%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n017.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 08:41:51 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 SAT
% 0.08/0.19 % Computer : n017.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 16:10:37 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.26 % (524821)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (524827)% WARNING: option uhcvi not known.
% 0.08/0.26 % (524827)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3776756896:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.26 % (524827)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.26 % (524827)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.26 % (524827) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-524821-524827"...
% 0.08/0.26 % (524827)...printing done.
% 0.08/0.26 % (524826)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1093926330_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.26 % (524829)dis+10_1_sil=32000:sp=arity:random_seed=1763623247:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.26 % (524828)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1293988342:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.26 % (524830)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=582028765:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.26 % (524831)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=689424561:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.26 % (524827)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% 0.08/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.26 thf(func_def_0, type, cP: ($i > $i > $o)).
% 0.08/0.26 thf(func_def_1, type, g: ($i > $i)).
% 0.08/0.26 thf(func_def_2, type, cM: ($i > $o)).
% 0.08/0.26 thf(func_def_3, type, cQ: ($i > $o)).
% 0.08/0.26 thf(func_def_4, type, f: ($i > $i > $i)).
% 0.08/0.26 thf(func_def_9, type, sK1: ($i > $i)).
% 0.08/0.26 thf(f1,conjecture,(
% 0.08/0.26 (! [X5 : $i] : ((cQ @ X5) => ~(cM @ (g @ X5))) & ! [X3 : $i] : ? [X4 : $i] : (((cQ @ (f @ X3 @ X4)) & (cM @ X3)) | (cP @ X3 @ X4)) & ! [X0 : $i] : (? [X1 : $i] : (cP @ X0 @ X1) => ! [X2 : $i] : (cP @ X2 @ X2))) => ! [X3 : $i] : ? [X4 : $i] : ((cP @ X3 @ X3) & (cP @ (g @ X3) @ X4))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX2115)).
% 0.08/0.26 thf(f2,negated_conjecture,(
% 0.08/0.26 ~((! [X5 : $i] : ((cQ @ X5) => ~(cM @ (g @ X5))) & ! [X3 : $i] : ? [X4 : $i] : (((cQ @ (f @ X3 @ X4)) & (cM @ X3)) | (cP @ X3 @ X4)) & ! [X0 : $i] : (? [X1 : $i] : (cP @ X0 @ X1) => ! [X2 : $i] : (cP @ X2 @ X2))) => ! [X3 : $i] : ? [X4 : $i] : ((cP @ X3 @ X3) & (cP @ (g @ X3) @ X4)))),
% 0.08/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/0.26 thf(f3,plain,(
% 0.08/0.26 ~((! [X0 : $i] : ((cQ @ X0) => ~(cM @ (g @ X0))) & ! [X1 : $i] : ? [X2 : $i] : (((cQ @ (f @ X1 @ X2)) & (cM @ X1)) | (cP @ X1 @ X2)) & ! [X3 : $i] : (? [X4 : $i] : (cP @ X3 @ X4) => ! [X5 : $i] : (cP @ X5 @ X5))) => ! [X6 : $i] : ? [X7 : $i] : ((cP @ X6 @ X6) & (cP @ (g @ X6) @ X7)))),
% 0.08/0.26 inference(rectify,[],[f2])).
% 0.08/0.26 thf(f4,plain,(
% 0.08/0.26 ~((! [X0 : $i] : ((((cQ @ X0)) = $true) => ~ (((cM @ (g @ X0))) = $true)) & ! [X1 : $i] : ? [X2 : $i] : (((((cQ @ (f @ X1 @ X2))) = $true) & (((cM @ X1)) = $true)) | (((cP @ X1 @ X2)) = $true)) & ! [X3 : $i] : (? [X4 : $i] : (((cP @ X3 @ X4)) = $true) => ! [X5 : $i] : (((cP @ X5 @ X5)) = $true))) => ! [X6 : $i] : ? [X7 : $i] : ((((cP @ X6 @ X6)) = $true) & (((cP @ (g @ X6) @ X7)) = $true)))),
% 0.08/0.26 inference(fool_elimination,[],[f3])).
