%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO381^5 : 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 : n001.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 08:47:33 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO381^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n001.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 16:55:36 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 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
% 0.09/0.25 % (1502245)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.25 % (1502253)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=3498466690: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)
% 0.09/0.25 % (1502253) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1502245-1502253"...
% 0.09/0.25 % (1502253)...printing done.
% 0.09/0.25 % (1502253)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% 0.09/0.25 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.25 thf(func_def_0, type, cR: ($i > $i > $o)).
% 0.09/0.25 thf(func_def_4, type, sK0: ($i > $i)).
% 0.09/0.25 thf(func_def_5, type, sK1: ($i > $i)).
% 0.09/0.25 thf(f1,conjecture,(
% 0.09/0.25 ? [X0 : $i] : (? [X1 : $i] : ! [X2 : $i] : (cR @ X1 @ X2) <=> ! [X3 : $i] : (cR @ X0 @ X3))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX_2002_12_17)).
% 0.09/0.25 thf(f2,negated_conjecture,(
% 0.09/0.25 ~ ? [X0 : $i] : (? [X1 : $i] : ! [X2 : $i] : (cR @ X1 @ X2) <=> ! [X3 : $i] : (cR @ X0 @ X3))),
% 0.09/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.25 thf(f3,plain,(
% 0.09/0.25 ~ ? [X0 : $i] : (? [X1 : $i] : ! [X2 : $i] : (cR @ X1 @ X2) <=> ! [X3 : $i] : (cR @ X0 @ X3))),
% 0.09/0.25 inference(rectify,[],[f2])).
% 0.09/0.25 thf(f4,plain,(
% 0.09/0.25 ~ ? [X0 : $i] : (! [X3 : $i] : (((cR @ X0 @ X3)) = $true) <=> ? [X1 : $i] : ! [X2 : $i] : (((cR @ X1 @ X2)) = $true))),
% 0.09/0.25 inference(fool_elimination,[],[f3])).
% 0.09/0.25 thf(f5,plain,(
% 0.09/0.25 ! [X0 : $i] : (! [X3 : $i] : (((cR @ X0 @ X3)) = $true) <~> ? [X1 : $i] : ! [X2 : $i] : (((cR @ X1 @ X2)) = $true))),
% 0.09/0.25 inference(ennf_transformation,[],[f4])).
% 0.09/0.25 thf(f6,plain,(
% 0.09/0.25 ! [X0 : $i] : ((! [X1 : $i] : ? [X2 : $i] : (((cR @ X1 @ X2)) != $true) | ? [X3 : $i] : (((cR @ X0 @ X3)) != $true)) & (? [X1 : $i] : ! [X2 : $i] : (((cR @ X1 @ X2)) = $true) | ! [X3 : $i] : (((cR @ X0 @ X3)) = $true)))),
% 0.09/0.25 inference(nnf_transformation,[],[f5])).
% 0.09/0.25 thf(f7,plain,(
% 0.09/0.25 ! [X0 : $i] : ((! [X1 : $i] : ? [X2 : $i] : (((cR @ X1 @ X2)) != $true) | ? [X3 : $i] : (((cR @ X0 @ X3)) != $true)) & (? [X4 : $i] : ! [X5 : $i] : (((cR @ X4 @ X5)) = $true) | ! [X6 : $i] : (((cR @ X0 @ X6)) = $true)))),
% 0.09/0.25 inference(rectify,[],[f6])).
% 0.09/0.25 thf(f8,plain,(
% 0.09/0.25 ! [X0 : $i] : ((! [X1 : $i] : ($true != ((cR @ X1 @ (sK0 @ X1)))) | ($true != ((cR @ X0 @ (sK1 @ X0))))) & (! [X5 : $i] : (((cR @ sK2 @ X5)) = $true) | ! [X6 : $i] : (((cR @ X0 @ X6)) = $true)))),
% 0.09/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK2]),skolemize(X3,sK1 @ X0),skolemize(X3,sK1 @ X0),skolemize(X4,sK2)],[f7])).
% 0.09/0.25 thf(f9,plain,(
% 0.09/0.25 ( ! [X0 : $i,X6 : $i,X5 : $i] : ((((cR @ X0 @ X6)) = $true) | (((cR @ sK2 @ X5)) = $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f10,plain,(
% 0.09/0.25 ( ! [X0 : $i,X1 : $i] : (($true != ((cR @ X0 @ (sK1 @ X0)))) | ($true != ((cR @ X1 @ (sK0 @ X1))))) )),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f13,definition,(
% 0.09/0.25 spl3_1 <=> ! [X5 : $i] : (((cR @ sK2 @ X5)) = $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.09/0.25 thf(f14,plain,(
% 0.09/0.25 ( ! [X5 : $i] : ((((cR @ sK2 @ X5)) = $true)) ) | ~spl3_1),
% 0.09/0.25 inference(avatar_component_clause,[],[f13])).
% 0.09/0.25 thf(f16,definition,(
% 0.09/0.25 spl3_2 <=> ! [X6 : $i,X0 : $i] : (((cR @ X0 @ X6)) = $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.09/0.25 thf(f17,plain,(
% 0.09/0.25 ( ! [X0 : $i,X6 : $i] : ((((cR @ X0 @ X6)) = $true)) ) | ~spl3_2),
% 0.09/0.25 inference(avatar_component_clause,[],[f16])).
