%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV385^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:38:33 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV385^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 15:42:55 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.28 % (888275)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (888285)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3668273015:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (888286)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (888286)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
% 0.21/0.28 % (888280)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1387029544:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (888281)lrs+10_16_si=on:nwc=1.5:random_seed=1373945904:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (888282)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=326065740:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (888284)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2966569904:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (888283)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=2693313615: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)
% 0.21/0.28 % (888286)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=1904030927:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (888282) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-888275-888282"...
% 0.21/0.28 % (888284) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-888275-888284"...
% 0.21/0.28 % (888282)...printing done.
% 0.21/0.28 % (888286) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-888275-888286"...
% 0.21/0.28 % (888280) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-888275-888280"...
% 0.21/0.28 % (888282)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, b: $tType).
% 0.21/0.28 thf(type_def_6, type, a: $tType).
% 0.21/0.28 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, x: b).
% 0.21/0.28 thf(func_def_1, type, y: a).
% 0.21/0.28 thf(func_def_3, type, vAND: ($o > $o > $o)).
% 0.21/0.28 thf(func_def_4, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_5, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.28 thf(func_def_6, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.28 thf(func_def_7, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_8, type, sK0: ((b > a) > a)).
% 0.21/0.28 thf(func_def_9, type, sK1: ((b > a) > b)).
% 0.21/0.28 thf(func_def_12, type, sK2: ((b > a) > b > b)).
% 0.21/0.28 thf(func_def_13, type, sK3: ((b > a) > b > b)).
% 0.21/0.28 thf(f1,conjecture,(
% 0.21/0.28 ? [X0 : (b > a)] : (! [X2 : a] : ((y = X2) => ? [X3 : b] : ((^[X4 : b] : ((x = X4) & (X2 = ((X0 @ X4))))) = (((^[X5 : b, X6 : b] : ((X5 = X6))) @ X3)))) & ! [X1 : b] : ((x = X1) => (y = ((X0 @ X1)))))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX6004_pme)).
% 0.21/0.28 thf(f2,negated_conjecture,(
% 0.21/0.28 ~ ? [X0 : (b > a)] : (! [X2 : a] : ((y = X2) => ? [X3 : b] : ((^[X4 : b] : ((x = X4) & (X2 = ((X0 @ X4))))) = (((^[X5 : b, X6 : b] : ((X5 = X6))) @ X3)))) & ! [X1 : b] : ((x = X1) => (y = ((X0 @ X1)))))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.28 thf(f3,plain,(
% 0.21/0.28 ~ ? [X0 : (b > a)] : (! [X1 : a] : ((y = X1) => ? [X2 : b] : ((^[X3 : b] : ((x = X3) & (((X0 @ X3)) = X1))) = (((^[X4 : b, X5 : b] : ((X4 = X5))) @ X2)))) & ! [X6 : b] : ((x = X6) => (y = ((X0 @ X6)))))),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 ~ ? [X0 : (b > a)] : (! [X1 : a] : ((y = X1) => ? [X2 : b] : ((((^[Y0 : b]: ((^[Y1 : b]: (Y0 = Y1)))) @ X2)) = (^[Y0 : b]: (((X0 @ Y0) = X1) & (x = Y0))))) & ! [X6 : b] : ((x = X6) => (y = ((X0 @ X6)))))),
% 0.21/0.28 inference(fool_elimination,[],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ~ ? [X0 : (b > a)] : (! [X1 : a] : ((y = X1) => ? [X2 : b] : ((((^[Y0 : b]: ((^[Y1 : b]: (Y0 = Y1)))) @ X2)) = (^[Y0 : b]: (((X0 @ Y0) = X1) & (x = Y0))))) & ! [X3 : b] : ((x = X3) => (y = ((X0 @ X3)))))),
% 0.21/0.28 inference(rectify,[],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ! [X0 : (b > a)] : (? [X1 : a] : (! [X2 : b] : ((((^[Y0 : b]: ((^[Y1 : b]: (Y0 = Y1)))) @ X2)) != (^[Y0 : b]: (((X0 @ Y0) = X1) & (x = Y0)))) & (y = X1)) | ? [X3 : b] : ((x = X3) & (y != ((X0 @ X3)))))),
% 0.21/0.28 inference(ennf_transformation,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ! [X0 : (b > a)] : ((! [X2 : b] : ((((^[Y0 : b]: ((^[Y1 : b]: (Y0 = Y1)))) @ X2)) != (^[Y0 : b]: (((X0 @ Y0) = (sK0 @ X0)) & (x = Y0)))) & (y = ((sK0 @ X0)))) | ((x = ((sK1 @ X0))) & (y != ((X0 @ (sK1 @ X0))))))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK1 @ X0),skolemize(X3,sK1 @ X0)],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ( ! [X0 : (b > a)] : ((y != ((X0 @ (sK1 @ X0)))) | (y = ((sK0 @ X0)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f7])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ( ! [X2 : b,X0 : (b > a)] : (((((^[Y0 : b]: ((^[Y1 : b]: (Y0 = Y1)))) @ X2)) != (^[Y0 : b]: (((X0 @ Y0) = (sK0 @ X0)) & (x = Y0)))) | (y != ((X0 @ (sK1 @ X0))))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f7])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 ( ! [X2 : b,X0 : (b > a)] : ((((= @ X2)) != (^[Y0 : b]: (((X0 @ Y0) = (sK0 @ X0)) & (x = Y0)))) | (y != ((X0 @ (sK1 @ X0))))) )),
% 0.21/0.28 inference(beta-eta_normalization,[],[f10])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 (y = ((sK0 @ (^[Y0 : b]: (y))))) | (y != (((^[Y0 : b]: (y)) @ (sK1 @ (^[Y0 : b]: (y))))))),
% 0.21/0.28 inference(imitation,[],[f8])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 (y != y) | (y = ((sK0 @ (^[Y0 : b]: (y)))))),
% 0.21/0.28 inference(beta-eta_normalization,[],[f16])).
