%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET610^5 : 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 : n018.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 08:23:21 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET610^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:41:11 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.29 % (79295)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (79304)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=673943931: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)
% 0.22/0.29 % (79304) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-79295-79304"...
% 0.22/0.29 % (79304)...printing done.
% 0.22/0.29 % (79303)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1331078364:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (79301)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4165287660:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (79304)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% 0.22/0.29 thf(type_def_5, type, a: $tType).
% 0.22/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.29 thf(func_def_1, type, vAND: ($o > $o > $o)).
% 0.22/0.29 thf(func_def_2, type, vNOT: ($o > $o)).
% 0.22/0.29 thf(func_def_3, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.29 thf(func_def_4, type, vOR: ($o > $o > $o)).
% 0.22/0.29 thf(func_def_5, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.29 thf(func_def_6, type, sK0: (a > $o)).
% 0.22/0.29 thf(func_def_7, type, sK1: (a > $o)).
% 0.22/0.29 thf(func_def_11, type, sK3: a).
% 0.22/0.29 thf(f1,conjecture,(
% 0.22/0.29 ! [X1 : (a > $o),X0 : (a > $o)] : ((^[X2 : a] : (((X0 @ X2) | (X1 @ X2)) & ~(X1 @ X2))) = (^[X2 : a] : ((X0 @ X2) & ~(X1 @ X2))))),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_83_pme)).
% 0.22/0.29 thf(f2,negated_conjecture,(
% 0.22/0.29 ~ ! [X1 : (a > $o),X0 : (a > $o)] : ((^[X2 : a] : (((X0 @ X2) | (X1 @ X2)) & ~(X1 @ X2))) = (^[X2 : a] : ((X0 @ X2) & ~(X1 @ X2))))),
% 0.22/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.29 thf(f3,plain,(
% 0.22/0.29 ~ ! [X0 : (a > $o),X1 : (a > $o)] : ((^[X2 : a] : (((X1 @ X2) | (X0 @ X2)) & ~(X0 @ X2))) = (^[X3 : a] : ((X1 @ X3) & ~(X0 @ X3))))),
% 0.22/0.29 inference(rectify,[],[f2])).
% 0.22/0.29 thf(f4,plain,(
% 0.22/0.29 ~ ! [X0 : (a > $o),X1 : (a > $o)] : ((^[Y0 : a]: ((~ (X0 @ Y0)) & ((X0 @ Y0) | (X1 @ Y0)))) = (^[Y0 : a]: ((~ (X0 @ Y0)) & (X1 @ Y0))))),
% 0.22/0.29 inference(fool_elimination,[],[f3])).
% 0.22/0.29 thf(f5,plain,(
% 0.22/0.29 ? [X1 : (a > $o),X0 : (a > $o)] : ((^[Y0 : a]: ((~ (X0 @ Y0)) & ((X0 @ Y0) | (X1 @ Y0)))) != (^[Y0 : a]: ((~ (X0 @ Y0)) & (X1 @ Y0))))),
% 0.22/0.29 inference(ennf_transformation,[],[f4])).
% 0.22/0.29 thf(f6,plain,(
% 0.22/0.29 ? [X0 : (a > $o),X1 : (a > $o)] : ((^[Y0 : a]: ((~ (X1 @ Y0)) & (X0 @ Y0))) != (^[Y0 : a]: ((~ (X1 @ Y0)) & ((X1 @ Y0) | (X0 @ Y0)))))),
% 0.22/0.29 inference(rectify,[],[f5])).
% 0.22/0.29 thf(f7,plain,(
% 0.22/0.29 ((^[Y0 : a]: ((~ (sK1 @ Y0)) & ((sK1 @ Y0) | (sK0 @ Y0)))) != (^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))))),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6])).
% 0.22/0.29 thf(f8,plain,(
% 0.22/0.29 ((^[Y0 : a]: ((~ (sK1 @ Y0)) & ((sK1 @ Y0) | (sK0 @ Y0)))) != (^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))))),
% 0.22/0.29 inference(cnf_transformation,[],[f7])).
