%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN364^5 : 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 : n016.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 08:41:40 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 : SYN364^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n016.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 16:20:05 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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
% 0.09/0.25 % (544868)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.25 % (544875)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=412706106:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.25 % (544875) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-544868-544875"...
% 0.09/0.25 % (544875)...printing done.
% 0.09/0.25 % (544875)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) > $tType).
% 0.09/0.25 thf(func_def_0, type, cP: ($i > $i > $o)).
% 0.09/0.25 thf(func_def_1, type, g: ($i > $i)).
% 0.09/0.25 thf(func_def_2, type, cM: ($i > $o)).
% 0.09/0.25 thf(func_def_3, type, cQ: ($i > $o)).
% 0.09/0.25 thf(func_def_4, type, f: ($i > $i > $i)).
% 0.09/0.25 thf(func_def_8, type, sK0: ($i > $i)).
% 0.09/0.25 thf(f1,conjecture,(
% 0.09/0.25 (! [X0 : $i] : (? [X1 : $i] : (cP @ X0 @ X1) => ! [X2 : $i] : (cP @ X2 @ X2)) & ! [X3 : $i] : ? [X4 : $i] : ((cP @ X3 @ X4) | ((cM @ X3) & (cQ @ (f @ X3 @ X4)))) & ! [X5 : $i] : ((cQ @ X5) => ~(cM @ (g @ X5)))) => ! [X3 : $i] : ? [X4 : $i] : ((cP @ (g @ X3) @ X4) & (cP @ X3 @ X3))),
% 0.09/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX2115)).
% 0.09/0.25 thf(f2,negated_conjecture,(
% 0.09/0.25 ~((! [X0 : $i] : (? [X1 : $i] : (cP @ X0 @ X1) => ! [X2 : $i] : (cP @ X2 @ X2)) & ! [X3 : $i] : ? [X4 : $i] : ((cP @ X3 @ X4) | ((cM @ X3) & (cQ @ (f @ X3 @ X4)))) & ! [X5 : $i] : ((cQ @ X5) => ~(cM @ (g @ X5)))) => ! [X3 : $i] : ? [X4 : $i] : ((cP @ (g @ X3) @ X4) & (cP @ X3 @ 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] : (cP @ X0 @ X1) => ! [X2 : $i] : (cP @ X2 @ X2)) & ! [X3 : $i] : ? [X4 : $i] : ((cP @ X3 @ X4) | ((cM @ X3) & (cQ @ (f @ X3 @ X4)))) & ! [X5 : $i] : ((cQ @ X5) => ~(cM @ (g @ X5)))) => ! [X6 : $i] : ? [X7 : $i] : ((cP @ (g @ X6) @ X7) & (cP @ X6 @ X6)))),
% 0.09/0.25 inference(rectify,[],[f2])).
% 0.09/0.25 thf(f4,plain,(
% 0.09/0.25 ~((! [X0 : $i] : (? [X1 : $i] : (((cP @ X0 @ X1)) = $true) => ! [X2 : $i] : (((cP @ X2 @ X2)) = $true)) & ! [X3 : $i] : ? [X4 : $i] : ((((cP @ X3 @ X4)) = $true) | ((((cQ @ (f @ X3 @ X4))) = $true) & (((cM @ X3)) = $true))) & ! [X5 : $i] : ((((cQ @ X5)) = $true) => ~ (((cM @ (g @ X5))) = $true))) => ! [X6 : $i] : ? [X7 : $i] : ((((cP @ (g @ X6) @ X7)) = $true) & (((cP @ X6 @ X6)) = $true)))),
% 0.09/0.25 inference(fool_elimination,[],[f3])).
