%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV603^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:38:50 AM UTC 2026
% Result : Theorem 0.19s 0.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV603^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n013.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 15:59:07 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.30 % (2290899)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.30 % (2290911)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1693410527:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.30 % (2290911)Instruction limit reached!
% 0.19/0.30 % (2290911)------------------------------
% 0.19/0.30 % (2290911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (2290911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (2290911)CaDiCaL version: 2.1.3
% 0.19/0.30 % (2290911)Termination reason: Instruction limit
% 0.19/0.30 % (2290911)Termination phase: Saturation
% 0.19/0.30 % (2290911)Time elapsed: 0.002 s
% 0.19/0.30 % (2290911)Peak memory usage: 12 MB
% 0.19/0.30 % (2290911)Instructions burned: 4 (million)
% 0.19/0.30 % (2290915)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.30 % (2290915)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
% 0.19/0.30 % (2290910)lrs+10_16_si=on:nwc=1.5:random_seed=3642253643:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.30 % (2290909)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=361735094:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.30 % (2290913)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3482970105:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.30 % (2290912)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=1796564545: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)
% 0.19/0.30 % (2290914)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3193336240:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.30 % (2290915)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=2889588963:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.30 % (2290909) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2290899-2290909"...
% 0.19/0.30 % (2290913) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2290899-2290913"...
% 0.19/0.30 % (2290909)...printing done.
% 0.19/0.30 % (2290913)...printing done.
% 0.19/0.30 % (2290913)Refutation found. Thanks to Tanya!
% 0.19/0.30 % SZS status Theorem for theBenchmark
% 0.19/0.30 % SZS output start Proof for theBenchmark
% 0.19/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.30 thf(type_def_6, type, sK0: $tType).
% 0.19/0.30 thf(func_def_0, type, in: !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.19/0.30 thf(func_def_1, type, univ: !>[X0: $tType]:((X0 > $o))).
% 0.19/0.30 thf(func_def_2, type, insert: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > $o))).
% 0.19/0.30 thf(func_def_6, type, sK1: sK0).
% 0.19/0.30 thf(func_def_7, type, sK2: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.19/0.30 thf(func_def_8, type, sK3: sK0).
% 0.19/0.30 thf(f1,axiom,(
% 0.19/0.30 ! [X0 : $tType,X3 : (X0 > $o),X1 : X0,X2 : X0] : (((in @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = (X1 = X2) | (in @ X0 @ X1 @ X3))),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred_set/IN_INSERT_')).
% 0.19/0.30 thf(f2,axiom,(
% 0.19/0.30 ! [X0 : $tType,X1 : X0] : (in @ X0 @ X1 @ univ @ X0)),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred_set/IN_UNIV_')).
% 0.19/0.30 thf(f3,axiom,(
% 0.19/0.30 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((X1 = X2) = ! [X3 : X0] : (((in @ X0 @ X3 @ X1)) = ((in @ X0 @ X3 @ X2))))),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred_set/EXTENSION_')).
% 0.19/0.30 thf(f4,conjecture,(
% 0.19/0.30 ! [X0 : $tType,X1 : X0] : (((insert @ X0 @ X1 @ univ @ X0)) = univ @ X0)),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred_set/INSERT_UNIV_')).
% 0.19/0.30 thf(f5,negated_conjecture,(
% 0.19/0.30 ~ ! [X0 : $tType,X1 : X0] : (((insert @ X0 @ X1 @ univ @ X0)) = univ @ X0)),
% 0.19/0.30 inference(negated_conjecture,[status(cth)],[f4])).
% 0.19/0.30 thf(f6,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : X0] : (in @ X0 @ X1 @ univ @ X0)),
% 0.19/0.30 inference(rectify,[],[f2])).
% 0.19/0.30 thf(f7,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : X0] : (((in @ X0 @ X1 @ univ @ X0)) = $true)),
% 0.19/0.30 inference(fool_elimination,[],[f6])).