% 0.22/0.29 thf(f11,definition,(
% 0.22/0.29 spl2_1 <=> ((^[Y0 : a]: ((~ (sK1 @ Y0)) & ((sK1 @ Y0) | (sK0 @ Y0)))) = (^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.22/0.29 thf(f13,plain,(
% 0.22/0.29 ((^[Y0 : a]: ((~ (sK1 @ Y0)) & ((sK1 @ Y0) | (sK0 @ Y0)))) != (^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0)))) | spl2_1),
% 0.22/0.29 inference(avatar_component_clause,[],[f11])).
% 0.22/0.29 thf(f14,plain,(
% 0.22/0.29 ~spl2_1),
% 0.22/0.29 inference(avatar_split_clause,[],[f8,f11])).
% 0.22/0.29 thf(f15,plain,(
% 0.22/0.29 ((((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) @ sK3)) != (((^[Y0 : a]: ((~ (sK1 @ Y0)) & ((sK1 @ Y0) | (sK0 @ Y0)))) @ sK3))) | spl2_1),
% 0.22/0.29 inference(negative_extensionality,[],[f13])).
% 0.22/0.29 thf(f16,plain,(
% 0.22/0.29 ($true = (((^[Y0 : a]: ((~ (sK1 @ Y0)) & ((sK1 @ Y0) | (sK0 @ Y0)))) @ sK3))) | ((((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) @ sK3)) = $true) | spl2_1),
% 0.22/0.29 inference(xor_proxy_clausification,[],[f15])).
% 0.22/0.29 thf(f17,plain,(
% 0.22/0.29 ((((^[Y0 : a]: ((~ (sK1 @ Y0)) & (sK0 @ Y0))) @ sK3)) = $false) | ($false = (((^[Y0 : a]: ((~ (sK1 @ Y0)) & ((sK1 @ Y0) | (sK0 @ Y0)))) @ sK3))) | spl2_1),
% 0.22/0.29 inference(xor_proxy_clausification,[],[f15])).
% 0.22/0.29 thf(f18,plain,(
% 0.22/0.29 ($false = (((~ (sK1 @ sK3)) & (sK0 @ sK3)))) | ($false = (((~ (sK1 @ sK3)) & ((sK1 @ sK3) | (sK0 @ sK3))))) | spl2_1),
% 0.22/0.29 inference(beta-eta_normalization,[],[f17])).
% 0.22/0.29 thf(f19,plain,(
% 0.22/0.29 ($false = ((~ (sK1 @ sK3)))) | ($false = ((sK0 @ sK3))) | ($false = (((~ (sK1 @ sK3)) & ((sK1 @ sK3) | (sK0 @ sK3))))) | spl2_1),
% 0.22/0.29 inference(and_proxy_clausification,[],[f18])).
% 0.22/0.29 thf(f20,plain,(
% 0.22/0.29 ($true = ((sK1 @ sK3))) | ($false = ((sK0 @ sK3))) | ($false = (((~ (sK1 @ sK3)) & ((sK1 @ sK3) | (sK0 @ sK3))))) | spl2_1),
% 0.22/0.29 inference(not_proxy_clausification,[],[f19])).
% 0.22/0.29 thf(f21,plain,(
% 0.22/0.29 ($false = ((sK0 @ sK3))) | ($false = (((sK1 @ sK3) | (sK0 @ sK3)))) | ($false = ((~ (sK1 @ sK3)))) | ($true = ((sK1 @ sK3))) | spl2_1),
% 0.22/0.29 inference(and_proxy_clausification,[],[f20])).
% 0.22/0.29 thf(f22,plain,(
% 0.22/0.29 ($false = ((~ (sK1 @ sK3)))) | ($false = ((sK0 @ sK3))) | ($true = ((sK1 @ sK3))) | ($false = ((sK0 @ sK3))) | spl2_1),
% 0.22/0.29 inference(or_proxy_clausification,[],[f21])).
