%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO109^5 : 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 : 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 08:46:38 AM UTC 2026
% Result : Theorem 0.24s 0.28s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO109^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:36:53 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.24/0.28 % (1510025)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.28 % (1510030)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1314212952:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.28 % (1510030) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1510025-1510030"...
% 0.24/0.28 % (1510030)...printing done.
% 0.24/0.28 % (1510030)Refutation found. Thanks to Tanya!
% 0.24/0.28 % SZS status Theorem for theBenchmark
% 0.24/0.28 % SZS output start Proof for theBenchmark
% 0.24/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.28 thf(func_def_0, type, cP: ($i > $o)).
% 0.24/0.28 thf(func_def_1, type, cN: ($i > $i > $o)).
% 0.24/0.28 thf(func_def_2, type, cM: ($i > $i > $o)).
% 0.24/0.28 thf(func_def_6, type, sK0: ($i > $i)).
% 0.24/0.28 thf(f1,conjecture,(
% 0.24/0.28 (! [X0 : $i] : (? [X1 : $i] : ((cM @ X0 @ X1) | (cN @ X0 @ X1)) => (cP @ X0)) & ! [X2 : $i,X5 : $i] : (((cN @ X2 @ X5) | (cM @ X2 @ X5)) => ((cM @ X5 @ X5) | (cN @ X5 @ X2) | (cN @ X5 @ X5) | (cM @ X5 @ X2))) & ! [X2 : $i] : ? [X3 : $i] : (! [X4 : $i] : (cM @ X3 @ X4) | (cN @ X3 @ X2))) => ! [X5 : $i] : (cP @ X5)),
% 0.24/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM271)).
% 0.24/0.28 thf(f2,negated_conjecture,(
% 0.24/0.28 ~((! [X0 : $i] : (? [X1 : $i] : ((cM @ X0 @ X1) | (cN @ X0 @ X1)) => (cP @ X0)) & ! [X2 : $i,X5 : $i] : (((cN @ X2 @ X5) | (cM @ X2 @ X5)) => ((cM @ X5 @ X5) | (cN @ X5 @ X2) | (cN @ X5 @ X5) | (cM @ X5 @ X2))) & ! [X2 : $i] : ? [X3 : $i] : (! [X4 : $i] : (cM @ X3 @ X4) | (cN @ X3 @ X2))) => ! [X5 : $i] : (cP @ X5))),
% 0.24/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.24/0.28 thf(f3,plain,(
% 0.24/0.28 ~((! [X0 : $i] : (? [X1 : $i] : ((cM @ X0 @ X1) | (cN @ X0 @ X1)) => (cP @ X0)) & ! [X2 : $i,X3 : $i] : (((cN @ X2 @ X3) | (cM @ X2 @ X3)) => ((cM @ X3 @ X3) | (cN @ X3 @ X2) | (cN @ X3 @ X3) | (cM @ X3 @ X2))) & ! [X4 : $i] : ? [X5 : $i] : (! [X6 : $i] : (cM @ X5 @ X6) | (cN @ X5 @ X4))) => ! [X7 : $i] : (cP @ X7))),
% 0.24/0.28 inference(rectify,[],[f2])).
% 0.24/0.28 thf(f4,plain,(
% 0.24/0.28 ~((! [X4 : $i] : ? [X5 : $i] : (! [X6 : $i] : (((cM @ X5 @ X6)) = $true) | (((cN @ X5 @ X4)) = $true)) & ! [X0 : $i] : (? [X1 : $i] : ((((cN @ X0 @ X1)) = $true) | (((cM @ X0 @ X1)) = $true)) => (((cP @ X0)) = $true)) & ! [X2 : $i,X3 : $i] : ((($true = ((cM @ X2 @ X3))) | (((cN @ X2 @ X3)) = $true)) => ((((cN @ X3 @ X3)) = $true) | (((cM @ X3 @ X3)) = $true) | (((cN @ X3 @ X2)) = $true) | (((cM @ X3 @ X2)) = $true)))) => ! [X7 : $i] : (((cP @ X7)) = $true))),
% 0.24/0.28 inference(fool_elimination,[],[f3])).
