%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU664^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:35 AM UTC 2026
% Result : Theorem 0.08s 0.17s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU664^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 14:04:05 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % (156229)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.17 % (156240)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.17 % (156240)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.08/0.17 % (156234)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2002866679:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.17 % (156235)lrs+10_16_si=on:nwc=1.5:random_seed=2183149164:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.17 % (156239)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1197923886:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.17 % (156236)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1204623405:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.17 % (156237)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2501950825:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.08/0.17 % (156238)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=281157115:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.17 % (156240)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=793627254:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.17 % (156236)Refutation not found, incomplete strategy
% 0.08/0.17 % (156236)------------------------------
% 0.08/0.17 % (156236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (156236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (156236)CaDiCaL version: 2.1.3
% 0.08/0.17 % (156236)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.17 % (156236)Time elapsed: 0.001 s
% 0.08/0.17 % (156236)Peak memory usage: 12 MB
% 0.08/0.17 % (156236)Instructions burned: 3 (million)
% 0.08/0.17 % (156236)------------------------------
% 0.08/0.17 % (156236)------------------------------
% 0.08/0.17 % (156234) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-156229-156234"...
% 0.08/0.17 % (156235)Instruction limit reached!
% 0.08/0.17 % (156235)------------------------------
% 0.08/0.17 % (156235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (156235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (156235)CaDiCaL version: 2.1.3
% 0.08/0.17 % (156235)Termination reason: Instruction limit
% 0.08/0.17 % (156235)Termination phase: Saturation
% 0.08/0.17 % (156235)Time elapsed: 0.005 s
% 0.08/0.17 % (156235)Peak memory usage: 12 MB
% 0.08/0.17 % (156235)Instructions burned: 18 (million)
% 0.08/0.17 % (156234)...printing done.
% 0.08/0.17 % (156239) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-156229-156239"...
% 0.08/0.17 % (156234)Refutation found. Thanks to Tanya!
% 0.08/0.17 % SZS status Theorem for theBenchmark
% 0.08/0.17 % SZS output start Proof for theBenchmark
% 0.08/0.17 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.17 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.08/0.17 thf(func_def_1, type, kpair: ($i > $i > $i)).
% 0.08/0.17 thf(func_def_2, type, cartprod: ($i > $i > $i)).
% 0.08/0.17 thf(func_def_3, type, cartprodmempair1: $o).
% 0.08/0.17 thf(func_def_5, type, kfst: ($i > $i)).
% 0.08/0.17 thf(func_def_6, type, ksnd: ($i > $i)).
% 0.08/0.17 thf(func_def_7, type, cartprodfstpairEq: $o).
% 0.08/0.17 thf(func_def_8, type, cartprodsndpairEq: $o).
% 0.08/0.17 thf(func_def_17, type, sK6: ($i > $i > $i > $i)).
% 0.08/0.17 thf(func_def_18, type, sK7: ($i > $i > $i > $i)).
% 0.08/0.17 thf(func_def_27, type, vNOT: ($o > $o)).
% 0.08/0.17 thf(f1,axiom,(
% 0.08/0.17 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ? [X3 : $i] : (? [X4 : $i] : ((in @ X4 @ X1) & (X2 = ((kpair @ X3 @ X4)))) & (in @ X3 @ X0))) = cartprodmempair1)),
% 0.08/0.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1)).
% 0.08/0.17 thf(f2,axiom,(
% 0.08/0.17 (cartprodfstpairEq = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((kfst @ (kpair @ X2 @ X3))) = X2))))),
% 0.08/0.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq)).
% 0.08/0.17 thf(f3,axiom,(
% 0.08/0.17 (cartprodsndpairEq = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (((ksnd @ (kpair @ X2 @ X3))) = X3))))),
% 0.08/0.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq)).
% 0.08/0.17 thf(f4,conjecture,(
% 0.08/0.17 cartprodmempair1 => (cartprodfstpairEq => (cartprodsndpairEq => ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (((kpair @ (kfst @ X2) @ (ksnd @ X2))) = X2))))),
% 0.08/0.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq)).
