%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU527_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 : Tue Sep 29 12:53:37 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU527_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 05:41:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 Running first-order model finding
% 0.13/0.39 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
% 0.13/0.43 % (883475)Will run a generic schedule for satisfiability detection.
% 0.13/0.43 % (883485)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1257004744:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.43 % (883485) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-883475-883485"...
% 0.13/0.43 % (883485)...printing done.
% 0.13/0.43 % (883485)Refutation found. Thanks to Tanya!
% 0.13/0.43 % SZS status Theorem for theBenchmark
% 0.13/0.43 % SZS output start Proof for theBenchmark
% 0.13/0.43 tff(f1,axiom,(
% 0.13/0.43 (emptysetE = ! [X0 : $i] : (in(X0,emptyset) => ! [X1 : $o] : X1))),
% 0.13/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE)).
% 0.13/0.43 tff(f2,axiom,(
% 0.13/0.43 (setadjoinE = ! [X0 : $i,X1 : $i,X2 : $i] : (in(X2,setadjoin(X0,X1)) => ! [X3 : $o] : ((X2 = X0 => X3) => ((in(X2,X1) => X3) => X3))))),
% 0.13/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE)).
% 0.13/0.43 tff(f3,conjecture,(
% 0.13/0.43 emptysetE => (setadjoinE => ! [X0 : $i,X1 : $i] : (in(X0,setadjoin(X1,emptyset)) => X0 = X1))),
% 0.13/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit)).
% 0.13/0.43 tff(f4,negated_conjecture,(
% 0.13/0.43 ~(emptysetE => (setadjoinE => ! [X0 : $i,X1 : $i] : (in(X0,setadjoin(X1,emptyset)) => X0 = X1)))),
% 0.13/0.43 inference(negated_conjecture,[status(cth)],[f3])).
% 0.13/0.43 tff(f5,plain,(
% 0.13/0.43 (emptysetE = ! [X0 : $i] : (in(X0,emptyset) => ! [X1 : $o] : X1))),
% 0.13/0.43 inference(rectify,[],[f1])).
% 0.13/0.43 tff(f6,plain,(
% 0.13/0.43 emptysetE <=> ! [X0 : $i] : (in(X0,emptyset) => ! [X1 : $o] : ($true = X1))),
% 0.13/0.43 inference(fool_elimination,[],[f5])).
% 0.13/0.43 tff(f7,plain,(
% 0.13/0.43 (setadjoinE = ! [X0 : $i,X1 : $i,X2 : $i] : (in(X2,setadjoin(X0,X1)) => ! [X3 : $o] : ((X2 = X0 => X3) => ((in(X2,X1) => X3) => X3))))),
% 0.13/0.43 inference(rectify,[],[f2])).
% 0.13/0.43 tff(f8,plain,(
% 0.13/0.43 setadjoinE <=> ! [X0 : $i,X1 : $i,X2 : $i] : (in(X2,setadjoin(X0,X1)) => ! [X3 : $o] : ((X0 = X2 => ($true = X3)) => ((in(X2,X1) => ($true = X3)) => ($true = X3))))),
% 0.13/0.43 inference(fool_elimination,[],[f7])).
% 0.13/0.43 tff(f9,plain,(
% 0.13/0.43 setadjoinE => ! [X0 : $i,X1 : $i,X2 : $i] : (in(X2,setadjoin(X0,X1)) => ! [X3 : $o] : ((X0 = X2 => ($true = X3)) => ((in(X2,X1) => ($true = X3)) => ($true = X3))))),
% 0.13/0.43 inference(unused_predicate_definition_removal,[],[f8])).
% 0.13/0.43 tff(f10,plain,(
% 0.13/0.43 emptysetE => ! [X0 : $i] : (in(X0,emptyset) => ! [X1 : $o] : ($true = X1))),
% 0.13/0.43 inference(unused_predicate_definition_removal,[],[f6])).
% 0.13/0.43 tff(f11,plain,(
% 0.13/0.43 ! [X0 : $i] : (! [X1 : $o] : ($true = X1) | ~in(X0,emptyset)) | ~emptysetE),
% 0.13/0.43 inference(ennf_transformation,[],[f10])).