% 0.24/0.28 thf(f5,plain,(
% 0.24/0.28 ? [X7 : $i] : (((cP @ X7)) != $true) & (! [X4 : $i] : ? [X5 : $i] : (! [X6 : $i] : (((cM @ X5 @ X6)) = $true) | (((cN @ X5 @ X4)) = $true)) & ! [X0 : $i] : (! [X1 : $i] : ((((cN @ X0 @ X1)) != $true) & (((cM @ X0 @ X1)) != $true)) | (((cP @ X0)) = $true)) & ! [X2 : $i,X3 : $i] : (((((cN @ X3 @ X3)) = $true) | (((cM @ X3 @ X3)) = $true) | (((cN @ X3 @ X2)) = $true) | (((cM @ X3 @ X2)) = $true)) | ((((cN @ X2 @ X3)) != $true) & ($true != ((cM @ X2 @ X3))))))),
% 0.24/0.28 inference(ennf_transformation,[],[f4])).
% 0.24/0.28 thf(f6,plain,(
% 0.24/0.28 ! [X2 : $i,X3 : $i] : ((((cN @ X3 @ X3)) = $true) | ((((cN @ X2 @ X3)) != $true) & ($true != ((cM @ X2 @ X3)))) | (((cM @ X3 @ X3)) = $true) | (((cN @ X3 @ X2)) = $true) | (((cM @ X3 @ X2)) = $true)) & ! [X4 : $i] : ? [X5 : $i] : (! [X6 : $i] : (((cM @ X5 @ X6)) = $true) | (((cN @ X5 @ X4)) = $true)) & ! [X0 : $i] : (! [X1 : $i] : ((((cN @ X0 @ X1)) != $true) & (((cM @ X0 @ X1)) != $true)) | (((cP @ X0)) = $true)) & ? [X7 : $i] : (((cP @ X7)) != $true)),
% 0.24/0.28 inference(flattening,[],[f5])).
% 0.24/0.28 thf(f7,plain,(
% 0.24/0.28 ! [X0 : $i,X1 : $i] : (($true = ((cN @ X1 @ X1))) | ((((cN @ X0 @ X1)) != $true) & (((cM @ X0 @ X1)) != $true)) | ($true = ((cM @ X1 @ X1))) | (((cN @ X1 @ X0)) = $true) | (((cM @ X1 @ X0)) = $true)) & ! [X2 : $i] : ? [X3 : $i] : (! [X4 : $i] : (((cM @ X3 @ X4)) = $true) | (((cN @ X3 @ X2)) = $true)) & ! [X5 : $i] : (! [X6 : $i] : (($true != ((cN @ X5 @ X6))) & (((cM @ X5 @ X6)) != $true)) | (((cP @ X5)) = $true)) & ? [X7 : $i] : (((cP @ X7)) != $true)),
% 0.24/0.28 inference(rectify,[],[f6])).
% 0.24/0.28 thf(f8,plain,(
% 0.24/0.28 ! [X0 : $i,X1 : $i] : (($true = ((cN @ X1 @ X1))) | ((((cN @ X0 @ X1)) != $true) & (((cM @ X0 @ X1)) != $true)) | ($true = ((cM @ X1 @ X1))) | (((cN @ X1 @ X0)) = $true) | (((cM @ X1 @ X0)) = $true)) & ! [X2 : $i] : (! [X4 : $i] : ($true = ((cM @ (sK0 @ X2) @ X4))) | ($true = ((cN @ (sK0 @ X2) @ X2)))) & ! [X5 : $i] : (! [X6 : $i] : (($true != ((cN @ X5 @ X6))) & (((cM @ X5 @ X6)) != $true)) | (((cP @ X5)) = $true)) & (((cP @ sK1)) != $true)),
% 0.24/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1]),skolemize(X3,sK0 @ X2),skolemize(X7,sK1)],[f7])).