% 0.08/0.17 thf(f5,negated_conjecture,(
% 0.08/0.17 ~(cartprodmempair1 => (cartprodfstpairEq => (cartprodsndpairEq => ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (((kpair @ (kfst @ X2) @ (ksnd @ X2))) = X2)))))),
% 0.08/0.17 inference(negated_conjecture,[status(cth)],[f4])).
% 0.08/0.17 thf(f6,plain,(
% 0.08/0.17 (cartprodfstpairEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X2) => (((kfst @ (kpair @ X0 @ X3))) = X0))))),
% 0.08/0.17 inference(rectify,[],[f2])).
% 0.08/0.17 thf(f7,plain,(
% 0.08/0.17 (cartprodfstpairEq = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X0 @ X1)) = $true) => ! [X3 : $i] : (($true = ((in @ X3 @ X2))) => (((kfst @ (kpair @ X0 @ X3))) = X0)))),
% 0.08/0.17 inference(fool_elimination,[],[f6])).
% 0.08/0.17 thf(f8,plain,(
% 0.08/0.17 ~(cartprodmempair1 => (cartprodfstpairEq => (cartprodsndpairEq => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (cartprod @ X2 @ X1)) => (((kpair @ (kfst @ X0) @ (ksnd @ X0))) = X0)))))),
% 0.08/0.17 inference(rectify,[],[f5])).
% 0.08/0.17 thf(f9,plain,(
% 0.08/0.17 ~((cartprodmempair1 = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X0 @ (cartprod @ X2 @ X1))) = $true) => (((kpair @ (kfst @ X0) @ (ksnd @ X0))) = X0)))))),
% 0.08/0.17 inference(fool_elimination,[],[f8])).
% 0.08/0.17 thf(f10,plain,(
% 0.08/0.17 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X1 @ X0)) => ? [X3 : $i] : (? [X4 : $i] : ((in @ X4 @ X0) & (X2 = ((kpair @ X3 @ X4)))) & (in @ X3 @ X1))) = cartprodmempair1)),
% 0.08/0.17 inference(rectify,[],[f1])).
% 0.08/0.17 thf(f11,plain,(
% 0.08/0.17 ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X2 @ (cartprod @ X1 @ X0))) = $true) => ? [X3 : $i] : (? [X4 : $i] : ((((kpair @ X3 @ X4)) = X2) & (((in @ X4 @ X0)) = $true)) & (((in @ X3 @ X1)) = $true))) <=> (cartprodmempair1 = $true)),
% 0.08/0.17 inference(fool_elimination,[],[f10])).
% 0.08/0.17 thf(f12,plain,(
% 0.08/0.17 (cartprodsndpairEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ! [X3 : $i] : ((in @ X3 @ X2) => (((ksnd @ (kpair @ X0 @ X3))) = X3))))),
% 0.08/0.17 inference(rectify,[],[f3])).
% 0.08/0.17 thf(f13,plain,(
% 0.08/0.17 ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X0 @ X1)) = $true) => ! [X3 : $i] : (($true = ((in @ X3 @ X2))) => (((ksnd @ (kpair @ X0 @ X3))) = X3))) <=> (cartprodsndpairEq = $true)),
% 0.08/0.17 inference(fool_elimination,[],[f12])).
% 0.08/0.17 thf(f14,plain,(
% 0.08/0.17 (cartprodsndpairEq = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | ! [X3 : $i] : (($true != ((in @ X3 @ X2))) | (((ksnd @ (kpair @ X0 @ X3))) = X3)))),
% 0.08/0.17 inference(ennf_transformation,[],[f13])).
% 0.08/0.17 thf(f15,plain,(
% 0.08/0.17 (cartprodmempair1 = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((kpair @ X3 @ X4)) = X2) & (((in @ X4 @ X0)) = $true)) & (((in @ X3 @ X1)) = $true)) | (((in @ X2 @ (cartprod @ X1 @ X0))) != $true))),
% 0.08/0.17 inference(ennf_transformation,[],[f11])).