% 0.08/0.26 thf(f5,plain,(
% 0.08/0.26 ~((! [X0 : $i] : ((((cQ @ X0)) = $true) => (((cM @ (g @ X0))) != $true)) & ! [X1 : $i] : ? [X2 : $i] : (((((cQ @ (f @ X1 @ X2))) = $true) & (((cM @ X1)) = $true)) | (((cP @ X1 @ X2)) = $true)) & ! [X3 : $i] : (? [X4 : $i] : (((cP @ X3 @ X4)) = $true) => ! [X5 : $i] : (((cP @ X5 @ X5)) = $true))) => ! [X6 : $i] : ? [X7 : $i] : ((((cP @ X6 @ X6)) = $true) & (((cP @ (g @ X6) @ X7)) = $true)))),
% 0.08/0.26 inference(flattening,[],[f4])).
% 0.08/0.26 thf(f6,plain,(
% 0.08/0.26 ? [X6 : $i] : ! [X7 : $i] : ((((cP @ X6 @ X6)) != $true) | (((cP @ (g @ X6) @ X7)) != $true)) & (! [X0 : $i] : ((((cM @ (g @ X0))) != $true) | (((cQ @ X0)) != $true)) & ! [X1 : $i] : ? [X2 : $i] : (((((cQ @ (f @ X1 @ X2))) = $true) & (((cM @ X1)) = $true)) | (((cP @ X1 @ X2)) = $true)) & ! [X3 : $i] : (! [X5 : $i] : (((cP @ X5 @ X5)) = $true) | ! [X4 : $i] : (((cP @ X3 @ X4)) != $true)))),
% 0.08/0.26 inference(ennf_transformation,[],[f5])).
% 0.08/0.26 thf(f7,plain,(
% 0.08/0.26 ? [X6 : $i] : ! [X7 : $i] : ((((cP @ X6 @ X6)) != $true) | (((cP @ (g @ X6) @ X7)) != $true)) & ! [X0 : $i] : ((((cM @ (g @ X0))) != $true) | (((cQ @ X0)) != $true)) & ! [X1 : $i] : ? [X2 : $i] : (((((cQ @ (f @ X1 @ X2))) = $true) & (((cM @ X1)) = $true)) | (((cP @ X1 @ X2)) = $true)) & ! [X3 : $i] : (! [X5 : $i] : (((cP @ X5 @ X5)) = $true) | ! [X4 : $i] : (((cP @ X3 @ X4)) != $true))),
% 0.08/0.26 inference(flattening,[],[f6])).
% 0.08/0.26 thf(f8,plain,(
% 0.08/0.26 ? [X0 : $i] : ! [X1 : $i] : (($true != ((cP @ X0 @ X0))) | ($true != ((cP @ (g @ X0) @ X1)))) & ! [X2 : $i] : (($true != ((cM @ (g @ X2)))) | ($true != ((cQ @ X2)))) & ! [X3 : $i] : ? [X4 : $i] : (((((cQ @ (f @ X3 @ X4))) = $true) & (((cM @ X3)) = $true)) | (((cP @ X3 @ X4)) = $true)) & ! [X5 : $i] : (! [X6 : $i] : (((cP @ X6 @ X6)) = $true) | ! [X7 : $i] : ($true != ((cP @ X5 @ X7))))),
% 0.08/0.26 inference(rectify,[],[f7])).
% 0.08/0.26 thf(f9,plain,(
% 0.08/0.26 ! [X1 : $i] : (($true != ((cP @ sK0 @ sK0))) | ($true != ((cP @ (g @ sK0) @ X1)))) & ! [X2 : $i] : (($true != ((cM @ (g @ X2)))) | ($true != ((cQ @ X2)))) & ! [X3 : $i] : ((($true = ((cQ @ (f @ X3 @ (sK1 @ X3))))) & (((cM @ X3)) = $true)) | ($true = ((cP @ X3 @ (sK1 @ X3))))) & ! [X5 : $i] : (! [X6 : $i] : (((cP @ X6 @ X6)) = $true) | ! [X7 : $i] : ($true != ((cP @ X5 @ X7))))),
% 0.08/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,sK0),skolemize(X4,sK1 @ X3)],[f8])).