% 0.21/0.28 thf(f18,plain,(
% 0.21/0.28 (y = ((sK0 @ (^[Y0 : b]: (y)))))),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f17])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 ( ! [X2 : b,X0 : (b > a)] : ((y != ((X0 @ (sK1 @ X0)))) | ((((^[Y0 : b]: (((X0 @ Y0) = (sK0 @ X0)) & (x = Y0))) @ (sK3 @ X0 @ X2))) != ((X2 = (sK3 @ X0 @ X2))))) )),
% 0.21/0.28 inference(negative_extensionality,[],[f15])).
% 0.21/0.28 thf(f22,plain,(
% 0.21/0.28 ( ! [X2 : b,X0 : (b > a)] : ((((((X0 @ (sK3 @ X0 @ X2)) = (sK0 @ X0)) & (x = (sK3 @ X0 @ X2)))) != ((X2 = (sK3 @ X0 @ X2)))) | (y != ((X0 @ (sK1 @ X0))))) )),
% 0.21/0.28 inference(beta-eta_normalization,[],[f21])).
% 0.21/0.28 thf(f41,plain,(
% 0.21/0.28 ( ! [X0 : b] : ((y != (((^[Y0 : b]: (y)) @ (sK1 @ (^[Y0 : b]: (y)))))) | ((((((^[Y0 : b]: (y)) @ (sK3 @ (^[Y0 : b]: (y)) @ X0)) = y) & (x = (sK3 @ (^[Y0 : b]: (y)) @ X0)))) != ((X0 = (sK3 @ (^[Y0 : b]: (y)) @ X0))))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f22,f18])).
% 0.21/0.28 thf(f42,plain,(
% 0.21/0.28 ( ! [X0 : b] : ((y != y) | (((X0 = (sK3 @ (^[Y0 : b]: (y)) @ X0))) != (((y = y) & (x = (sK3 @ (^[Y0 : b]: (y)) @ X0)))))) )),
% 0.21/0.28 inference(beta-eta_normalization,[],[f41])).
% 0.21/0.28 thf(f43,plain,(
% 0.21/0.28 ( ! [X0 : b] : ((((X0 = (sK3 @ (^[Y0 : b]: (y)) @ X0))) != (((y = y) & (x = (sK3 @ (^[Y0 : b]: (y)) @ X0)))))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f42])).
% 0.21/0.28 thf(f44,plain,(
% 0.21/0.28 ( ! [X0 : b] : (((($true & (x = (sK3 @ (^[Y0 : b]: (y)) @ X0)))) != ((X0 = (sK3 @ (^[Y0 : b]: (y)) @ X0))))) )),
% 0.21/0.28 inference(boolean_simplification,[],[f43])).
% 0.21/0.28 thf(f45,plain,(
% 0.21/0.28 ( ! [X0 : b] : ((((x = (sK3 @ (^[Y0 : b]: (y)) @ X0))) != ((X0 = (sK3 @ (^[Y0 : b]: (y)) @ X0))))) )),
% 0.21/0.28 inference(boolean_simplification,[],[f44])).
% 0.21/0.28 thf(f46,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(equality_resolution,[],[f45])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (888282)------------------------------
% 0.21/0.28 % (888282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (888282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (888282)CaDiCaL version: 2.1.3
% 0.21/0.28 % (888282)Termination reason: Refutation
% 0.21/0.28 % (888282)Time elapsed: 0.004 s
% 0.21/0.28 % (888282)Peak memory usage: 12 MB
% 0.21/0.28 % (888282)Instructions burned: 5 (million)
% 0.21/0.28 % (888275)Success in time 0.04 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------