% 0.08/0.17 thf(f16,plain,(
% 0.08/0.17 ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X0 @ X1)) != $true) | ! [X3 : $i] : (($true != ((in @ X3 @ X2))) | (((kfst @ (kpair @ X0 @ X3))) = X0))) <=> (cartprodfstpairEq = $true)),
% 0.08/0.17 inference(ennf_transformation,[],[f7])).
% 0.08/0.17 thf(f17,plain,(
% 0.08/0.17 ((? [X2 : $i,X1 : $i,X0 : $i] : ((((kpair @ (kfst @ X0) @ (ksnd @ X0))) != X0) & (((in @ X0 @ (cartprod @ X2 @ X1))) = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempair1 = $true)),
% 0.08/0.17 inference(ennf_transformation,[],[f9])).
% 0.08/0.17 thf(f18,plain,(
% 0.08/0.17 (cartprodmempair1 = $true) & (cartprodsndpairEq = $true) & ? [X2 : $i,X1 : $i,X0 : $i] : ((((kpair @ (kfst @ X0) @ (ksnd @ X0))) != X0) & (((in @ X0 @ (cartprod @ X2 @ X1))) = $true)) & (cartprodfstpairEq = $true)),
% 0.08/0.17 inference(flattening,[],[f17])).
% 0.08/0.17 thf(f19,plain,(
% 0.08/0.17 (cartprodmempair1 = $true) & (cartprodsndpairEq = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : ((((kpair @ (kfst @ X2) @ (ksnd @ X2))) != X2) & (((in @ X2 @ (cartprod @ X0 @ X1))) = $true)) & (cartprodfstpairEq = $true)),
% 0.08/0.17 inference(rectify,[],[f18])).
% 0.08/0.17 thf(f20,plain,(
% 0.08/0.17 (cartprodmempair1 = $true) & (cartprodsndpairEq = $true) & ((sK2 != ((kpair @ (kfst @ sK2) @ (ksnd @ sK2)))) & ($true = ((in @ sK2 @ (cartprod @ sK0 @ sK1))))) & (cartprodfstpairEq = $true)),
% 0.08/0.17 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19])).
% 0.08/0.17 thf(f21,plain,(
% 0.08/0.17 ((cartprodmempair1 = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((((kpair @ X3 @ X4)) != X2) | (((in @ X4 @ X0)) != $true)) | (((in @ X3 @ X1)) != $true)) & (((in @ X2 @ (cartprod @ X1 @ X0))) = $true))) & (! [X1 : $i,X2 : $i,X0 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((kpair @ X3 @ X4)) = X2) & (((in @ X4 @ X0)) = $true)) & (((in @ X3 @ X1)) = $true)) | (((in @ X2 @ (cartprod @ X1 @ X0))) != $true)) | (cartprodmempair1 != $true))),
% 0.08/0.17 inference(nnf_transformation,[],[f15])).
% 0.08/0.17 thf(f22,plain,(
% 0.08/0.17 ((cartprodmempair1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((((kpair @ X3 @ X4)) != X1) | (((in @ X4 @ X2)) != $true)) | (((in @ X3 @ X0)) != $true)) & (((in @ X1 @ (cartprod @ X0 @ X2))) = $true))) & (! [X5 : $i,X6 : $i,X7 : $i] : (? [X8 : $i] : (? [X9 : $i] : ((((kpair @ X8 @ X9)) = X6) & (((in @ X9 @ X7)) = $true)) & (((in @ X8 @ X5)) = $true)) | ($true != ((in @ X6 @ (cartprod @ X5 @ X7))))) | (cartprodmempair1 != $true))),
% 0.08/0.17 inference(rectify,[],[f21])).
% 0.08/0.17 thf(f23,plain,(
% 0.08/0.17 ((cartprodmempair1 = $true) | (! [X3 : $i] : (! [X4 : $i] : ((((kpair @ X3 @ X4)) != sK4) | (((in @ X4 @ sK5)) != $true)) | (((in @ X3 @ sK3)) != $true)) & (((in @ sK4 @ (cartprod @ sK3 @ sK5))) = $true))) & (! [X5 : $i,X6 : $i,X7 : $i] : ((((((kpair @ (sK6 @ X7 @ X6 @ X5) @ (sK7 @ X7 @ X6 @ X5))) = X6) & ($true = ((in @ (sK7 @ X7 @ X6 @ X5) @ X7)))) & (((in @ (sK6 @ X7 @ X6 @ X5) @ X5)) = $true)) | ($true != ((in @ X6 @ (cartprod @ X5 @ X7))))) | (cartprodmempair1 != $true))),
% 0.08/0.17 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,vAPP,vAPP]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X9,sK7 @ X7 @ X6 @ X5),skolemize(X9,sK7 @ X7 @ X6 @ X5)],[f22])).
