%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO107^5 : 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 : n019.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 08:46:37 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO107^5 : 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 : n019.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 16:34:08 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.19/0.27 % (1011115)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (1011121)lrs+10_16_si=on:nwc=1.5:random_seed=867591266:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.27 % (1011121) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1011115-1011121"...
% 0.19/0.27 % (1011121)...printing done.
% 0.19/0.27 % (1011121)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.27 thf(func_def_0, type, cP: ($i > $o)).
% 0.19/0.27 thf(func_def_5, type, sK1: ($i > $i)).
% 0.19/0.27 thf(f1,conjecture,(
% 0.19/0.27 ? [X0 : $i] : ((cP @ X0) => ! [X1 : $i] : (cP @ X1)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cP @ X0) => (cP @ X1))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM66)).
% 0.19/0.27 thf(f2,negated_conjecture,(
% 0.19/0.27 ~(? [X0 : $i] : ((cP @ X0) => ! [X1 : $i] : (cP @ X1)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cP @ X0) => (cP @ X1)))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.27 thf(f3,plain,(
% 0.19/0.27 ~(? [X0 : $i] : ((cP @ X0) => ! [X1 : $i] : (cP @ X1)) <=> ? [X2 : $i] : ! [X3 : $i] : ((cP @ X2) => (cP @ X3)))),
% 0.19/0.27 inference(rectify,[],[f2])).
% 0.19/0.27 thf(f4,plain,(
% 0.19/0.27 ~(? [X2 : $i] : ! [X3 : $i] : ((((cP @ X2)) = $true) => ($true = ((cP @ X3)))) <=> ? [X0 : $i] : ((((cP @ X0)) = $true) => ! [X1 : $i] : (((cP @ X1)) = $true)))),
% 0.19/0.27 inference(fool_elimination,[],[f3])).
% 0.19/0.27 thf(f5,plain,(
% 0.19/0.27 ? [X2 : $i] : ! [X3 : $i] : (($true = ((cP @ X3))) | (((cP @ X2)) != $true)) <~> ? [X0 : $i] : ((((cP @ X0)) != $true) | ! [X1 : $i] : (((cP @ X1)) = $true))),
% 0.19/0.27 inference(ennf_transformation,[],[f4])).
% 0.19/0.27 thf(f6,plain,(
% 0.19/0.27 (! [X0 : $i] : ((((cP @ X0)) = $true) & ? [X1 : $i] : (((cP @ X1)) != $true)) | ! [X2 : $i] : ? [X3 : $i] : (($true != ((cP @ X3))) & (((cP @ X2)) = $true))) & (? [X0 : $i] : ((((cP @ X0)) != $true) | ! [X1 : $i] : (((cP @ X1)) = $true)) | ? [X2 : $i] : ! [X3 : $i] : (($true = ((cP @ X3))) | (((cP @ X2)) != $true)))),
% 0.19/0.27 inference(nnf_transformation,[],[f5])).
% 0.19/0.27 thf(f7,plain,(
% 0.19/0.27 (! [X0 : $i] : ((((cP @ X0)) = $true) & ? [X1 : $i] : (((cP @ X1)) != $true)) | ! [X2 : $i] : ? [X3 : $i] : (($true != ((cP @ X3))) & (((cP @ X2)) = $true))) & (? [X4 : $i] : (($true != ((cP @ X4))) | ! [X5 : $i] : (((cP @ X5)) = $true)) | ? [X6 : $i] : ! [X7 : $i] : (($true = ((cP @ X7))) | ($true != ((cP @ X6)))))),
% 0.19/0.27 inference(rectify,[],[f6])).
% 0.19/0.27 thf(f8,plain,(
% 0.19/0.27 (! [X0 : $i] : ((((cP @ X0)) = $true) & ($true != ((cP @ sK0)))) | ! [X2 : $i] : (($true != ((cP @ (sK1 @ X2)))) & (((cP @ X2)) = $true))) & (((((cP @ sK2)) != $true) | ! [X5 : $i] : (((cP @ X5)) = $true)) | ! [X7 : $i] : (($true = ((cP @ X7))) | ($true != ((cP @ sK3)))))),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,sK2,sK3]),skolemize(X1,sK0),skolemize(X3,sK1 @ X2),skolemize(X4,sK2),skolemize(X6,sK3)],[f7])).