% 0.08/0.26 thf(f10,plain,(
% 0.08/0.26 ( ! [X6 : $i,X7 : $i,X5 : $i] : ((((cP @ X6 @ X6)) = $true) | ($true != ((cP @ X5 @ X7)))) )),
% 0.08/0.26 inference(cnf_transformation,[],[f9])).
% 0.08/0.26 thf(f11,plain,(
% 0.08/0.26 ( ! [X3 : $i] : ((((cM @ X3)) = $true) | ($true = ((cP @ X3 @ (sK1 @ X3))))) )),
% 0.08/0.26 inference(cnf_transformation,[],[f9])).
% 0.08/0.26 thf(f12,plain,(
% 0.08/0.26 ( ! [X3 : $i] : (($true = ((cQ @ (f @ X3 @ (sK1 @ X3))))) | ($true = ((cP @ X3 @ (sK1 @ X3))))) )),
% 0.08/0.26 inference(cnf_transformation,[],[f9])).
% 0.08/0.26 thf(f13,plain,(
% 0.08/0.26 ( ! [X2 : $i] : (($true != ((cM @ (g @ X2)))) | ($true != ((cQ @ X2)))) )),
% 0.08/0.26 inference(cnf_transformation,[],[f9])).
% 0.08/0.26 thf(f14,plain,(
% 0.08/0.26 ( ! [X1 : $i] : (($true != ((cP @ sK0 @ sK0))) | ($true != ((cP @ (g @ sK0) @ X1)))) )),
% 0.08/0.26 inference(cnf_transformation,[],[f9])).
% 0.08/0.26 thf(f18,definition,(
% 0.08/0.26 spl2_1 <=> ! [X5 : $i,X7 : $i] : ($true != ((cP @ X5 @ X7)))),
% 0.08/0.26 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.08/0.26 thf(f19,plain,(
% 0.08/0.26 ( ! [X7 : $i,X5 : $i] : (($true != ((cP @ X5 @ X7)))) ) | ~spl2_1),
% 0.08/0.26 inference(avatar_component_clause,[],[f18])).
% 0.08/0.26 thf(f21,definition,(
% 0.08/0.26 spl2_2 <=> ! [X6 : $i] : (((cP @ X6 @ X6)) = $true)),
% 0.08/0.26 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.08/0.26 thf(f22,plain,(
% 0.08/0.26 ( ! [X6 : $i] : ((((cP @ X6 @ X6)) = $true)) ) | ~spl2_2),
% 0.08/0.26 inference(avatar_component_clause,[],[f21])).
% 0.08/0.26 thf(f23,plain,(
% 0.08/0.26 spl2_1 | spl2_2),
% 0.08/0.26 inference(avatar_split_clause,[],[f10,f21,f18])).
% 0.08/0.26 thf(f25,definition,(
% 0.08/0.26 spl2_3 <=> ! [X1 : $i] : ($true != ((cP @ (g @ sK0) @ X1)))),
% 0.08/0.26 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.08/0.26 thf(f26,plain,(
% 0.08/0.26 ( ! [X1 : $i] : (($true != ((cP @ (g @ sK0) @ X1)))) ) | ~spl2_3),
% 0.08/0.26 inference(avatar_component_clause,[],[f25])).
% 0.08/0.26 thf(f28,definition,(
% 0.08/0.26 spl2_4 <=> ($true = ((cP @ sK0 @ sK0)))),
% 0.08/0.26 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.08/0.26 thf(f30,plain,(
% 0.08/0.26 ($true != ((cP @ sK0 @ sK0))) | spl2_4),
% 0.08/0.26 inference(avatar_component_clause,[],[f28])).
% 0.08/0.26 thf(f31,plain,(
% 0.08/0.26 spl2_3 | ~spl2_4),
% 0.08/0.26 inference(avatar_split_clause,[],[f14,f28,f25])).