% 0.08/0.17 thf(f24,plain,(
% 0.08/0.17 ((cartprodsndpairEq = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X0 @ X1)) = $true) & ? [X3 : $i] : (($true = ((in @ X3 @ X2))) & (((ksnd @ (kpair @ X0 @ X3))) != X3)))) & (! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | ! [X3 : $i] : (($true != ((in @ X3 @ X2))) | (((ksnd @ (kpair @ X0 @ X3))) = X3))) | (cartprodsndpairEq != $true))),
% 0.08/0.17 inference(nnf_transformation,[],[f14])).
% 0.08/0.17 thf(f25,plain,(
% 0.08/0.17 ((cartprodsndpairEq = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X2)) = $true) & ? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & (((ksnd @ (kpair @ X0 @ X3))) != X3)))) & (! [X4 : $i,X5 : $i,X6 : $i] : ((((in @ X4 @ X6)) != $true) | ! [X7 : $i] : (($true != ((in @ X7 @ X5))) | (((ksnd @ (kpair @ X4 @ X7))) = X7))) | (cartprodsndpairEq != $true))),
% 0.08/0.17 inference(rectify,[],[f24])).
% 0.08/0.17 thf(f26,plain,(
% 0.08/0.17 ((cartprodsndpairEq = $true) | ((((in @ sK8 @ sK10)) = $true) & ((((in @ sK11 @ sK9)) = $true) & (((ksnd @ (kpair @ sK8 @ sK11))) != sK11)))) & (! [X4 : $i,X5 : $i,X6 : $i] : ((((in @ X4 @ X6)) != $true) | ! [X7 : $i] : (($true != ((in @ X7 @ X5))) | (((ksnd @ (kpair @ X4 @ X7))) = X7))) | (cartprodsndpairEq != $true))),
% 0.08/0.17 inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11)],[f25])).
% 0.08/0.17 thf(f27,plain,(
% 0.08/0.17 (! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X0 @ X1)) != $true) | ! [X3 : $i] : (($true != ((in @ X3 @ X2))) | (((kfst @ (kpair @ X0 @ X3))) = X0))) | (cartprodfstpairEq != $true)) & ((cartprodfstpairEq = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X0 @ X1)) = $true) & ? [X3 : $i] : (($true = ((in @ X3 @ X2))) & (((kfst @ (kpair @ X0 @ X3))) != X0))))),
% 0.08/0.17 inference(nnf_transformation,[],[f16])).
% 0.08/0.17 thf(f28,plain,(
% 0.08/0.17 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) != $true) | ! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | (((kfst @ (kpair @ X2 @ X3))) = X2))) | (cartprodfstpairEq != $true)) & ((cartprodfstpairEq = $true) | ? [X4 : $i,X5 : $i,X6 : $i] : ((((in @ X6 @ X4)) = $true) & ? [X7 : $i] : (($true = ((in @ X7 @ X5))) & (((kfst @ (kpair @ X6 @ X7))) != X6))))),
% 0.08/0.17 inference(rectify,[],[f27])).
% 0.08/0.17 thf(f29,plain,(
% 0.08/0.17 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) != $true) | ! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | (((kfst @ (kpair @ X2 @ X3))) = X2))) | (cartprodfstpairEq != $true)) & ((cartprodfstpairEq = $true) | ((((in @ sK14 @ sK12)) = $true) & ((((in @ sK15 @ sK13)) = $true) & (((kfst @ (kpair @ sK14 @ sK15))) != sK14))))),
% 0.08/0.17 inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X4,sK12),skolemize(X5,sK13),skolemize(X6,sK14),skolemize(X7,sK15)],[f28])).