% 0.22/0.29 thf(f26,plain,(
% 0.22/0.29 ($false = ((sK0 @ sK3))) | ($true = ((sK1 @ sK3))) | ($true = ((sK1 @ sK3))) | ($false = ((sK0 @ sK3))) | spl2_1),
% 0.22/0.29 inference(not_proxy_clausification,[],[f22])).
% 0.22/0.29 thf(f27,plain,(
% 0.22/0.29 ($true = ((sK1 @ sK3))) | ($false = ((sK0 @ sK3))) | spl2_1),
% 0.22/0.29 inference(duplicate_literal_removal,[],[f26])).
% 0.22/0.29 thf(f28,plain,(
% 0.22/0.29 ($true = (((~ (sK1 @ sK3)) & ((sK1 @ sK3) | (sK0 @ sK3))))) | ($true = (((~ (sK1 @ sK3)) & (sK0 @ sK3)))) | spl2_1),
% 0.22/0.29 inference(beta-eta_normalization,[],[f16])).
% 0.22/0.29 thf(f29,plain,(
% 0.22/0.29 ($true = (((~ (sK1 @ sK3)) & (sK0 @ sK3)))) | ($true = (((sK1 @ sK3) | (sK0 @ sK3)))) | spl2_1),
% 0.22/0.29 inference(and_proxy_clausification,[],[f28])).
% 0.22/0.29 thf(f30,plain,(
% 0.22/0.29 ($true = (((~ (sK1 @ sK3)) & (sK0 @ sK3)))) | (((~ (sK1 @ sK3))) = $true) | spl2_1),
% 0.22/0.29 inference(and_proxy_clausification,[],[f28])).
% 0.22/0.29 thf(f32,plain,(
% 0.22/0.29 (((~ (sK1 @ sK3))) = $true) | (((~ (sK1 @ sK3))) = $true) | spl2_1),
% 0.22/0.29 inference(and_proxy_clausification,[],[f30])).
% 0.22/0.29 thf(f33,plain,(
% 0.22/0.29 ($false = ((sK1 @ sK3))) | ($false = ((sK1 @ sK3))) | spl2_1),
% 0.22/0.29 inference(not_proxy_clausification,[],[f32])).
% 0.22/0.29 thf(f34,plain,(
% 0.22/0.29 ($false = ((sK1 @ sK3))) | spl2_1),
% 0.22/0.29 inference(duplicate_literal_removal,[],[f33])).
% 0.22/0.29 thf(f36,plain,(
% 0.22/0.29 ($true = (((sK1 @ sK3) | (sK0 @ sK3)))) | ($true = ((sK0 @ sK3))) | spl2_1),
% 0.22/0.29 inference(and_proxy_clausification,[],[f29])).
% 0.22/0.29 thf(f40,plain,(
% 0.22/0.29 ($true = ((sK0 @ sK3))) | ($true = ((sK1 @ sK3))) | ($true = ((sK0 @ sK3))) | spl2_1),
% 0.22/0.29 inference(or_proxy_clausification,[],[f36])).
% 0.22/0.29 thf(f41,plain,(
% 0.22/0.29 ($true = ((sK0 @ sK3))) | ($true = ((sK1 @ sK3))) | spl2_1),
% 0.22/0.29 inference(duplicate_literal_removal,[],[f40])).
% 0.22/0.29 thf(f43,definition,(
% 0.22/0.29 spl2_2 <=> ($false = ((sK0 @ sK3)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.22/0.29 thf(f47,definition,(
% 0.22/0.29 spl2_3 <=> ($true = ((sK1 @ sK3)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.22/0.29 thf(f49,plain,(
% 0.22/0.29 ($true = ((sK1 @ sK3))) | ~spl2_3),
% 0.22/0.29 inference(avatar_component_clause,[],[f47])).
% 0.22/0.29 thf(f50,plain,(
% 0.22/0.29 spl2_2 | spl2_3 | spl2_1),
% 0.22/0.29 inference(avatar_split_clause,[],[f27,f11,f47,f43])).