% 0.13/0.43 tff(f12,plain,(
% 0.13/0.43 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $o] : ((($true = X3) | (($true != X3) & in(X2,X1))) | (($true != X3) & X0 = X2)) | ~in(X2,setadjoin(X0,X1))) | ~setadjoinE),
% 0.13/0.43 inference(ennf_transformation,[],[f9])).
% 0.13/0.43 tff(f13,plain,(
% 0.13/0.43 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $o] : (($true = X3) | (($true != X3) & in(X2,X1)) | (($true != X3) & X0 = X2)) | ~in(X2,setadjoin(X0,X1))) | ~setadjoinE),
% 0.13/0.43 inference(flattening,[],[f12])).
% 0.13/0.43 tff(f14,plain,(
% 0.13/0.43 (? [X0 : $i,X1 : $i] : (X0 != X1 & in(X0,setadjoin(X1,emptyset))) & setadjoinE) & emptysetE),
% 0.13/0.43 inference(ennf_transformation,[],[f4])).
% 0.13/0.43 tff(f15,plain,(
% 0.13/0.43 ? [X0 : $i,X1 : $i] : (X0 != X1 & in(X0,setadjoin(X1,emptyset))) & setadjoinE & emptysetE),
% 0.13/0.43 inference(flattening,[],[f14])).
% 0.13/0.43 tff(f16,plain,(
% 0.13/0.43 (sK0 != sK1 & in(sK0,setadjoin(sK1,emptyset))) & setadjoinE & emptysetE),
% 0.13/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15])).
% 0.13/0.43 tff(f17,plain,(
% 0.13/0.43 ( ! [X0 : $i,X1 : $o] : (($true = X1) | ~in(X0,emptyset) | ~emptysetE) )),
% 0.13/0.43 inference(cnf_transformation,[],[f11])).
% 0.13/0.43 tff(f18,plain,(
% 0.13/0.43 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (($true = X3) | in(X2,X1) | X0 = X2 | ~in(X2,setadjoin(X0,X1)) | ~setadjoinE) )),
% 0.13/0.43 inference(cnf_transformation,[],[f13])).
% 0.13/0.43 tff(f22,plain,(
% 0.13/0.43 emptysetE),
% 0.13/0.43 inference(cnf_transformation,[],[f16])).
% 0.13/0.43 tff(f23,plain,(
% 0.13/0.43 setadjoinE),
% 0.13/0.43 inference(cnf_transformation,[],[f16])).
% 0.13/0.43 tff(f24,plain,(
% 0.13/0.43 in(sK0,setadjoin(sK1,emptyset))),
% 0.13/0.43 inference(cnf_transformation,[],[f16])).
% 0.13/0.43 tff(f25,plain,(
% 0.13/0.43 sK0 != sK1),
% 0.13/0.43 inference(cnf_transformation,[],[f16])).
% 0.13/0.43 tff(f26,definition,(
% 0.13/0.43 ($true != $false)),
% 0.13/0.43 introduced(theory,[fool_distinctness_axiom])).
% 0.13/0.43 tff(f29,plain,(
% 0.13/0.43 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (($true = X3) | in(X2,X1) | X0 = X2 | ~in(X2,setadjoin(X0,X1))) )),
% 0.13/0.43 inference(forward_subsumption_resolution,[],[f18,f23])).
% 0.13/0.43 tff(f30,plain,(
% 0.13/0.43 ( ! [X0 : $i,X1 : $o] : (($true = X1) | ~in(X0,emptyset)) )),
% 0.13/0.43 inference(forward_subsumption_resolution,[],[f17,f22])).
% 0.13/0.43 tff(f32,definition,(
% 0.13/0.43 spl2_1 <=> ! [X2 : $i,X0 : $i,X1 : $i] : (in(X2,X1) | ~in(X2,setadjoin(X0,X1)) | X0 = X2)),
% 0.13/0.43 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.13/0.43 tff(f33,plain,(
% 0.13/0.43 ( ! [X2 : $i,X0 : $i,X1 : $i] : (~in(X2,setadjoin(X0,X1)) | in(X2,X1) | X0 = X2) ) | ~spl2_1),
% 0.13/0.43 inference(avatar_component_clause,[],[f32])).
% 0.13/0.43 tff(f35,definition,(
% 0.13/0.43 spl2_2 <=> ! [X3 : $o] : ($true = X3)),
% 0.13/0.43 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.13/0.43 tff(f36,plain,(
% 0.13/0.43 ( ! [X3 : $o] : (($true = X3)) ) | ~spl2_2),
% 0.13/0.43 inference(avatar_component_clause,[],[f35])).