% 0.19/0.30 thf(f8,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : (X0 > $o),X2 : X0,X3 : X0] : (((in @ X0 @ X2 @ (insert @ X0 @ X3 @ X1))) = (X2 = X3) | (in @ X0 @ X2 @ X1))),
% 0.19/0.30 inference(rectify,[],[f1])).
% 0.19/0.30 thf(f9,plain,(
% 0.19/0.30 ! [X0 : $tType,X2 : X0,X3 : X0,X1 : (X0 > $o)] : (((((in @ X0 @ X2 @ X1)) = $true) | (X2 = X3)) <=> (((in @ X0 @ X2 @ (insert @ X0 @ X3 @ X1))) = $true))),
% 0.19/0.30 inference(fool_elimination,[],[f8])).
% 0.19/0.30 thf(f10,plain,(
% 0.19/0.30 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((X1 = X2) <=> ! [X3 : X0] : (((in @ X0 @ X3 @ X1)) = ((in @ X0 @ X3 @ X2))))),
% 0.19/0.30 inference(fool_elimination,[],[f3])).
% 0.19/0.30 thf(f11,plain,(
% 0.19/0.30 ? [X0 : $tType,X1 : X0] : (univ @ X0 != ((insert @ X0 @ X1 @ univ @ X0)))),
% 0.19/0.30 inference(ennf_transformation,[],[f5])).
% 0.19/0.30 thf(f12,plain,(
% 0.19/0.30 (((insert @ sK0 @ sK1 @ univ @ sK0)) != univ @ sK0)),
% 0.19/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11])).
% 0.19/0.30 thf(f13,plain,(
% 0.19/0.30 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((X1 = X2) | ? [X3 : X0] : (((in @ X0 @ X3 @ X1)) != ((in @ X0 @ X3 @ X2)))) & (! [X3 : X0] : (((in @ X0 @ X3 @ X1)) = ((in @ X0 @ X3 @ X2))) | (X1 != X2)))),
% 0.19/0.30 inference(nnf_transformation,[],[f10])).
% 0.19/0.30 thf(f14,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((X1 = X2) | ? [X3 : X0] : (((in @ X0 @ X3 @ X1)) != ((in @ X0 @ X3 @ X2)))) & (! [X4 : X0] : (((in @ X0 @ X4 @ X1)) = ((in @ X0 @ X4 @ X2))) | (X1 != X2)))),
% 0.19/0.30 inference(rectify,[],[f13])).
% 0.19/0.30 thf(f15,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((X1 = X2) | (((in @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X2)) != ((in @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X1)))) & (! [X4 : X0] : (((in @ X0 @ X4 @ X1)) = ((in @ X0 @ X4 @ X2))) | (X1 != X2)))),
% 0.19/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK2 @ X0 @ X2 @ X1)],[f14])).
% 0.19/0.30 thf(f16,plain,(
% 0.19/0.30 ! [X0 : $tType,X2 : X0,X3 : X0,X1 : (X0 > $o)] : ((((((in @ X0 @ X2 @ X1)) = $true) | (X2 = X3)) | (((in @ X0 @ X2 @ (insert @ X0 @ X3 @ X1))) != $true)) & ((((in @ X0 @ X2 @ (insert @ X0 @ X3 @ X1))) = $true) | ((((in @ X0 @ X2 @ X1)) != $true) & (X2 != X3))))),
% 0.19/0.30 inference(nnf_transformation,[],[f9])).
% 0.19/0.30 thf(f17,plain,(
% 0.19/0.30 ! [X0 : $tType,X2 : X0,X3 : X0,X1 : (X0 > $o)] : (((((in @ X0 @ X2 @ X1)) = $true) | (X2 = X3) | (((in @ X0 @ X2 @ (insert @ X0 @ X3 @ X1))) != $true)) & ((((in @ X0 @ X2 @ (insert @ X0 @ X3 @ X1))) = $true) | ((((in @ X0 @ X2 @ X1)) != $true) & (X2 != X3))))),
% 0.19/0.30 inference(flattening,[],[f16])).