% 0.09/0.25 thf(f5,plain,(
% 0.09/0.25 ~((! [X5 : $i] : ((((cQ @ X5)) = $true) => (((cM @ (g @ X5))) != $true)) & ! [X3 : $i] : ? [X4 : $i] : ((((cP @ X3 @ X4)) = $true) | ((((cQ @ (f @ X3 @ X4))) = $true) & (((cM @ X3)) = $true))) & ! [X0 : $i] : (? [X1 : $i] : (((cP @ X0 @ X1)) = $true) => ! [X2 : $i] : (((cP @ X2 @ X2)) = $true))) => ! [X6 : $i] : ? [X7 : $i] : ((((cP @ (g @ X6) @ X7)) = $true) & (((cP @ X6 @ X6)) = $true)))),
% 0.09/0.25 inference(flattening,[],[f4])).
% 0.09/0.25 thf(f6,plain,(
% 0.09/0.25 ? [X6 : $i] : ! [X7 : $i] : ((((cP @ (g @ X6) @ X7)) != $true) | (((cP @ X6 @ X6)) != $true)) & (! [X5 : $i] : ((((cM @ (g @ X5))) != $true) | (((cQ @ X5)) != $true)) & ! [X3 : $i] : ? [X4 : $i] : ((((cP @ X3 @ X4)) = $true) | ((((cQ @ (f @ X3 @ X4))) = $true) & (((cM @ X3)) = $true))) & ! [X0 : $i] : (! [X1 : $i] : (((cP @ X0 @ X1)) != $true) | ! [X2 : $i] : (((cP @ X2 @ X2)) = $true)))),
% 0.09/0.25 inference(ennf_transformation,[],[f5])).
% 0.09/0.25 thf(f7,plain,(
% 0.09/0.25 ! [X3 : $i] : ? [X4 : $i] : ((((cP @ X3 @ X4)) = $true) | ((((cQ @ (f @ X3 @ X4))) = $true) & (((cM @ X3)) = $true))) & ! [X0 : $i] : (! [X1 : $i] : (((cP @ X0 @ X1)) != $true) | ! [X2 : $i] : (((cP @ X2 @ X2)) = $true)) & ? [X6 : $i] : ! [X7 : $i] : ((((cP @ (g @ X6) @ X7)) != $true) | (((cP @ X6 @ X6)) != $true)) & ! [X5 : $i] : ((((cM @ (g @ X5))) != $true) | (((cQ @ X5)) != $true))),
% 0.09/0.25 inference(flattening,[],[f6])).
% 0.09/0.25 thf(f8,plain,(
% 0.09/0.25 ! [X0 : $i] : ? [X1 : $i] : ((((cP @ X0 @ X1)) = $true) | ((((cQ @ (f @ X0 @ X1))) = $true) & (((cM @ X0)) = $true))) & ! [X2 : $i] : (! [X3 : $i] : (((cP @ X2 @ X3)) != $true) | ! [X4 : $i] : (((cP @ X4 @ X4)) = $true)) & ? [X5 : $i] : ! [X6 : $i] : ((((cP @ (g @ X5) @ X6)) != $true) | (((cP @ X5 @ X5)) != $true)) & ! [X7 : $i] : (($true != ((cM @ (g @ X7)))) | (((cQ @ X7)) != $true))),
% 0.09/0.25 inference(rectify,[],[f7])).
% 0.09/0.25 thf(f9,plain,(
% 0.09/0.25 ! [X0 : $i] : ((((cP @ X0 @ (sK0 @ X0))) = $true) | ((((cQ @ (f @ X0 @ (sK0 @ X0)))) = $true) & (((cM @ X0)) = $true))) & ! [X2 : $i] : (! [X3 : $i] : (((cP @ X2 @ X3)) != $true) | ! [X4 : $i] : (((cP @ X4 @ X4)) = $true)) & ! [X6 : $i] : ((((cP @ (g @ sK1) @ X6)) != $true) | (((cP @ sK1 @ sK1)) != $true)) & ! [X7 : $i] : (($true != ((cM @ (g @ X7)))) | (((cQ @ X7)) != $true))),
% 0.09/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1]),skolemize(X1,sK0 @ X0),skolemize(X5,sK1)],[f8])).
