%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO526^1 : 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 : n008.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 08:48:11 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 : SYO526^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n008.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 17:13:24 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.21/0.28 % (3451077)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (3451085)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=2718383249: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 % (3451085) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3451077-3451085"...
% 0.21/0.28 % (3451085)...printing done.
% 0.21/0.28 % (3451085)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, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, a: $o).
% 0.21/0.28 thf(func_def_1, type, b: $o).
% 0.21/0.28 thf(func_def_2, type, f: ($i > $o)).
% 0.21/0.28 thf(func_def_3, type, g: ($i > $o)).
% 0.21/0.28 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.28 thf(f1,axiom,(
% 0.21/0.28 a <=> b),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab)).
% 0.21/0.28 thf(f2,axiom,(
% 0.21/0.28 (f = g)),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fg)).
% 0.21/0.28 thf(f3,axiom,(
% 0.21/0.28 (f = (^[X0 : $i] : (a)))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fa)).
% 0.21/0.28 thf(f4,conjecture,(
% 0.21/0.28 (g = (^[X0 : $i] : (b)))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',gb)).
% 0.21/0.28 thf(f5,negated_conjecture,(
% 0.21/0.28 ~ (g = (^[X0 : $i] : (b)))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 (f = (^[Y0 : $i]: (a)))),
% 0.21/0.28 inference(fool_elimination,[],[f3])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ~ (g = (^[Y0 : $i]: (b)))),
% 0.21/0.28 inference(fool_elimination,[],[f5])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 a <=> b),
% 0.21/0.28 inference(rectify,[],[f1])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 (a = b)),
% 0.21/0.28 inference(fool_elimination,[],[f8])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 (g != (^[Y0 : $i]: (b)))),
% 0.21/0.28 inference(flattening,[],[f7])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 (f = (^[Y0 : $i]: (a)))),
% 0.21/0.28 inference(cnf_transformation,[],[f6])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 (f = g)),
% 0.21/0.28 inference(cnf_transformation,[],[f2])).
% 0.21/0.28 thf(f13,plain,(
% 0.21/0.28 (g != (^[Y0 : $i]: (b)))),
% 0.21/0.28 inference(cnf_transformation,[],[f10])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 (a = b)),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 (b = $false) | (a = $true)),
% 0.21/0.28 inference(iff_proxy_clausification,[],[f14])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 (a = $false) | (b = $true)),
% 0.21/0.28 inference(iff_proxy_clausification,[],[f14])).
% 0.21/0.28 thf(f19,definition,(
% 0.21/0.28 spl0_1 <=> (b = $true)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 (b = $true) | ~spl0_1),
% 0.21/0.28 inference(avatar_component_clause,[],[f19])).
% 0.21/0.28 thf(f23,definition,(
% 0.21/0.28 spl0_2 <=> (a = $false)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.21/0.28 thf(f25,plain,(
% 0.21/0.28 (a = $false) | ~spl0_2),
% 0.21/0.28 inference(avatar_component_clause,[],[f23])).
% 0.21/0.28 thf(f26,plain,(
% 0.21/0.28 spl0_1 | spl0_2),
% 0.21/0.28 inference(avatar_split_clause,[],[f17,f23,f19])).
% 0.21/0.28 thf(f28,definition,(
% 0.21/0.28 spl0_3 <=> (b = $false)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.21/0.28 thf(f30,plain,(
% 0.21/0.28 (b = $false) | ~spl0_3),
% 0.21/0.28 inference(avatar_component_clause,[],[f28])).
% 0.21/0.28 thf(f32,definition,(
% 0.21/0.28 spl0_4 <=> (a = $true)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.21/0.28 thf(f34,plain,(
% 0.21/0.28 (a = $true) | ~spl0_4),
% 0.21/0.28 inference(avatar_component_clause,[],[f32])).
% 0.21/0.28 thf(f35,plain,(
% 0.21/0.28 spl0_3 | spl0_4),
% 0.21/0.28 inference(avatar_split_clause,[],[f16,f32,f28])).
% 0.21/0.28 thf(f37,definition,(
% 0.21/0.28 spl0_5 <=> (f = g)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 0.21/0.28 thf(f40,plain,(
% 0.21/0.28 spl0_5),
% 0.21/0.28 inference(avatar_split_clause,[],[f12,f37])).
% 0.21/0.28 thf(f42,definition,(
% 0.21/0.28 spl0_6 <=> (f = (^[Y0 : $i]: (a)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition])).