% 0.19/0.30 thf(f18,plain,(
% 0.19/0.30 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : (X0 > $o)] : (((((in @ X0 @ X1 @ X3)) = $true) | (X1 = X2) | (((in @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) != $true)) & ((((in @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = $true) | ((((in @ X0 @ X1 @ X3)) != $true) & (X1 != X2))))),
% 0.19/0.30 inference(rectify,[],[f17])).
% 0.19/0.30 thf(f19,plain,(
% 0.19/0.30 (((insert @ sK0 @ sK1 @ univ @ sK0)) != univ @ sK0)),
% 0.19/0.30 inference(cnf_transformation,[],[f12])).
% 0.19/0.30 thf(f20,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X1 : X0] : ((((in @ X0 @ X1 @ univ @ X0)) = $true)) )),
% 0.19/0.30 inference(cnf_transformation,[],[f7])).
% 0.19/0.30 thf(f22,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((((in @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X2)) != ((in @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X1))) | (X1 = X2)) )),
% 0.19/0.30 inference(cnf_transformation,[],[f15])).
% 0.19/0.30 thf(f24,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X2 : X0,X3 : (X0 > $o),X1 : X0] : ((((in @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = $true) | (((in @ X0 @ X1 @ X3)) != $true)) )),
% 0.19/0.30 inference(cnf_transformation,[],[f18])).
% 0.19/0.30 thf(f30,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((((in @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X2)) = $false) | ($false = ((in @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X1))) | (X1 = X2)) )),
% 0.19/0.30 inference(xor_proxy_clausification,[],[f22])).
% 0.19/0.30 thf(f70,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X1 : (X0 > $o)] : ((univ @ X0 = X1) | (((in @ X0 @ (sK2 @ X0 @ X1 @ univ @ X0) @ X1)) = $false) | ($false = $true)) )),
% 0.19/0.30 inference(superposition,[],[f30,f20])).
% 0.19/0.30 thf(f85,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X1 : (X0 > $o)] : ((((in @ X0 @ (sK2 @ X0 @ X1 @ univ @ X0) @ X1)) = $false) | (univ @ X0 = X1)) )),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f70])).
% 0.19/0.30 thf(f106,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : ((univ @ X0 = ((insert @ X0 @ X1 @ X2))) | (((in @ X0 @ (sK2 @ X0 @ (insert @ X0 @ X1 @ X2) @ univ @ X0) @ X2)) != $true) | ($false = $true)) )),
% 0.19/0.30 inference(superposition,[],[f24,f85])).
% 0.19/0.30 thf(f107,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : ((((in @ X0 @ (sK2 @ X0 @ (insert @ X0 @ X1 @ X2) @ univ @ X0) @ X2)) != $true) | (univ @ X0 = ((insert @ X0 @ X1 @ X2)))) )),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f106])).
% 0.19/0.30 thf(f127,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | (univ @ X0 = ((insert @ X0 @ X1 @ univ @ X0)))) )),
% 0.19/0.30 inference(superposition,[],[f107,f20])).
% 0.19/0.30 thf(f132,plain,(
% 0.19/0.30 ( ! [X0 : $tType,X1 : X0] : ((univ @ X0 = ((insert @ X0 @ X1 @ univ @ X0)))) )),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f127])).
% 0.19/0.30 thf(f135,plain,(
% 0.19/0.30 (univ @ sK0 != univ @ sK0)),
% 0.19/0.30 inference(superposition,[],[f19,f132])).
% 0.19/0.30 thf(f140,plain,(
% 0.19/0.30 $false),
% 0.19/0.30 inference(trivial_inequality_removal,[],[f135])).
% 0.19/0.30 % SZS output end Proof for theBenchmark
% 0.19/0.30 % (2290913)------------------------------
% 0.19/0.30 % (2290913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (2290913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (2290913)CaDiCaL version: 2.1.3
% 0.19/0.30 % (2290913)Termination reason: Refutation
% 0.19/0.30 % (2290913)Time elapsed: 0.009 s
% 0.19/0.30 % (2290913)Peak memory usage: 12 MB
% 0.19/0.30 % (2290913)Instructions burned: 14 (million)
% 0.19/0.30 % (2290899)Success in time 0.054 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------