% 0.09/0.25 thf(f10,plain,(
% 0.09/0.25 ( ! [X7 : $i] : (($true != ((cM @ (g @ X7)))) | (((cQ @ X7)) != $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f9])).
% 0.09/0.25 thf(f11,plain,(
% 0.09/0.25 ( ! [X6 : $i] : ((((cP @ (g @ sK1) @ X6)) != $true) | (((cP @ sK1 @ sK1)) != $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f9])).
% 0.09/0.25 thf(f12,plain,(
% 0.09/0.25 ( ! [X2 : $i,X3 : $i,X4 : $i] : ((((cP @ X2 @ X3)) != $true) | (((cP @ X4 @ X4)) = $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f9])).
% 0.09/0.25 thf(f13,plain,(
% 0.09/0.25 ( ! [X0 : $i] : ((((cP @ X0 @ (sK0 @ X0))) = $true) | (((cM @ X0)) = $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f9])).
% 0.09/0.25 thf(f14,plain,(
% 0.09/0.25 ( ! [X0 : $i] : ((((cQ @ (f @ X0 @ (sK0 @ X0)))) = $true) | (((cP @ X0 @ (sK0 @ X0))) = $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f9])).
% 0.09/0.25 thf(f18,definition,(
% 0.09/0.25 spl2_1 <=> (((cP @ sK1 @ sK1)) = $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.09/0.25 thf(f20,plain,(
% 0.09/0.25 (((cP @ sK1 @ sK1)) != $true) | spl2_1),
% 0.09/0.25 inference(avatar_component_clause,[],[f18])).
% 0.09/0.25 thf(f22,definition,(
% 0.09/0.25 spl2_2 <=> ! [X6 : $i] : (((cP @ (g @ sK1) @ X6)) != $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.09/0.25 thf(f23,plain,(
% 0.09/0.25 ( ! [X6 : $i] : ((((cP @ (g @ sK1) @ X6)) != $true)) ) | ~spl2_2),
% 0.09/0.25 inference(avatar_component_clause,[],[f22])).
% 0.09/0.25 thf(f24,plain,(
% 0.09/0.25 ~spl2_1 | spl2_2),
% 0.09/0.25 inference(avatar_split_clause,[],[f11,f22,f18])).
% 0.09/0.25 thf(f26,definition,(
% 0.09/0.25 spl2_3 <=> ! [X2 : $i,X3 : $i] : (((cP @ X2 @ X3)) != $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.09/0.25 thf(f27,plain,(
% 0.09/0.25 ( ! [X2 : $i,X3 : $i] : ((((cP @ X2 @ X3)) != $true)) ) | ~spl2_3),
% 0.09/0.25 inference(avatar_component_clause,[],[f26])).
% 0.09/0.25 thf(f29,definition,(
% 0.09/0.25 spl2_4 <=> ! [X4 : $i] : (((cP @ X4 @ X4)) = $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.09/0.25 thf(f30,plain,(
% 0.09/0.25 ( ! [X4 : $i] : ((((cP @ X4 @ X4)) = $true)) ) | ~spl2_4),
% 0.09/0.25 inference(avatar_component_clause,[],[f29])).
% 0.09/0.25 thf(f31,plain,(
% 0.09/0.25 spl2_3 | spl2_4),
% 0.09/0.25 inference(avatar_split_clause,[],[f12,f29,f26])).
% 0.09/0.25 thf(f32,plain,(
% 0.09/0.25 ( ! [X0 : $i] : ((((cM @ X0)) = $true) | ($true != $true)) ) | ~spl2_3),
% 0.09/0.25 inference(constrained_superposition,[],[f27,f13])).
% 0.09/0.25 thf(f33,plain,(
% 0.09/0.25 ( ! [X0 : $i] : ((((cM @ X0)) = $true)) ) | ~spl2_3),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f32])).
% 0.09/0.25 thf(f34,plain,(
% 0.09/0.25 ( ! [X0 : $i] : (($true != $true) | ($true != ((cQ @ X0)))) ) | ~spl2_3),
% 0.09/0.25 inference(constrained_superposition,[],[f10,f33])).
