%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV434^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:38:38 AM UTC 2026
% Result : Theorem 0.25s 0.42s
% Output : Refutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV434^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n005.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 15:46:46 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.30 Running higher-order theorem proving
% 0.25/0.32 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
% 0.25/0.42 % (1831687)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.42 % (1831698)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.42 % (1831698)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
% 0.25/0.42 % (1831698)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=4252750688:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.42 % (1831695)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=159053910: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)
% 0.25/0.42 % (1831698) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1831687-1831698"...
% 0.25/0.42 % (1831698)...printing done.
% 0.25/0.42 % (1831698)Refutation found. Thanks to Tanya!
% 0.25/0.42 % SZS status Theorem for theBenchmark
% 0.25/0.42 % SZS output start Proof for theBenchmark
% 0.25/0.42 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.25/0.42 thf(func_def_0, type, f: ($o > $i)).
% 0.25/0.42 thf(func_def_2, type, sK0: ($i > $o)).
% 0.25/0.42 thf(f1,axiom,(
% 0.25/0.42 ! [X0 : $i] : ? [X1 : $o] : (((f @ X1)) = X0)),
% 0.25/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fsurj)).
% 0.25/0.42 thf(f2,conjecture,(
% 0.25/0.42 ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | (X1 = X2) | (X0 = X1))),
% 0.25/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',less3)).
% 0.25/0.42 thf(f3,negated_conjecture,(
% 0.25/0.42 ~ ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | (X1 = X2) | (X0 = X1))),
% 0.25/0.42 inference(negated_conjecture,[status(cth)],[f2])).
% 0.25/0.42 thf(f4,plain,(
% 0.25/0.42 ~ ! [X0 : $i,X1 : $i,X2 : $i] : ((X0 = X2) | (X1 = X2) | (X0 = X1))),
% 0.25/0.42 inference(rectify,[],[f3])).
% 0.25/0.42 thf(f5,plain,(
% 0.25/0.42 ? [X1 : $i,X0 : $i,X2 : $i] : ((X0 != X2) & (X0 != X1) & (X1 != X2))),
% 0.25/0.42 inference(ennf_transformation,[],[f4])).
% 0.25/0.42 thf(f6,plain,(
% 0.25/0.42 ! [X0 : $i] : (((f @ (sK0 @ X0))) = X0)),
% 0.25/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f1])).
% 0.25/0.42 thf(f7,plain,(
% 0.25/0.42 ? [X0 : $i,X1 : $i,X2 : $i] : ((X1 != X2) & (X0 != X1) & (X0 != X2))),
% 0.25/0.42 inference(rectify,[],[f5])).
% 0.25/0.42 thf(f8,plain,(
% 0.25/0.42 (sK3 != sK2) & (sK2 != sK1) & (sK3 != sK1)),
% 0.25/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f7])).
% 0.25/0.42 thf(f9,plain,(
% 0.25/0.42 ( ! [X0 : $i] : ((((f @ (sK0 @ X0))) = X0)) )),
% 0.25/0.42 inference(cnf_transformation,[],[f6])).
% 0.25/0.42 thf(f10,plain,(
% 0.25/0.42 (sK3 != sK1)),
% 0.25/0.42 inference(cnf_transformation,[],[f8])).
% 0.25/0.42 thf(f11,plain,(
% 0.25/0.42 (sK2 != sK1)),
% 0.25/0.42 inference(cnf_transformation,[],[f8])).
% 0.25/0.42 thf(f12,plain,(
% 0.25/0.42 (sK3 != sK2)),
% 0.25/0.42 inference(cnf_transformation,[],[f8])).
% 0.25/0.42 thf(f14,definition,(
% 0.25/0.42 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.25/0.42 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.25/0.42 thf(f22,plain,(
% 0.25/0.42 ( ! [X0 : $i] : (($false = ((sK0 @ X0))) | (((f @ $true)) = X0)) )),
% 0.25/0.42 inference(constrained_superposition,[],[f9,f14])).