% 0.22/0.29 thf(f52,definition,(
% 0.22/0.29 spl2_4 <=> ($false = ((sK1 @ sK3)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.22/0.29 thf(f54,plain,(
% 0.22/0.29 ($false = ((sK1 @ sK3))) | ~spl2_4),
% 0.22/0.29 inference(avatar_component_clause,[],[f52])).
% 0.22/0.29 thf(f55,plain,(
% 0.22/0.29 spl2_4 | spl2_1),
% 0.22/0.29 inference(avatar_split_clause,[],[f34,f11,f52])).
% 0.22/0.29 thf(f57,definition,(
% 0.22/0.29 spl2_5 <=> ($true = ((sK0 @ sK3)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition])).
% 0.22/0.29 thf(f61,plain,(
% 0.22/0.29 spl2_3 | spl2_5 | spl2_1),
% 0.22/0.29 inference(avatar_split_clause,[],[f41,f11,f57,f47])).
% 0.22/0.29 thf(f63,plain,(
% 0.22/0.29 ($false = $true) | (~spl2_3 | ~spl2_4)),
% 0.22/0.29 inference(superposition,[],[f49,f54])).
% 0.22/0.29 thf(f66,plain,(
% 0.22/0.29 $false | (~spl2_3 | ~spl2_4)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f63])).
% 0.22/0.29 thf(f67,plain,(
% 0.22/0.29 ~spl2_3 | ~spl2_4),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f66])).
% 0.22/0.29 thf(f68,definition,(
% 0.22/0.29 ($false != ((sK1 @ sK3))) | ($false != ((sK0 @ sK3))) | ($true != ((sK0 @ sK3))) | ($true = ((sK1 @ sK3)))),
% 0.22/0.29 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.29 cnf(s1, plain, ~spl2_1, inference(sat_conversion,[],[f14])).
% 0.22/0.29 cnf(s2, plain, spl2_1 | spl2_2 | spl2_3, inference(sat_conversion,[],[f50])).
% 0.22/0.29 cnf(s3, plain, spl2_1 | spl2_4, inference(sat_conversion,[],[f55])).
% 0.22/0.29 cnf(s5, plain, spl2_1 | spl2_3 | spl2_5, inference(sat_conversion,[],[f61])).
% 0.22/0.29 cnf(s7, plain, ~spl2_3 | ~spl2_4, inference(sat_conversion,[],[f67])).
% 0.22/0.29 cnf(s8, plain, ~spl2_2 | spl2_3 | ~spl2_4 | ~spl2_5, inference(sat_conversion,[],[f68])).
% 0.22/0.29 cnf(s9, plain, spl2_4, inference(rat,[],[s3,s1])).
% 0.22/0.29 cnf(s10, plain, ~spl2_3, inference(rat,[],[s7,s9])).
% 0.22/0.29 cnf(s11, plain, spl2_5, inference(rat,[],[s5,s1,s10])).
% 0.22/0.29 cnf(s12, plain, spl2_2, inference(rat,[],[s2,s1,s10])).
% 0.22/0.29 cnf(s13, plain, $false, inference(rat,[],[s8,s10,s9,s11,s12])).
% 0.22/0.29 thf(f69,plain,(
% 0.22/0.29 $false),
% 0.22/0.29 inference(avatar_sat_refutation,[],[s13])).
% 0.22/0.29 % SZS output end Proof for theBenchmark
% 0.22/0.29 % (79304)------------------------------
% 0.22/0.29 % (79304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (79304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (79304)CaDiCaL version: 2.1.3
% 0.22/0.29 % (79304)Termination reason: Refutation
% 0.22/0.29 % (79304)Time elapsed: 0.002 s
% 0.22/0.29 % (79304)Peak memory usage: 13 MB
% 0.22/0.29 % (79304)Instructions burned: 3 (million)
% 0.22/0.29 % (79295)Success in time 0.038 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------