% 0.08/0.26 thf(f32,plain,(
% 0.08/0.26 $false | (~spl2_2 | spl2_4)),
% 0.08/0.26 inference(forward_subsumption_resolution,[],[f30,f22])).
% 0.08/0.26 thf(f33,plain,(
% 0.08/0.26 ~spl2_2 | spl2_4),
% 0.08/0.26 inference(avatar_contradiction_clause,[],[f32])).
% 0.08/0.26 thf(f34,plain,(
% 0.08/0.26 ( ! [X3 : $i] : ((((cM @ X3)) = $true)) ) | ~spl2_1),
% 0.08/0.26 inference(forward_subsumption_resolution,[],[f11,f19])).
% 0.08/0.26 thf(f35,plain,(
% 0.08/0.26 ( ! [X2 : $i] : (($true != ((cQ @ X2)))) ) | ~spl2_1),
% 0.08/0.26 inference(backward_subsumption_resolution,[],[f13,f34])).
% 0.08/0.26 thf(f36,plain,(
% 0.08/0.26 ( ! [X3 : $i] : (($true = ((cP @ X3 @ (sK1 @ X3))))) ) | ~spl2_1),
% 0.08/0.26 inference(forward_subsumption_resolution,[],[f12,f35])).
% 0.08/0.26 thf(f37,plain,(
% 0.08/0.26 $false | ~spl2_1),
% 0.08/0.26 inference(forward_subsumption_resolution,[],[f36,f19])).
% 0.08/0.26 thf(f38,plain,(
% 0.08/0.26 ~spl2_1),
% 0.08/0.26 inference(avatar_contradiction_clause,[],[f37])).
% 0.08/0.26 thf(f39,plain,(
% 0.08/0.26 ($true != $true) | (~spl2_2 | ~spl2_3)),
% 0.08/0.26 inference(constrained_superposition,[],[f26,f22])).
% 0.08/0.26 thf(f40,plain,(
% 0.08/0.26 $false | (~spl2_2 | ~spl2_3)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f39])).
% 0.08/0.26 thf(f41,plain,(
% 0.08/0.26 ~spl2_2 | ~spl2_3),
% 0.08/0.26 inference(avatar_contradiction_clause,[],[f40])).
% 0.08/0.26 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f23])).
% 0.08/0.26 cnf(s2, plain, spl2_3 | ~spl2_4, inference(sat_conversion,[],[f31])).
% 0.08/0.26 cnf(s3, plain, ~spl2_2 | spl2_4, inference(sat_conversion,[],[f33])).
% 0.08/0.26 cnf(s4, plain, ~spl2_1, inference(sat_conversion,[],[f38])).
% 0.08/0.26 cnf(s5, plain, ~spl2_2 | ~spl2_3, inference(sat_conversion,[],[f41])).
% 0.08/0.26 cnf(s6, plain, spl2_2, inference(rat,[],[s1,s4])).
% 0.08/0.26 cnf(s7, plain, ~spl2_3, inference(rat,[],[s5,s6])).
% 0.08/0.26 cnf(s8, plain, spl2_4, inference(rat,[],[s3,s6])).
% 0.08/0.26 cnf(s9, plain, $false, inference(rat,[],[s2,s8,s7])).
% 0.08/0.26 thf(f42,plain,(
% 0.08/0.26 $false),
% 0.08/0.26 inference(avatar_sat_refutation,[],[s9])).
% 0.08/0.26 % SZS output end Proof for theBenchmark
% 0.08/0.26 % (524827)------------------------------
% 0.08/0.26 % (524827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (524827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (524827)CaDiCaL version: 2.1.3
% 0.08/0.26 % (524827)Termination reason: Refutation
% 0.08/0.26 % (524827)Time elapsed: 0.002 s
% 0.08/0.26 % (524827)Peak memory usage: 12 MB
% 0.08/0.26 % (524827)Instructions burned: 4 (million)
% 0.08/0.26 % (524821)Success in time 0.029 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------