% 0.08/0.17 thf(f30,plain,(
% 0.08/0.17 (cartprodfstpairEq = $true)),
% 0.08/0.17 inference(cnf_transformation,[],[f20])).
% 0.08/0.17 thf(f31,plain,(
% 0.08/0.17 ($true = ((in @ sK2 @ (cartprod @ sK0 @ sK1))))),
% 0.08/0.17 inference(cnf_transformation,[],[f20])).
% 0.08/0.17 thf(f32,plain,(
% 0.08/0.17 (sK2 != ((kpair @ (kfst @ sK2) @ (ksnd @ sK2))))),
% 0.08/0.17 inference(cnf_transformation,[],[f20])).
% 0.08/0.17 thf(f33,plain,(
% 0.08/0.17 (cartprodsndpairEq = $true)),
% 0.08/0.17 inference(cnf_transformation,[],[f20])).
% 0.08/0.17 thf(f34,plain,(
% 0.08/0.17 (cartprodmempair1 = $true)),
% 0.08/0.17 inference(cnf_transformation,[],[f20])).
% 0.08/0.17 thf(f35,plain,(
% 0.08/0.17 ( ! [X6 : $i,X7 : $i,X5 : $i] : ((((in @ (sK6 @ X7 @ X6 @ X5) @ X5)) = $true) | ($true != ((in @ X6 @ (cartprod @ X5 @ X7)))) | (cartprodmempair1 != $true)) )),
% 0.08/0.17 inference(cnf_transformation,[],[f23])).
% 0.08/0.17 thf(f36,plain,(
% 0.08/0.17 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true = ((in @ (sK7 @ X7 @ X6 @ X5) @ X7))) | ($true != ((in @ X6 @ (cartprod @ X5 @ X7)))) | (cartprodmempair1 != $true)) )),
% 0.08/0.17 inference(cnf_transformation,[],[f23])).
% 0.08/0.17 thf(f37,plain,(
% 0.08/0.17 ( ! [X6 : $i,X7 : $i,X5 : $i] : ((((kpair @ (sK6 @ X7 @ X6 @ X5) @ (sK7 @ X7 @ X6 @ X5))) = X6) | ($true != ((in @ X6 @ (cartprod @ X5 @ X7)))) | (cartprodmempair1 != $true)) )),
% 0.08/0.17 inference(cnf_transformation,[],[f23])).
% 0.08/0.17 thf(f40,plain,(
% 0.08/0.17 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X6)) != $true) | ($true != ((in @ X7 @ X5))) | (((ksnd @ (kpair @ X4 @ X7))) = X7) | (cartprodsndpairEq != $true)) )),
% 0.08/0.17 inference(cnf_transformation,[],[f26])).
% 0.08/0.17 thf(f47,plain,(
% 0.08/0.17 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X3 @ X1)) != $true) | (((kfst @ (kpair @ X2 @ X3))) = X2) | (cartprodfstpairEq != $true)) )),
% 0.08/0.17 inference(cnf_transformation,[],[f29])).
% 0.08/0.17 thf(f52,plain,(
% 0.08/0.17 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != ((in @ X6 @ (cartprod @ X5 @ X7)))) | (((kpair @ (sK6 @ X7 @ X6 @ X5) @ (sK7 @ X7 @ X6 @ X5))) = X6) | ($true != $true)) )),
% 0.08/0.17 inference(definition_unfolding,[],[f37,f34])).
% 0.08/0.17 thf(f53,plain,(
% 0.08/0.17 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != ((in @ X6 @ (cartprod @ X5 @ X7)))) | ($true != $true) | ($true = ((in @ (sK7 @ X7 @ X6 @ X5) @ X7)))) )),
% 0.08/0.17 inference(definition_unfolding,[],[f36,f34])).
% 0.08/0.17 thf(f54,plain,(
% 0.08/0.17 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != $true) | (((in @ (sK6 @ X7 @ X6 @ X5) @ X5)) = $true) | ($true != ((in @ X6 @ (cartprod @ X5 @ X7))))) )),
% 0.08/0.17 inference(definition_unfolding,[],[f35,f34])).