% 0.09/0.25 thf(f35,plain,(
% 0.09/0.25 ( ! [X0 : $i] : (($true != ((cQ @ X0)))) ) | ~spl2_3),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f34])).
% 0.09/0.25 thf(f36,plain,(
% 0.09/0.25 ( ! [X0 : $i] : ((((cP @ X0 @ (sK0 @ X0))) = $true) | ($true != $true)) ) | ~spl2_3),
% 0.09/0.25 inference(constrained_superposition,[],[f35,f14])).
% 0.09/0.25 thf(f37,plain,(
% 0.09/0.25 ( ! [X0 : $i] : ((((cP @ X0 @ (sK0 @ X0))) = $true)) ) | ~spl2_3),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f36])).
% 0.09/0.25 thf(f38,plain,(
% 0.09/0.25 $false | ~spl2_3),
% 0.09/0.25 inference(forward_subsumption_resolution,[],[f37,f27])).
% 0.09/0.25 thf(f39,plain,(
% 0.09/0.25 ~spl2_3),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f38])).
% 0.09/0.25 thf(f40,plain,(
% 0.09/0.25 ($true != $true) | (spl2_1 | ~spl2_4)),
% 0.09/0.25 inference(constrained_superposition,[],[f20,f30])).
% 0.09/0.25 thf(f41,plain,(
% 0.09/0.25 $false | (spl2_1 | ~spl2_4)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f40])).
% 0.09/0.25 thf(f42,plain,(
% 0.09/0.25 spl2_1 | ~spl2_4),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f41])).
% 0.09/0.25 thf(f44,plain,(
% 0.09/0.25 ($true != $true) | (~spl2_2 | ~spl2_4)),
% 0.09/0.25 inference(constrained_superposition,[],[f23,f30])).
% 0.09/0.25 thf(f46,plain,(
% 0.09/0.25 $false | (~spl2_2 | ~spl2_4)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f44])).
% 0.09/0.25 thf(f47,plain,(
% 0.09/0.25 ~spl2_2 | ~spl2_4),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f46])).
% 0.09/0.25 cnf(s1, plain, ~spl2_1 | spl2_2, inference(sat_conversion,[],[f24])).
% 0.09/0.25 cnf(s2, plain, spl2_3 | spl2_4, inference(sat_conversion,[],[f31])).
% 0.09/0.25 cnf(s3, plain, ~spl2_3, inference(sat_conversion,[],[f39])).
% 0.09/0.25 cnf(s4, plain, spl2_1 | ~spl2_4, inference(sat_conversion,[],[f42])).
% 0.09/0.25 cnf(s5, plain, ~spl2_2 | ~spl2_4, inference(sat_conversion,[],[f47])).
% 0.09/0.25 cnf(s6, plain, spl2_4, inference(rat,[],[s2,s3])).
% 0.09/0.25 cnf(s7, plain, ~spl2_2, inference(rat,[],[s5,s6])).
% 0.09/0.25 cnf(s8, plain, spl2_1, inference(rat,[],[s4,s6])).
% 0.09/0.25 cnf(s9, plain, $false, inference(rat,[],[s1,s7,s8])).
% 0.09/0.25 thf(f48,plain,(
% 0.09/0.25 $false),
% 0.09/0.25 inference(avatar_sat_refutation,[],[s9])).
% 0.09/0.25 % SZS output end Proof for theBenchmark
% 0.09/0.25 % (544875)------------------------------
% 0.09/0.25 % (544875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (544875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (544875)CaDiCaL version: 2.1.3
% 0.09/0.25 % (544875)Termination reason: Refutation
% 0.09/0.25 % (544875)Time elapsed: 0.002 s
% 0.09/0.25 % (544875)Peak memory usage: 13 MB
% 0.09/0.25 % (544875)Instructions burned: 4 (million)
% 0.09/0.25 % (544868)Success in time 0.018 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------