% 0.24/0.28 thf(f9,plain,(
% 0.24/0.28 (((cP @ sK1)) != $true)),
% 0.24/0.28 inference(cnf_transformation,[],[f8])).
% 0.24/0.28 thf(f10,plain,(
% 0.24/0.28 ( ! [X6 : $i,X5 : $i] : ((((cM @ X5 @ X6)) != $true) | (((cP @ X5)) = $true)) )),
% 0.24/0.28 inference(cnf_transformation,[],[f8])).
% 0.24/0.28 thf(f11,plain,(
% 0.24/0.28 ( ! [X6 : $i,X5 : $i] : (($true != ((cN @ X5 @ X6))) | (((cP @ X5)) = $true)) )),
% 0.24/0.28 inference(cnf_transformation,[],[f8])).
% 0.24/0.28 thf(f12,plain,(
% 0.24/0.28 ( ! [X2 : $i,X4 : $i] : (($true = ((cN @ (sK0 @ X2) @ X2))) | ($true = ((cM @ (sK0 @ X2) @ X4)))) )),
% 0.24/0.28 inference(cnf_transformation,[],[f8])).
% 0.24/0.28 thf(f13,plain,(
% 0.24/0.28 ( ! [X0 : $i,X1 : $i] : ((((cM @ X0 @ X1)) != $true) | (((cN @ X1 @ X0)) = $true) | (((cM @ X1 @ X0)) = $true) | ($true = ((cM @ X1 @ X1))) | ($true = ((cN @ X1 @ X1)))) )),
% 0.24/0.28 inference(cnf_transformation,[],[f8])).
% 0.24/0.28 thf(f14,plain,(
% 0.24/0.28 ( ! [X0 : $i,X1 : $i] : ((((cN @ X0 @ X1)) != $true) | ($true = ((cM @ X1 @ X1))) | (((cN @ X1 @ X0)) = $true) | (((cM @ X1 @ X0)) = $true) | ($true = ((cN @ X1 @ X1)))) )),
% 0.24/0.28 inference(cnf_transformation,[],[f8])).
% 0.24/0.28 thf(f23,plain,(
% 0.24/0.28 ( ! [X0 : $i,X1 : $i] : ((((cN @ X1 @ (sK0 @ X0))) = $true) | ($true = ((cN @ (sK0 @ X0) @ X0))) | ($true != $true) | ($true = ((cM @ X1 @ X1))) | ($true = ((cN @ X1 @ X1))) | (((cM @ X1 @ (sK0 @ X0))) = $true)) )),
% 0.24/0.28 inference(constrained_superposition,[],[f13,f12])).
% 0.24/0.28 thf(f24,plain,(
% 0.24/0.28 ( ! [X0 : $i,X1 : $i] : (($true = ((cN @ (sK0 @ X0) @ X0))) | (((cM @ X1 @ (sK0 @ X0))) = $true) | ($true = ((cM @ X1 @ X1))) | (((cN @ X1 @ (sK0 @ X0))) = $true) | ($true = ((cN @ X1 @ X1)))) )),
% 0.24/0.28 inference(trivial_inequality_removal,[],[f23])).
% 0.24/0.28 thf(f31,plain,(
% 0.24/0.28 ( ! [X0 : $i,X1 : $i] : (($true = ((cN @ (sK0 @ X1) @ X1))) | ($true = ((cN @ X0 @ X0))) | (((cP @ X0)) = $true) | ($true != $true) | (((cM @ X0 @ (sK0 @ X1))) = $true) | ($true = ((cN @ X0 @ (sK0 @ X1))))) )),
% 0.24/0.28 inference(constrained_superposition,[],[f10,f24])).