% 0.08/0.17 thf(f58,plain,(
% 0.08/0.17 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X7 @ X5))) | ($true != $true) | (((in @ X4 @ X6)) != $true) | (((ksnd @ (kpair @ X4 @ X7))) = X7)) )),
% 0.08/0.17 inference(definition_unfolding,[],[f40,f33])).
% 0.08/0.17 thf(f59,plain,(
% 0.08/0.17 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((in @ X2 @ X0)) != $true) | (((in @ X3 @ X1)) != $true) | (((kfst @ (kpair @ X2 @ X3))) = X2)) )),
% 0.08/0.17 inference(definition_unfolding,[],[f47,f30])).
% 0.08/0.17 thf(f63,plain,(
% 0.08/0.17 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != ((in @ X6 @ (cartprod @ X5 @ X7)))) | (((in @ (sK6 @ X7 @ X6 @ X5) @ X5)) = $true)) )),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f54])).
% 0.08/0.17 thf(f64,plain,(
% 0.08/0.17 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != ((in @ X6 @ (cartprod @ X5 @ X7)))) | (((kpair @ (sK6 @ X7 @ X6 @ X5) @ (sK7 @ X7 @ X6 @ X5))) = X6)) )),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f52])).
% 0.08/0.17 thf(f65,plain,(
% 0.08/0.17 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X7 @ X5))) | (((in @ X4 @ X6)) != $true) | (((ksnd @ (kpair @ X4 @ X7))) = X7)) )),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f58])).
% 0.08/0.17 thf(f66,plain,(
% 0.08/0.17 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X3 @ X1)) != $true) | (((kfst @ (kpair @ X2 @ X3))) = X2) | (((in @ X2 @ X0)) != $true)) )),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f59])).
% 0.08/0.17 thf(f67,plain,(
% 0.08/0.17 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != ((in @ X6 @ (cartprod @ X5 @ X7)))) | ($true = ((in @ (sK7 @ X7 @ X6 @ X5) @ X7)))) )),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f53])).
% 0.08/0.17 thf(f76,plain,(
% 0.08/0.17 (((in @ (sK6 @ sK1 @ sK2 @ sK0) @ sK0)) = $true) | ($true != $true)),
% 0.08/0.17 inference(constrained_superposition,[],[f63,f31])).
% 0.08/0.17 thf(f77,plain,(
% 0.08/0.17 (((in @ (sK6 @ sK1 @ sK2 @ sK0) @ sK0)) = $true)),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f76])).
% 0.08/0.17 thf(f90,plain,(
% 0.08/0.17 ($true != $true) | (((in @ (sK7 @ sK1 @ sK2 @ sK0) @ sK1)) = $true)),
% 0.08/0.17 inference(constrained_superposition,[],[f67,f31])).
% 0.08/0.17 thf(f91,plain,(
% 0.08/0.17 (((in @ (sK7 @ sK1 @ sK2 @ sK0) @ sK1)) = $true)),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f90])).
% 0.08/0.17 thf(f94,plain,(
% 0.08/0.17 ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | (((kfst @ (kpair @ X0 @ (sK7 @ sK1 @ sK2 @ sK0)))) = X0) | ($true != $true)) )),
% 0.08/0.17 inference(constrained_superposition,[],[f66,f91])).
% 0.08/0.17 thf(f96,plain,(
% 0.08/0.17 ( ! [X0 : $i,X1 : $i] : ((((sK7 @ sK1 @ sK2 @ sK0)) = ((ksnd @ (kpair @ X0 @ (sK7 @ sK1 @ sK2 @ sK0))))) | (((in @ X0 @ X1)) != $true) | ($true != $true)) )),
% 0.08/0.17 inference(constrained_superposition,[],[f65,f91])).
% 0.08/0.17 thf(f97,plain,(
% 0.08/0.17 ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | (((sK7 @ sK1 @ sK2 @ sK0)) = ((ksnd @ (kpair @ X0 @ (sK7 @ sK1 @ sK2 @ sK0)))))) )),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f96])).
