%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO358^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:47:31 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO358^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.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 16:50:29 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.27 % (2742816)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (2742824)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=3106013026: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)
% 0.22/0.27 % (2742824) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2742816-2742824"...
% 0.22/0.27 % (2742824)...printing done.
% 0.22/0.27 % (2742824)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% 0.22/0.27 thf(type_def_5, type, atype: $tType).
% 0.22/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.27 thf(func_def_0, type, a: $o).
% 0.22/0.27 thf(func_def_1, type, v: atype).
% 0.22/0.27 thf(func_def_2, type, b: $o).
% 0.22/0.27 thf(func_def_3, type, u: atype).
% 0.22/0.27 thf(func_def_7, type, sK0: (atype > $o)).
% 0.22/0.27 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.22/0.27 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.27 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.27 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.27 thf(f1,conjecture,(
% 0.22/0.27 ! [X0 : (atype > $o)] : ((X0 @ u) => (X0 @ v)) => ! [X1 : (atype > $o)] : (((~a | a) & (X1 @ u)) => ((b | ~b) & (X1 @ v)))),
% 0.22/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cE2LEIBEQ1_pme)).
% 0.22/0.27 thf(f2,negated_conjecture,(
% 0.22/0.27 ~(! [X0 : (atype > $o)] : ((X0 @ u) => (X0 @ v)) => ! [X1 : (atype > $o)] : (((~a | a) & (X1 @ u)) => ((b | ~b) & (X1 @ v))))),
% 0.22/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.27 thf(f3,plain,(
% 0.22/0.27 ~(! [X0 : (atype > $o)] : ((X0 @ u) => (X0 @ v)) => ! [X1 : (atype > $o)] : (((~a | a) & (X1 @ u)) => ((b | ~b) & (X1 @ v))))),
% 0.22/0.27 inference(rectify,[],[f2])).
% 0.22/0.27 thf(f4,plain,(
% 0.22/0.27 ~(! [X0 : (atype > $o)] : ((((X0 @ u)) = $true) => (((X0 @ v)) = $true)) => ! [X1 : (atype > $o)] : (((~ (a = $true) | (a = $true)) & (((X1 @ u)) = $true)) => (((b = $true) | ~ (b = $true)) & (((X1 @ v)) = $true))))),
% 0.22/0.27 inference(fool_elimination,[],[f3])).
% 0.22/0.27 thf(f5,plain,(
% 0.22/0.27 ~(! [X0 : (atype > $o)] : ((((X0 @ u)) = $true) => (((X0 @ v)) = $true)) => ! [X1 : (atype > $o)] : ((((a != $true) | (a = $true)) & (((X1 @ u)) = $true)) => (((b = $true) | (b != $true)) & (((X1 @ v)) = $true))))),
% 0.22/0.27 inference(flattening,[],[f4])).
% 0.22/0.27 thf(f6,plain,(
% 0.22/0.27 ? [X1 : (atype > $o)] : (((((X1 @ v)) != $true) | ((b != $true) & (b = $true))) & (((a != $true) | (a = $true)) & (((X1 @ u)) = $true))) & ! [X0 : (atype > $o)] : ((((X0 @ u)) != $true) | (((X0 @ v)) = $true))),
% 0.22/0.27 inference(ennf_transformation,[],[f5])).
% 0.22/0.27 thf(f7,plain,(
% 0.22/0.27 ! [X0 : (atype > $o)] : ((((X0 @ u)) != $true) | (((X0 @ v)) = $true)) & ? [X1 : (atype > $o)] : (((a != $true) | (a = $true)) & (((X1 @ u)) = $true) & ((((X1 @ v)) != $true) | ((b != $true) & (b = $true))))),
% 0.22/0.27 inference(flattening,[],[f6])).
% 0.22/0.27 thf(f8,plain,(
% 0.22/0.27 ! [X0 : (atype > $o)] : ((((X0 @ u)) != $true) | (((X0 @ v)) = $true)) & (((a != $true) | (a = $true)) & (((sK0 @ u)) = $true) & ((((sK0 @ v)) != $true) | ((b != $true) & (b = $true))))),
% 0.22/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0)],[f7])).
