%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO101^5 : 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 : n002.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 0.21s 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 : SYO101^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:36:43 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.21/0.28 % (1508896)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (1508903)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3425176899:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (1508903) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1508896-1508903"...
% 0.21/0.28 % (1508903)...printing done.
% 0.21/0.28 % (1508903)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) > $tType).
% 0.21/0.28 thf(func_def_1, type, cR: ($i > $i > $o)).
% 0.21/0.28 thf(func_def_2, type, cP: ($i > $o)).
% 0.21/0.28 thf(func_def_6, type, sK0: ($i > $i)).
% 0.21/0.28 thf(func_def_7, type, sK1: ($i > $i)).
% 0.21/0.28 thf(f1,conjecture,(
% 0.21/0.28 ! [X0 : $i] : ? [X1 : $i] : ((cP @ X0) => ! [X2 : $i] : ((cP @ X2) & (cR @ X0 @ X1))) => ? [X3 : $i] : ! [X4 : $i] : ((cP @ X4) => (cR @ cW @ X3))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM83)).
% 0.21/0.28 thf(f2,negated_conjecture,(
% 0.21/0.28 ~(! [X0 : $i] : ? [X1 : $i] : ((cP @ X0) => ! [X2 : $i] : ((cP @ X2) & (cR @ X0 @ X1))) => ? [X3 : $i] : ! [X4 : $i] : ((cP @ X4) => (cR @ cW @ X3)))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.28 thf(f3,plain,(
% 0.21/0.28 ~(! [X0 : $i] : ? [X1 : $i] : ((cP @ X0) => ! [X2 : $i] : ((cP @ X2) & (cR @ X0 @ X1))) => ? [X3 : $i] : ! [X4 : $i] : ((cP @ X4) => (cR @ cW @ X3)))),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 ~(! [X0 : $i] : ? [X1 : $i] : ((((cP @ X0)) = $true) => ! [X2 : $i] : ((((cP @ X2)) = $true) & (((cR @ X0 @ X1)) = $true))) => ? [X3 : $i] : ! [X4 : $i] : ((((cP @ X4)) = $true) => (((cR @ cW @ X3)) = $true)))),
% 0.21/0.28 inference(fool_elimination,[],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ! [X3 : $i] : ? [X4 : $i] : ((((cR @ cW @ X3)) != $true) & (((cP @ X4)) = $true)) & ! [X0 : $i] : ? [X1 : $i] : ((((cP @ X0)) != $true) | ! [X2 : $i] : ((((cP @ X2)) = $true) & (((cR @ X0 @ X1)) = $true)))),
% 0.21/0.28 inference(ennf_transformation,[],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ! [X0 : $i] : ? [X1 : $i] : ((((cR @ cW @ X0)) != $true) & (((cP @ X1)) = $true)) & ! [X2 : $i] : ? [X3 : $i] : ((((cP @ X2)) != $true) | ! [X4 : $i] : ((((cP @ X4)) = $true) & (((cR @ X2 @ X3)) = $true)))),
% 0.21/0.28 inference(rectify,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ! [X0 : $i] : ((((cR @ cW @ X0)) != $true) & ($true = ((cP @ (sK0 @ X0))))) & ! [X2 : $i] : ((((cP @ X2)) != $true) | ! [X4 : $i] : ((((cP @ X4)) = $true) & ($true = ((cR @ X2 @ (sK1 @ X2))))))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK1 @ X2),skolemize(X3,sK1 @ X2)],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ( ! [X2 : $i] : ((((cP @ X2)) != $true) | ($true = ((cR @ X2 @ (sK1 @ X2))))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f7])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 ( ! [X2 : $i,X4 : $i] : ((((cP @ X2)) != $true) | (((cP @ X4)) = $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f7])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ( ! [X0 : $i] : (($true = ((cP @ (sK0 @ X0))))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f7])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 ( ! [X0 : $i] : ((((cR @ cW @ X0)) != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f7])).
% 0.21/0.28 thf(f15,definition,(
% 0.21/0.28 spl2_1 <=> ! [X2 : $i] : (((cP @ X2)) != $true)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 ( ! [X2 : $i] : ((((cP @ X2)) != $true)) ) | ~spl2_1),
% 0.21/0.28 inference(avatar_component_clause,[],[f15])).
% 0.21/0.28 thf(f18,definition,(
% 0.21/0.28 spl2_2 <=> ! [X4 : $i] : (((cP @ X4)) = $true)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.21/0.28 thf(f19,plain,(
% 0.21/0.28 ( ! [X4 : $i] : ((((cP @ X4)) = $true)) ) | ~spl2_2),
% 0.21/0.28 inference(avatar_component_clause,[],[f18])).
% 0.21/0.28 thf(f20,plain,(
% 0.21/0.28 spl2_1 | spl2_2),
% 0.21/0.28 inference(avatar_split_clause,[],[f9,f18,f15])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 ( ! [X0 : $i] : (($true != $true) | ($true = ((cR @ X0 @ (sK1 @ X0))))) ) | ~spl2_2),
% 0.21/0.28 inference(constrained_superposition,[],[f8,f19])).
% 0.21/0.28 thf(f24,plain,(
% 0.21/0.28 ( ! [X0 : $i] : (($true = ((cR @ X0 @ (sK1 @ X0))))) ) | ~spl2_2),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f21])).
% 0.21/0.28 thf(f25,plain,(
% 0.21/0.28 ($true != $true) | ~spl2_2),
% 0.21/0.28 inference(constrained_superposition,[],[f11,f24])).
% 0.21/0.28 thf(f26,plain,(
% 0.21/0.28 $false | ~spl2_2),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f25])).
% 0.21/0.28 thf(f27,plain,(
% 0.21/0.28 ~spl2_2),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f26])).
% 0.21/0.28 thf(f28,plain,(
% 0.21/0.28 ($true != $true) | ~spl2_1),
% 0.21/0.28 inference(constrained_superposition,[],[f16,f10])).
% 0.21/0.28 thf(f29,plain,(
% 0.21/0.28 $false | ~spl2_1),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f28])).
% 0.21/0.28 thf(f30,plain,(
% 0.21/0.28 ~spl2_1),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f29])).
% 0.21/0.28 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f20])).
% 0.21/0.28 cnf(s2, plain, ~spl2_2, inference(sat_conversion,[],[f27])).
% 0.21/0.28 cnf(s3, plain, ~spl2_1, inference(sat_conversion,[],[f30])).
% 0.21/0.28 cnf(s4, plain, $false, inference(rat,[],[s1,s2,s3])).
% 0.21/0.28 thf(f31,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(avatar_sat_refutation,[],[s4])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (1508903)------------------------------
% 0.21/0.28 % (1508903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1508903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1508903)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1508903)Termination reason: Refutation
% 0.21/0.28 % (1508903)Time elapsed: 0.002 s
% 0.21/0.28 % (1508903)Peak memory usage: 13 MB
% 0.21/0.28 % (1508903)Instructions burned: 2 (million)
% 0.21/0.28 % (1508896)Success in time 0.033 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------