% 0.24/0.28 thf(f42,plain,(
% 0.24/0.28 ( ! [X0 : $i,X1 : $i] : ((((cP @ X0)) = $true) | (((cM @ X0 @ (sK0 @ X1))) = $true) | ($true = ((cN @ X0 @ X0))) | ($true = ((cN @ X0 @ (sK0 @ X1)))) | ($true = ((cN @ (sK0 @ X1) @ X1)))) )),
% 0.24/0.28 inference(trivial_inequality_removal,[],[f31])).
% 0.24/0.28 thf(f44,plain,(
% 0.24/0.28 ( ! [X0 : $i,X1 : $i] : (($true = ((cN @ X0 @ X0))) | (((cP @ X0)) = $true) | ($true = ((cN @ X0 @ (sK0 @ X1)))) | ($true = ((cN @ (sK0 @ X1) @ X1)))) )),
% 0.24/0.28 inference(forward_subsumption_resolution,[],[f42,f10])).
% 0.24/0.28 thf(f46,plain,(
% 0.24/0.28 ( ! [X0 : $i,X1 : $i] : ((((cP @ X0)) = $true) | ($true = ((cN @ X0 @ (sK0 @ X1)))) | ($true = ((cN @ (sK0 @ X1) @ X1)))) )),
% 0.24/0.28 inference(forward_subsumption_resolution,[],[f44,f11])).
% 0.24/0.28 thf(f48,plain,(
% 0.24/0.28 ( ! [X0 : $i,X1 : $i] : (($true = ((cN @ (sK0 @ X1) @ X1))) | (((cP @ X0)) = $true)) )),
% 0.24/0.28 inference(forward_subsumption_resolution,[],[f46,f11])).
% 0.24/0.28 thf(f50,definition,(
% 0.24/0.28 spl2_1 <=> ! [X1 : $i] : ($true = ((cN @ (sK0 @ X1) @ X1)))),
% 0.24/0.28 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.24/0.28 thf(f51,plain,(
% 0.24/0.28 ( ! [X1 : $i] : (($true = ((cN @ (sK0 @ X1) @ X1)))) ) | ~spl2_1),
% 0.24/0.28 inference(avatar_component_clause,[],[f50])).
% 0.24/0.28 thf(f53,definition,(
% 0.24/0.28 spl2_2 <=> ! [X0 : $i] : (((cP @ X0)) = $true)),
% 0.24/0.28 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.24/0.28 thf(f54,plain,(
% 0.24/0.28 ( ! [X0 : $i] : ((((cP @ X0)) = $true)) ) | ~spl2_2),
% 0.24/0.28 inference(avatar_component_clause,[],[f53])).
% 0.24/0.28 thf(f56,plain,(
% 0.24/0.28 spl2_1 | spl2_2),
% 0.24/0.28 inference(avatar_split_clause,[],[f48,f53,f50])).
% 0.24/0.28 thf(f57,plain,(
% 0.24/0.28 ($true != $true) | ~spl2_2),
% 0.24/0.28 inference(constrained_superposition,[],[f9,f54])).
% 0.24/0.28 thf(f58,plain,(
% 0.24/0.28 $false | ~spl2_2),
% 0.24/0.28 inference(trivial_inequality_removal,[],[f57])).
% 0.24/0.28 thf(f59,plain,(
% 0.24/0.28 ~spl2_2),
% 0.24/0.28 inference(avatar_contradiction_clause,[],[f58])).
% 0.24/0.28 thf(f60,plain,(
% 0.24/0.28 ( ! [X0 : $i] : (($true = ((cN @ X0 @ X0))) | ($true = ((cM @ X0 @ (sK0 @ X0)))) | (((cM @ X0 @ X0)) = $true) | ($true != $true) | ($true = ((cN @ X0 @ (sK0 @ X0))))) ) | ~spl2_1),
% 0.24/0.28 inference(constrained_superposition,[],[f14,f51])).