% 0.13/0.43 tff(f37,plain,(
% 0.13/0.43 spl2_1 | spl2_2),
% 0.13/0.43 inference(avatar_split_clause,[],[f29,f35,f32])).
% 0.13/0.43 tff(f39,definition,(
% 0.13/0.43 spl2_3 <=> ! [X0 : $i] : ~in(X0,emptyset)),
% 0.13/0.43 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.13/0.43 tff(f40,plain,(
% 0.13/0.43 ( ! [X0 : $i] : (~in(X0,emptyset)) ) | ~spl2_3),
% 0.13/0.43 inference(avatar_component_clause,[],[f39])).
% 0.13/0.43 tff(f41,plain,(
% 0.13/0.43 spl2_3 | spl2_2),
% 0.13/0.43 inference(avatar_split_clause,[],[f30,f35,f39])).
% 0.13/0.43 tff(f42,plain,(
% 0.13/0.43 ( ! [X0 : $o,X1 : $o] : ((X0 = X1)) ) | ~spl2_2),
% 0.13/0.43 inference(superposition,[],[f36,f36])).
% 0.13/0.43 tff(f45,plain,(
% 0.13/0.43 ( ! [X0 : $o] : (($false != X0)) ) | ~spl2_2),
% 0.13/0.43 inference(superposition,[],[f26,f36])).
% 0.13/0.43 tff(f52,plain,(
% 0.13/0.43 $false | ~spl2_2),
% 0.13/0.43 inference(forward_subsumption_resolution,[],[f45,f42])).
% 0.13/0.43 tff(f53,plain,(
% 0.13/0.43 ~spl2_2),
% 0.13/0.43 inference(avatar_contradiction_clause,[],[f52])).
% 0.13/0.43 tff(f54,plain,(
% 0.13/0.43 in(sK0,emptyset) | sK0 = sK1 | ~spl2_1),
% 0.13/0.43 inference(resolution,[],[f33,f24])).
% 0.13/0.43 tff(f55,plain,(
% 0.13/0.43 sK0 = sK1 | (~spl2_1 | ~spl2_3)),
% 0.13/0.43 inference(forward_subsumption_resolution,[],[f54,f40])).
% 0.13/0.43 tff(f56,plain,(
% 0.13/0.43 $false | (~spl2_1 | ~spl2_3)),
% 0.13/0.43 inference(forward_subsumption_resolution,[],[f55,f25])).
% 0.13/0.43 tff(f57,plain,(
% 0.13/0.43 ~spl2_1 | ~spl2_3),
% 0.13/0.43 inference(avatar_contradiction_clause,[],[f56])).
% 0.13/0.43 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f37])).
% 0.13/0.43 cnf(s2, plain, spl2_2 | spl2_3, inference(sat_conversion,[],[f41])).
% 0.13/0.43 cnf(s5, plain, ~spl2_2, inference(sat_conversion,[],[f53])).
% 0.13/0.43 cnf(s6, plain, ~spl2_1 | ~spl2_3, inference(sat_conversion,[],[f57])).
% 0.13/0.43 cnf(s7, plain, spl2_3, inference(rat,[],[s2,s5])).
% 0.13/0.43 cnf(s8, plain, ~spl2_1, inference(rat,[],[s6,s7])).
% 0.13/0.43 cnf(s9, plain, $false, inference(rat,[],[s1,s5,s8])).
% 0.13/0.43 tff(f58,plain,(
% 0.13/0.43 $false),
% 0.13/0.43 inference(avatar_sat_refutation,[],[s9])).
% 0.13/0.43 % SZS output end Proof for theBenchmark
% 0.13/0.43 % (883485)------------------------------
% 0.13/0.43 % (883485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.43 % (883485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.43 % (883485)CaDiCaL version: 2.1.3
% 0.13/0.43 % (883485)Termination reason: Refutation
% 0.13/0.43 % (883485)Time elapsed: 0.002 s
% 0.13/0.43 % (883485)Peak memory usage: 12 MB
% 0.13/0.43 % (883485)Instructions burned: 2 (million)
% 0.13/0.43 % (883475)Success in time 0.026 s
% 0.13/0.43 % Vampire exiting
%------------------------------------------------------------------------------