% 0.21/0.28 thf(f45,plain,(
% 0.21/0.28 spl0_6),
% 0.21/0.28 inference(avatar_split_clause,[],[f11,f42])).
% 0.21/0.28 thf(f47,definition,(
% 0.21/0.28 spl0_7 <=> (g = (^[Y0 : $i]: (b)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition])).
% 0.21/0.28 thf(f50,plain,(
% 0.21/0.28 ~spl0_7),
% 0.21/0.28 inference(avatar_split_clause,[],[f13,f47])).
% 0.21/0.28 thf(f51,definition,(
% 0.21/0.28 (a != $false) | (b != $false) | (f != g) | (f != (^[Y0 : $i]: (a))) | (g = (^[Y0 : $i]: (b)))),
% 0.21/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.21/0.28 thf(f57,plain,(
% 0.21/0.28 ($false = $true) | (~spl0_1 | ~spl0_3)),
% 0.21/0.28 inference(superposition,[],[f21,f30])).
% 0.21/0.28 thf(f60,plain,(
% 0.21/0.28 $false | (~spl0_1 | ~spl0_3)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f57])).
% 0.21/0.28 thf(f61,plain,(
% 0.21/0.28 ~spl0_1 | ~spl0_3),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f60])).
% 0.21/0.28 thf(f62,plain,(
% 0.21/0.28 ($false = $true) | (~spl0_2 | ~spl0_4)),
% 0.21/0.28 inference(forward_demodulation,[],[f34,f25])).
% 0.21/0.28 thf(f63,plain,(
% 0.21/0.28 $false | (~spl0_2 | ~spl0_4)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f62])).
% 0.21/0.28 thf(f64,plain,(
% 0.21/0.28 ~spl0_2 | ~spl0_4),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f63])).
% 0.21/0.28 thf(f65,definition,(
% 0.21/0.28 (b != $true) | (a != $true) | (f != g) | (f != (^[Y0 : $i]: (a))) | (g = (^[Y0 : $i]: (b)))),
% 0.21/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.21/0.28 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f26])).
% 0.21/0.28 cnf(s2, plain, spl0_3 | spl0_4, inference(sat_conversion,[],[f35])).
% 0.21/0.28 cnf(s3, plain, spl0_5, inference(sat_conversion,[],[f40])).
% 0.21/0.28 cnf(s4, plain, spl0_6, inference(sat_conversion,[],[f45])).
% 0.21/0.28 cnf(s5, plain, ~spl0_7, inference(sat_conversion,[],[f50])).
% 0.21/0.28 cnf(s6, plain, ~spl0_2 | ~spl0_3 | ~spl0_5 | ~spl0_6 | spl0_7, inference(sat_conversion,[],[f51])).
% 0.21/0.28 cnf(s8, plain, ~spl0_1 | ~spl0_3, inference(sat_conversion,[],[f61])).
% 0.21/0.28 cnf(s9, plain, ~spl0_2 | ~spl0_4, inference(sat_conversion,[],[f64])).
% 0.21/0.28 cnf(s10, plain, ~spl0_1 | ~spl0_4 | ~spl0_5 | ~spl0_6 | spl0_7, inference(sat_conversion,[],[f65])).
% 0.21/0.28 cnf(s11, plain, ~spl0_2, inference(rat,[],[s2,s6,s9,s3,s4,s5])).
% 0.21/0.28 cnf(s12, plain, spl0_1, inference(rat,[],[s1,s11])).
% 0.21/0.28 cnf(s13, plain, ~spl0_4, inference(rat,[],[s10,s5,s4,s3,s12])).
% 0.21/0.28 cnf(s14, plain, ~spl0_3, inference(rat,[],[s8,s12])).
% 0.21/0.28 cnf(s15, plain, $false, inference(rat,[],[s2,s13,s14])).
% 0.21/0.28 thf(f66,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(avatar_sat_refutation,[],[s15])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (3451085)------------------------------
% 0.21/0.28 % (3451085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3451085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3451085)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3451085)Termination reason: Refutation
% 0.21/0.28 % (3451085)Time elapsed: 0.002 s
% 0.21/0.28 % (3451085)Peak memory usage: 13 MB
% 0.21/0.28 % (3451085)Instructions burned: 2 (million)
% 0.21/0.28 % (3451077)Success in time 0.027 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------