% 0.24/0.28 thf(f62,plain,(
% 0.24/0.28 ( ! [X0 : $i] : (($true = ((cM @ X0 @ (sK0 @ X0)))) | ($true = ((cN @ X0 @ X0))) | (((cM @ X0 @ X0)) = $true) | ($true = ((cN @ X0 @ (sK0 @ X0))))) ) | ~spl2_1),
% 0.24/0.28 inference(trivial_inequality_removal,[],[f60])).
% 0.24/0.28 thf(f65,plain,(
% 0.24/0.28 ( ! [X0 : $i] : ((((cM @ X0 @ X0)) = $true) | ($true = ((cN @ X0 @ X0))) | ($true = ((cN @ X0 @ (sK0 @ X0)))) | (((cP @ X0)) = $true) | ($true != $true)) ) | ~spl2_1),
% 0.24/0.28 inference(constrained_superposition,[],[f10,f62])).
% 0.24/0.28 thf(f67,plain,(
% 0.24/0.28 ( ! [X0 : $i] : (($true = ((cN @ X0 @ (sK0 @ X0)))) | ($true = ((cN @ X0 @ X0))) | (((cP @ X0)) = $true) | (((cM @ X0 @ X0)) = $true)) ) | ~spl2_1),
% 0.24/0.28 inference(trivial_inequality_removal,[],[f65])).
% 0.24/0.28 thf(f68,plain,(
% 0.24/0.28 ( ! [X0 : $i] : ((((cP @ X0)) = $true) | ($true = ((cN @ X0 @ X0))) | (((cM @ X0 @ X0)) = $true)) ) | ~spl2_1),
% 0.24/0.28 inference(forward_subsumption_resolution,[],[f67,f11])).
% 0.24/0.28 thf(f69,plain,(
% 0.24/0.28 ( ! [X0 : $i] : ((((cM @ X0 @ X0)) = $true) | (((cP @ X0)) = $true)) ) | ~spl2_1),
% 0.24/0.28 inference(forward_subsumption_resolution,[],[f68,f11])).
% 0.24/0.28 thf(f70,plain,(
% 0.24/0.28 ( ! [X0 : $i] : ((((cP @ X0)) = $true)) ) | ~spl2_1),
% 0.24/0.28 inference(forward_subsumption_resolution,[],[f69,f10])).
% 0.24/0.28 thf(f71,plain,(
% 0.24/0.28 spl2_2 | ~spl2_1),
% 0.24/0.28 inference(avatar_split_clause,[],[f70,f50,f53])).
% 0.24/0.28 cnf(s2, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f56])).
% 0.24/0.28 cnf(s3, plain, ~spl2_2, inference(sat_conversion,[],[f59])).
% 0.24/0.28 cnf(s4, plain, ~spl2_1 | spl2_2, inference(sat_conversion,[],[f71])).
% 0.24/0.28 cnf(s5, plain, ~spl2_1, inference(rat,[],[s4,s3])).
% 0.24/0.28 cnf(s6, plain, $false, inference(rat,[],[s2,s3,s5])).
% 0.24/0.28 thf(f72,plain,(
% 0.24/0.28 $false),
% 0.24/0.28 inference(avatar_sat_refutation,[],[s6])).
% 0.24/0.28 % SZS output end Proof for theBenchmark
% 0.24/0.28 % (1510030)------------------------------
% 0.24/0.28 % (1510030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.28 % (1510030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.28 % (1510030)CaDiCaL version: 2.1.3
% 0.24/0.28 % (1510030)Termination reason: Refutation
% 0.24/0.28 % (1510030)Time elapsed: 0.003 s
% 0.24/0.28 % (1510030)Peak memory usage: 13 MB
% 0.24/0.28 % (1510030)Instructions burned: 8 (million)
% 0.24/0.28 % (1510025)Success in time 0.019 s
% 0.24/0.28 % Vampire exiting
%------------------------------------------------------------------------------