% 0.25/0.42 thf(f24,plain,(
% 0.25/0.42 ( ! [X0 : $i] : ((((f @ $true)) = X0) | (((f @ $false)) = X0)) )),
% 0.25/0.42 inference(constrained_superposition,[],[f9,f22])).
% 0.25/0.42 thf(f27,plain,(
% 0.25/0.42 ( ! [X0 : $i,X1 : $i] : ((((f @ $false)) = X1) | (((f @ $false)) = X0) | (X0 = X1)) )),
% 0.25/0.42 inference(constrained_superposition,[],[f24,f24])).
% 0.25/0.42 thf(f32,definition,(
% 0.25/0.42 spl4_1 <=> ! [X0 : $i] : (((f @ $false)) = X0)),
% 0.25/0.42 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.25/0.42 thf(f33,plain,(
% 0.25/0.42 ( ! [X0 : $i] : ((((f @ $false)) = X0)) ) | ~spl4_1),
% 0.25/0.42 inference(avatar_component_clause,[],[f32])).
% 0.25/0.42 thf(f61,plain,(
% 0.25/0.42 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) ) | ~spl4_1),
% 0.25/0.42 inference(constrained_superposition,[],[f33,f33])).
% 0.25/0.42 thf(f76,plain,(
% 0.25/0.42 ( ! [X0 : $i] : ((sK2 != X0)) ) | ~spl4_1),
% 0.25/0.42 inference(constrained_superposition,[],[f11,f61])).
% 0.25/0.42 thf(f98,plain,(
% 0.25/0.42 $false | ~spl4_1),
% 0.25/0.42 inference(forward_subsumption_resolution,[],[f76,f61])).
% 0.25/0.42 thf(f99,plain,(
% 0.25/0.42 ~spl4_1),
% 0.25/0.42 inference(avatar_contradiction_clause,[],[f98])).
% 0.25/0.42 thf(f129,plain,(
% 0.25/0.42 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((f @ $false)) = X3) | (X0 = X2) | (X0 = X3) | (X0 = X1) | (X1 = X2)) )),
% 0.25/0.42 inference(constrained_superposition,[],[f27,f27])).
% 0.25/0.42 thf(f158,plain,(
% 0.25/0.42 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((f @ $false)) = X0) | (X1 = X2) | (((f @ $true)) = X1) | (X1 = X3) | (X2 = X3) | (((f @ $false)) = X0)) )),
% 0.25/0.42 inference(constrained_superposition,[],[f24,f129])).
% 0.25/0.42 thf(f175,plain,(
% 0.25/0.42 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X1 = X3) | (((f @ $false)) = X0) | (X2 = X3) | (((f @ $true)) = X1) | (X1 = X2)) )),
% 0.25/0.42 inference(duplicate_literal_removal,[],[f158])).
% 0.25/0.42 thf(f182,definition,(
% 0.25/0.42 spl4_4 <=> ! [X2 : $i,X1 : $i,X3 : $i] : ((X1 = X3) | (X1 = X2) | (((f @ $true)) = X1) | (X2 = X3))),
% 0.25/0.42 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.25/0.42 thf(f183,plain,(
% 0.25/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((f @ $true)) = X1) | (X1 = X2) | (X2 = X3) | (X1 = X3)) ) | ~spl4_4),
% 0.25/0.42 inference(avatar_component_clause,[],[f182])).
% 0.25/0.42 thf(f184,plain,(
% 0.25/0.42 spl4_1 | spl4_4),
% 0.25/0.42 inference(avatar_split_clause,[],[f175,f182,f32])).
% 0.25/0.42 thf(f216,plain,(
% 0.25/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X1 = X2) | (X0 = X1) | (((f @ $true)) != X1) | (X0 = X2)) ) | ~spl4_4),
% 0.25/0.42 inference(equality_factoring,[],[f183])).
% 0.25/0.42 thf(f225,plain,(
% 0.25/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X1 = X2) | (X0 = X1) | (X0 = X2)) ) | ~spl4_4),
% 0.25/0.42 inference(forward_subsumption_resolution,[],[f216,f183])).