% 0.08/0.17 thf(f98,plain,(
% 0.08/0.17 ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | (((kfst @ (kpair @ X0 @ (sK7 @ sK1 @ sK2 @ sK0)))) = X0)) )),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f94])).
% 0.08/0.17 thf(f103,plain,(
% 0.08/0.17 ($true != $true) | (((kfst @ (kpair @ (sK6 @ sK1 @ sK2 @ sK0) @ (sK7 @ sK1 @ sK2 @ sK0)))) = ((sK6 @ sK1 @ sK2 @ sK0)))),
% 0.08/0.17 inference(constrained_superposition,[],[f98,f77])).
% 0.08/0.17 thf(f107,plain,(
% 0.08/0.17 (((kfst @ (kpair @ (sK6 @ sK1 @ sK2 @ sK0) @ (sK7 @ sK1 @ sK2 @ sK0)))) = ((sK6 @ sK1 @ sK2 @ sK0)))),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f103])).
% 0.08/0.17 thf(f115,plain,(
% 0.08/0.17 (((sK7 @ sK1 @ sK2 @ sK0)) = ((ksnd @ (kpair @ (sK6 @ sK1 @ sK2 @ sK0) @ (sK7 @ sK1 @ sK2 @ sK0))))) | ($true != $true)),
% 0.08/0.17 inference(constrained_superposition,[],[f97,f77])).
% 0.08/0.17 thf(f119,plain,(
% 0.08/0.17 (((sK7 @ sK1 @ sK2 @ sK0)) = ((ksnd @ (kpair @ (sK6 @ sK1 @ sK2 @ sK0) @ (sK7 @ sK1 @ sK2 @ sK0)))))),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f115])).
% 0.08/0.17 thf(f120,plain,(
% 0.08/0.17 (((kpair @ (sK6 @ sK1 @ sK2 @ sK0) @ (sK7 @ sK1 @ sK2 @ sK0))) = sK2) | ($true != $true)),
% 0.08/0.17 inference(constrained_superposition,[],[f64,f31])).
% 0.08/0.17 thf(f121,plain,(
% 0.08/0.17 (((kpair @ (sK6 @ sK1 @ sK2 @ sK0) @ (sK7 @ sK1 @ sK2 @ sK0))) = sK2)),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f120])).
% 0.08/0.17 thf(f122,plain,(
% 0.08/0.17 (((ksnd @ sK2)) = ((sK7 @ sK1 @ sK2 @ sK0)))),
% 0.08/0.17 inference(constrained_superposition,[],[f119,f121])).
% 0.08/0.17 thf(f123,plain,(
% 0.08/0.17 (((kfst @ sK2)) = ((sK6 @ sK1 @ sK2 @ sK0)))),
% 0.08/0.17 inference(constrained_superposition,[],[f107,f121])).
% 0.08/0.17 thf(f135,plain,(
% 0.08/0.17 (((kpair @ (sK6 @ sK1 @ sK2 @ sK0) @ (ksnd @ sK2))) = sK2)),
% 0.08/0.17 inference(constrained_superposition,[],[f121,f122])).
% 0.08/0.17 thf(f138,plain,(
% 0.08/0.17 (sK2 = ((kpair @ (kfst @ sK2) @ (ksnd @ sK2))))),
% 0.08/0.17 inference(forward_demodulation,[],[f135,f123])).
% 0.08/0.17 thf(f141,plain,(
% 0.08/0.17 $false),
% 0.08/0.17 inference(forward_subsumption_resolution,[],[f138,f32])).
% 0.08/0.17 % SZS output end Proof for theBenchmark
% 0.08/0.17 % (156234)------------------------------
% 0.08/0.17 % (156234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (156234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (156234)CaDiCaL version: 2.1.3
% 0.08/0.17 % (156234)Termination reason: Refutation
% 0.08/0.17 % (156234)Time elapsed: 0.005 s
% 0.08/0.17 % (156234)Peak memory usage: 12 MB
% 0.08/0.17 % (156234)Instructions burned: 16 (million)
% 0.08/0.17 % (156229)Success in time 0.029 s
% 0.08/0.17 % Vampire exiting
%------------------------------------------------------------------------------