% 0.09/0.25 thf(f18,plain,(
% 0.09/0.25 spl3_1 | spl3_2),
% 0.09/0.25 inference(avatar_split_clause,[],[f9,f16,f13])).
% 0.09/0.25 thf(f20,definition,(
% 0.09/0.25 spl3_3 <=> ! [X0 : $i] : ($true != ((cR @ X0 @ (sK1 @ X0))))),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.09/0.25 thf(f21,plain,(
% 0.09/0.25 ( ! [X0 : $i] : (($true != ((cR @ X0 @ (sK1 @ X0))))) ) | ~spl3_3),
% 0.09/0.25 inference(avatar_component_clause,[],[f20])).
% 0.09/0.25 thf(f23,definition,(
% 0.09/0.25 spl3_4 <=> ! [X1 : $i] : ($true != ((cR @ X1 @ (sK0 @ X1))))),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.09/0.25 thf(f24,plain,(
% 0.09/0.25 ( ! [X1 : $i] : (($true != ((cR @ X1 @ (sK0 @ X1))))) ) | ~spl3_4),
% 0.09/0.25 inference(avatar_component_clause,[],[f23])).
% 0.09/0.25 thf(f25,plain,(
% 0.09/0.25 spl3_3 | spl3_4),
% 0.09/0.25 inference(avatar_split_clause,[],[f10,f23,f20])).
% 0.09/0.25 thf(f26,plain,(
% 0.09/0.25 $false | (~spl3_2 | ~spl3_3)),
% 0.09/0.25 inference(forward_subsumption_resolution,[],[f21,f17])).
% 0.09/0.25 thf(f27,plain,(
% 0.09/0.25 ~spl3_2 | ~spl3_3),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f26])).
% 0.09/0.25 thf(f28,plain,(
% 0.09/0.25 ($true != $true) | (~spl3_1 | ~spl3_3)),
% 0.09/0.25 inference(superposition,[],[f21,f14])).
% 0.09/0.25 thf(f29,plain,(
% 0.09/0.25 $false | (~spl3_1 | ~spl3_3)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f28])).
% 0.09/0.25 thf(f30,plain,(
% 0.09/0.25 ~spl3_1 | ~spl3_3),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f29])).
% 0.09/0.25 thf(f31,plain,(
% 0.09/0.25 $false | (~spl3_2 | ~spl3_4)),
% 0.09/0.25 inference(forward_subsumption_resolution,[],[f24,f17])).
% 0.09/0.25 thf(f32,plain,(
% 0.09/0.25 ~spl3_2 | ~spl3_4),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f31])).
% 0.09/0.25 thf(f33,plain,(
% 0.09/0.25 ($true != $true) | (~spl3_1 | ~spl3_4)),
% 0.09/0.25 inference(superposition,[],[f24,f14])).
% 0.09/0.25 thf(f34,plain,(
% 0.09/0.25 $false | (~spl3_1 | ~spl3_4)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f33])).
% 0.09/0.25 thf(f35,plain,(
% 0.09/0.25 ~spl3_1 | ~spl3_4),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f34])).
% 0.09/0.25 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f18])).
% 0.09/0.25 cnf(s2, plain, spl3_3 | spl3_4, inference(sat_conversion,[],[f25])).
% 0.09/0.25 cnf(s3, plain, ~spl3_2 | ~spl3_3, inference(sat_conversion,[],[f27])).
% 0.09/0.25 cnf(s4, plain, ~spl3_1 | ~spl3_3, inference(sat_conversion,[],[f30])).
% 0.09/0.25 cnf(s5, plain, ~spl3_2 | ~spl3_4, inference(sat_conversion,[],[f32])).
% 0.09/0.25 cnf(s6, plain, ~spl3_1 | ~spl3_4, inference(sat_conversion,[],[f35])).
% 0.09/0.25 cnf(s7, plain, ~spl3_2, inference(rat,[],[s2,s3,s5])).
% 0.09/0.25 cnf(s8, plain, spl3_1, inference(rat,[],[s1,s7])).
% 0.09/0.25 cnf(s9, plain, ~spl3_4, inference(rat,[],[s6,s8])).
% 0.09/0.25 cnf(s10, plain, ~spl3_3, inference(rat,[],[s4,s8])).
% 0.09/0.25 cnf(s11, plain, $false, inference(rat,[],[s2,s9,s10])).
% 0.09/0.25 thf(f36,plain,(
% 0.09/0.25 $false),
% 0.09/0.25 inference(avatar_sat_refutation,[],[s11])).
% 0.09/0.25 % SZS output end Proof for theBenchmark
% 0.09/0.25 % (1502253)------------------------------
% 0.09/0.25 % (1502253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (1502253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (1502253)CaDiCaL version: 2.1.3
% 0.09/0.25 % (1502253)Termination reason: Refutation
% 0.09/0.25 % (1502253)Time elapsed: 0.001 s
% 0.09/0.25 % (1502253)Peak memory usage: 13 MB
% 0.09/0.25 % (1502253)Instructions burned: 2 (million)
% 0.09/0.25 % (1502245)Success in time 0.024 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------