% 0.22/0.27 thf(f9,plain,(
% 0.22/0.27 (((sK0 @ v)) != $true) | (b = $true)),
% 0.22/0.27 inference(cnf_transformation,[],[f8])).
% 0.22/0.27 thf(f10,plain,(
% 0.22/0.27 (b != $true) | (((sK0 @ v)) != $true)),
% 0.22/0.27 inference(cnf_transformation,[],[f8])).
% 0.22/0.27 thf(f11,plain,(
% 0.22/0.27 (((sK0 @ u)) = $true)),
% 0.22/0.27 inference(cnf_transformation,[],[f8])).
% 0.22/0.27 thf(f13,plain,(
% 0.22/0.27 ( ! [X0 : (atype > $o)] : ((((X0 @ v)) = $true) | (((X0 @ u)) != $true)) )),
% 0.22/0.27 inference(cnf_transformation,[],[f8])).
% 0.22/0.27 thf(f16,definition,(
% 0.22/0.27 spl1_1 <=> (b = $true)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.22/0.27 thf(f20,definition,(
% 0.22/0.27 spl1_2 <=> (((sK0 @ v)) = $true)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.22/0.27 thf(f23,plain,(
% 0.22/0.27 spl1_1 | ~spl1_2),
% 0.22/0.27 inference(avatar_split_clause,[],[f9,f20,f16])).
% 0.22/0.27 thf(f25,definition,(
% 0.22/0.27 spl1_3 <=> (((sK0 @ u)) = $true)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.22/0.27 thf(f28,plain,(
% 0.22/0.27 spl1_3),
% 0.22/0.27 inference(avatar_split_clause,[],[f11,f25])).
% 0.22/0.27 thf(f29,plain,(
% 0.22/0.27 ~spl1_1 | ~spl1_2),
% 0.22/0.27 inference(avatar_split_clause,[],[f10,f20,f16])).
% 0.22/0.27 thf(f30,plain,(
% 0.22/0.27 (u = v)),
% 0.22/0.27 inference(leibniz_equality_elimination,[],[f13])).
% 0.22/0.27 thf(f41,definition,(
% 0.22/0.27 spl1_4 <=> (u = v)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 0.22/0.27 thf(f44,plain,(
% 0.22/0.27 spl1_4),
% 0.22/0.27 inference(avatar_split_clause,[],[f30,f41])).
% 0.22/0.27 thf(f45,definition,(
% 0.22/0.27 (u != v) | (((sK0 @ u)) != $true) | (((sK0 @ v)) = $true)),
% 0.22/0.27 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.27 cnf(s1, plain, spl1_1 | ~spl1_2, inference(sat_conversion,[],[f23])).
% 0.22/0.27 cnf(s2, plain, spl1_3, inference(sat_conversion,[],[f28])).
% 0.22/0.27 cnf(s3, plain, ~spl1_1 | ~spl1_2, inference(sat_conversion,[],[f29])).
% 0.22/0.27 cnf(s4, plain, spl1_4, inference(sat_conversion,[],[f44])).
% 0.22/0.27 cnf(s6, plain, spl1_2 | ~spl1_3 | ~spl1_4, inference(sat_conversion,[],[f45])).
% 0.22/0.27 cnf(s7, plain, spl1_2, inference(rat,[],[s6,s4,s2])).
% 0.22/0.27 cnf(s8, plain, ~spl1_1, inference(rat,[],[s3,s7])).
% 0.22/0.27 cnf(s9, plain, $false, inference(rat,[],[s1,s7,s8])).
% 0.22/0.27 thf(f46,plain,(
% 0.22/0.27 $false),
% 0.22/0.27 inference(avatar_sat_refutation,[],[s9])).
% 0.22/0.27 % SZS output end Proof for theBenchmark
% 0.22/0.27 % (2742824)------------------------------
% 0.22/0.27 % (2742824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (2742824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (2742824)CaDiCaL version: 2.1.3
% 0.22/0.27 % (2742824)Termination reason: Refutation
% 0.22/0.27 % (2742824)Time elapsed: 0.001 s
% 0.22/0.27 % (2742824)Peak memory usage: 13 MB
% 0.22/0.27 % (2742824)Instructions burned: 2 (million)
% 0.22/0.27 % (2742816)Success in time 0.016 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------