% 0.19/0.27 thf(f11,plain,(
% 0.19/0.27 ( ! [X2 : $i] : (($true != ((cP @ (sK1 @ X2)))) | ($true != ((cP @ sK0)))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f8])).
% 0.19/0.27 thf(f12,plain,(
% 0.19/0.27 ( ! [X2 : $i,X0 : $i] : ((((cP @ X0)) = $true) | (((cP @ X2)) = $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f8])).
% 0.19/0.27 thf(f21,definition,(
% 0.19/0.27 spl4_2 <=> ! [X7 : $i] : ($true = ((cP @ X7)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.19/0.27 thf(f22,plain,(
% 0.19/0.27 ( ! [X7 : $i] : (($true = ((cP @ X7)))) ) | ~spl4_2),
% 0.19/0.27 inference(avatar_component_clause,[],[f21])).
% 0.19/0.27 thf(f29,definition,(
% 0.19/0.27 spl4_4 <=> ($true = ((cP @ sK0)))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.19/0.27 thf(f31,plain,(
% 0.19/0.27 ($true != ((cP @ sK0))) | spl4_4),
% 0.19/0.27 inference(avatar_component_clause,[],[f29])).
% 0.19/0.27 thf(f34,definition,(
% 0.19/0.27 spl4_5 <=> ! [X2 : $i] : ($true != ((cP @ (sK1 @ X2))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.19/0.27 thf(f35,plain,(
% 0.19/0.27 ( ! [X2 : $i] : (($true != ((cP @ (sK1 @ X2))))) ) | ~spl4_5),
% 0.19/0.27 inference(avatar_component_clause,[],[f34])).
% 0.19/0.27 thf(f37,plain,(
% 0.19/0.27 spl4_2 | spl4_2),
% 0.19/0.27 inference(avatar_split_clause,[],[f12,f21,f21])).
% 0.19/0.27 thf(f38,plain,(
% 0.19/0.27 spl4_5 | ~spl4_4),
% 0.19/0.27 inference(avatar_split_clause,[],[f11,f29,f34])).
% 0.19/0.27 thf(f39,plain,(
% 0.19/0.27 ($true != $true) | (~spl4_2 | spl4_4)),
% 0.19/0.27 inference(constrained_superposition,[],[f31,f22])).
% 0.19/0.27 thf(f40,plain,(
% 0.19/0.27 $false | (~spl4_2 | spl4_4)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f39])).
% 0.19/0.27 thf(f41,plain,(
% 0.19/0.27 ~spl4_2 | spl4_4),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f40])).
% 0.19/0.27 thf(f42,plain,(
% 0.19/0.27 $false | (~spl4_2 | ~spl4_5)),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f35,f22])).
% 0.19/0.27 thf(f43,plain,(
% 0.19/0.27 ~spl4_2 | ~spl4_5),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f42])).
% 0.19/0.27 cnf(s5, plain, spl4_2 | spl4_2, inference(sat_conversion,[],[f37])).
% 0.19/0.27 cnf(s6, plain, spl4_2, inference(rat,[],[s5])).
% 0.19/0.27 cnf(s7, plain, ~spl4_4 | spl4_5, inference(sat_conversion,[],[f38])).
% 0.19/0.27 cnf(s8, plain, ~spl4_2 | spl4_4, inference(sat_conversion,[],[f41])).
% 0.19/0.27 cnf(s9, plain, ~spl4_2 | ~spl4_5, inference(sat_conversion,[],[f43])).
% 0.19/0.27 cnf(s10, plain, ~spl4_5, inference(rat,[],[s9,s6])).
% 0.19/0.27 cnf(s11, plain, spl4_4, inference(rat,[],[s8,s6])).
% 0.19/0.27 cnf(s12, plain, $false, inference(rat,[],[s7,s10,s11])).
% 0.19/0.27 thf(f44,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(avatar_sat_refutation,[],[s12])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (1011121)------------------------------
% 0.19/0.27 % (1011121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1011121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1011121)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1011121)Termination reason: Refutation
% 0.19/0.27 % (1011121)Time elapsed: 0.001 s
% 0.19/0.27 % (1011121)Peak memory usage: 13 MB
% 0.19/0.27 % (1011121)Instructions burned: 2 (million)
% 0.19/0.27 % (1011115)Success in time 0.028 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------