X7] : (((ksnd @ (kpair @ X6 @ X7)) != X7) & ($true = (in @ X7 @ X5)))) => (($true = (in @ sK2 @ sK0)) & ? [X7] : (((ksnd @ (kpair @ sK2 @ X7)) != X7) & ((in @ X7 @ sK1) = $true)))),
% 0.26/0.43 introduced(choice_axiom,[])).
% 0.26/0.43 thf(f23,plain,(
% 0.26/0.43 ? [X7] : (((ksnd @ (kpair @ sK2 @ X7)) != X7) & ((in @ X7 @ sK1) = $true)) => (((ksnd @ (kpair @ sK2 @ sK3)) != sK3) & ($true = (in @ sK3 @ sK1)))),
% 0.26/0.43 introduced(choice_axiom,[])).
% 0.26/0.43 thf(f21,plain,(
% 0.26/0.43 (! [X0,X1,X2] : (((in @ X2 @ X0) != $true) | ! [X3] : (((ksnd @ (kpair @ X2 @ X3)) = X3) | ($true != (in @ X3 @ X1)))) | (cartprodsndpairEq != $true)) & ((cartprodsndpairEq = $true) | ? [X4,X5,X6] : (((in @ X6 @ X4) = $true) & ? [X7] : (((ksnd @ (kpair @ X6 @ X7)) != X7) & ($true = (in @ X7 @ X5)))))),
% 0.26/0.43 inference(rectify,[],[f20])).
% 0.26/0.43 thf(f20,plain,(
% 0.26/0.43 (! [X1,X0,X2] : (((in @ X2 @ X1) != $true) | ! [X3] : (((ksnd @ (kpair @ X2 @ X3)) = X3) | ((in @ X3 @ X0) != $true))) | (cartprodsndpairEq != $true)) & ((cartprodsndpairEq = $true) | ? [X1,X0,X2] : (((in @ X2 @ X1) = $true) & ? [X3] : (((ksnd @ (kpair @ X2 @ X3)) != X3) & ((in @ X3 @ X0) = $true))))),
% 0.26/0.43 inference(nnf_transformation,[],[f19])).
% 0.26/0.43 thf(f19,plain,(
% 0.26/0.43 ! [X1,X0,X2] : (((in @ X2 @ X1) != $true) | ! [X3] : (((ksnd @ (kpair @ X2 @ X3)) = X3) | ((in @ X3 @ X0) != $true))) <=> (cartprodsndpairEq = $true)),
% 0.26/0.43 inference(ennf_transformation,[],[f14])).
% 0.26/0.43 thf(f14,plain,(
% 0.26/0.43 (cartprodsndpairEq = $true) <=> ! [X0,X1,X2] : (((in @ X2 @ X1) = $true) => ! [X3] : (((in @ X3 @ X0) = $true) => ((ksnd @ (kpair @ X2 @ X3)) = X3)))),
% 0.26/0.43 inference(fool_elimination,[],[f13])).
% 0.26/0.43 thf(f13,plain,(
% 0.26/0.43 (cartprodsndpairEq = ! [X0,X1,X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X0) => ((ksnd @ (kpair @ X2 @ X3)) = X3))))),
% 0.26/0.43 inference(rectify,[],[f3])).
% 0.26/0.43 thf(f3,axiom,(
% 0.26/0.43 (cartprodsndpairEq = ! [X1,X0,X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X1) => ((ksnd @ (kpair @ X3 @ X4)) = X4))))),
% 0.26/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndpairEq)).
% 0.26/0.43 % SZS output end Proof for theBenchmark
% 0.26/0.43 % (18898)------------------------------
% 0.26/0.43 % (18898)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.43 % (18898)Termination reason: Refutation
% 0.26/0.43
% 0.26/0.43 % (18898)Memory used [KB]: 5628
% 0.26/0.43 % (18898)Time elapsed: 0.015 s
% 0.26/0.43 % (18898)Instructions burned: 15 (million)
% 0.26/0.43 % (18898)------------------------------
% 0.26/0.43 % (18898)------------------------------
% 0.26/0.43 % (18892)Success in time 0.016 s
% 0.26/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------