% 0.25/0.42 thf(f231,plain,(
% 0.25/0.42 ( ! [X0 : $i,X1 : $i] : ((sK1 = X1) | (X0 = X1) | (sK2 != X0)) ) | ~spl4_4),
% 0.25/0.42 inference(constrained_superposition,[],[f11,f225])).
% 0.25/0.42 thf(f439,plain,(
% 0.25/0.42 ( ! [X0 : $i] : ((sK1 != sK1) | (sK2 != X0) | (sK3 = X0)) ) | ~spl4_4),
% 0.25/0.42 inference(constrained_superposition,[],[f10,f231])).
% 0.25/0.42 thf(f456,plain,(
% 0.25/0.42 ( ! [X0 : $i] : ((sK2 != X0) | (sK3 = X0)) ) | ~spl4_4),
% 0.25/0.42 inference(trivial_inequality_removal,[],[f439])).
% 0.25/0.42 thf(f480,definition,(
% 0.25/0.42 spl4_21 <=> ! [X2 : $i] : ((sK2 != X2) | (sK3 = X2))),
% 0.25/0.42 introduced(definition,[new_symbols(definition,[spl4_21])],[avatar_definition])).
% 0.25/0.42 thf(f481,plain,(
% 0.25/0.42 ( ! [X2 : $i] : ((sK3 = X2) | (sK2 != X2)) ) | ~spl4_21),
% 0.25/0.42 inference(avatar_component_clause,[],[f480])).
% 0.25/0.42 thf(f496,plain,(
% 0.25/0.42 spl4_21 | ~spl4_4),
% 0.25/0.42 inference(avatar_split_clause,[],[f456,f182,f480])).
% 0.25/0.42 thf(f505,plain,(
% 0.25/0.42 ( ! [X0 : $i] : ((sK2 != X0) | (sK2 != X0)) ) | ~spl4_21),
% 0.25/0.42 inference(constrained_superposition,[],[f12,f481])).
% 0.25/0.42 thf(f520,plain,(
% 0.25/0.42 ( ! [X0 : $i] : ((sK2 != X0)) ) | ~spl4_21),
% 0.25/0.42 inference(duplicate_literal_removal,[],[f505])).
% 0.25/0.42 thf(f544,plain,(
% 0.25/0.42 $false | ~spl4_21),
% 0.25/0.42 inference(equality_resolution,[],[f520])).
% 0.25/0.42 thf(f547,plain,(
% 0.25/0.42 ~spl4_21),
% 0.25/0.42 inference(avatar_contradiction_clause,[],[f544])).
% 0.25/0.42 cnf(s9, plain, ~spl4_1, inference(sat_conversion,[],[f99])).
% 0.25/0.42 cnf(s11, plain, spl4_1 | spl4_4, inference(sat_conversion,[],[f184])).
% 0.25/0.42 cnf(s49, plain, ~spl4_4 | spl4_21, inference(sat_conversion,[],[f496])).
% 0.25/0.42 cnf(s55, plain, ~spl4_21, inference(sat_conversion,[],[f547])).
% 0.25/0.42 cnf(s56, plain, ~spl4_4, inference(rat,[],[s49,s55])).
% 0.25/0.42 cnf(s58, plain, spl4_1, inference(rat,[],[s11,s56])).
% 0.25/0.42 cnf(s59, plain, $false, inference(rat,[],[s9,s58])).
% 0.25/0.42 thf(f550,plain,(
% 0.25/0.42 $false),
% 0.25/0.42 inference(avatar_sat_refutation,[],[s59])).
% 0.25/0.42 % SZS output end Proof for theBenchmark
% 0.25/0.42 % (1831698)------------------------------
% 0.25/0.42 % (1831698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.42 % (1831698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.42 % (1831698)CaDiCaL version: 2.1.3
% 0.25/0.42 % (1831698)Termination reason: Refutation
% 0.25/0.42 % (1831698)Time elapsed: 0.029 s
% 0.25/0.42 % (1831698)Peak memory usage: 13 MB
% 0.25/0.42 % (1831698)Instructions burned: 29 (million)
% 0.25/0.42 % (1831687)Success in time 0.085 s
% 0.25/0.42 % Vampire exiting
%------------------------------------------------------------------------------