%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP005+4 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 11:27:47 AM UTC 2026
% Result : Theorem 8.53s 3.02s
% Output : Refutation 11.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 65 ( 62 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1314,axiom,
! [X0,X1,X2,X3] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2),X3))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2))),c_2Epair_2ECURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2),X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) ).
fof(f1315,axiom,
! [X0,X1,X2,X3] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X3))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) ).
fof(f1401,axiom,
! [X0,X1,X2,X3] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X3))))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2ECURRY__UNCURRY__THM) ).
fof(f4978,axiom,
! [X0,X1,X2] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool)),c_2Eset__relation_2Erel__to__reln_2E0),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eset__relation_2Erel__to__reln_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).
fof(f4979,axiom,
! [X0,X1,X2] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),X2))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eset__relation_2Ereln__to__rel_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).
fof(f5132,axiom,
! [X0,X1] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool)),c_2Eset__relation_2Erel__to__reln_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY) ).
fof(f5133,axiom,
! [X0,X1] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))),c_2Epair_2ECURRY_2E0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Ereln__to__rel__IS__CURRY) ).
fof(f5134,conjecture,
! [X0,X1,X2] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2))))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Erel__to__reln__inv) ).
fof(f5135,negated_conjecture,
~ ! [X0,X1,X2] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2))))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),
inference(negated_conjecture,[status(cth)],[f5134]) ).
fof(f5290,plain,
? [X0,X1,X2] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2) != s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2))))),
inference(ennf_transformation,[],[f5135]) ).
fof(f6246,plain,
s(tyop_2Emin_2Efun(sK147,tyop_2Emin_2Efun(sK148,tyop_2Emin_2Ebool)),sK149) != s(tyop_2Emin_2Efun(sK147,tyop_2Emin_2Efun(sK148,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(sK147,sK148),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(sK147,tyop_2Emin_2Efun(sK148,tyop_2Emin_2Ebool)),sK149))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147,sK148,sK149]),skolemize(X0,sK147),skolemize(X1,sK148),skolemize(X2,sK149)],[f5290]) ).
fof(f8304,plain,
! [X2,X0,X1] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool)),c_2Eset__relation_2Erel__to__reln_2E0),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2))),
inference(cnf_transformation,[],[f4978]) ).
fof(f8305,plain,
! [X2,X0,X1] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),X2))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),X2))),
inference(cnf_transformation,[],[f4979]) ).
fof(f8599,plain,
! [X0,X1] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool)),c_2Eset__relation_2Erel__to__reln_2E0),
inference(cnf_transformation,[],[f5132]) ).
fof(f8600,plain,
! [X0,X1] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))),c_2Epair_2ECURRY_2E0),
inference(cnf_transformation,[],[f5133]) ).
fof(f8601,plain,
s(tyop_2Emin_2Efun(sK147,tyop_2Emin_2Efun(sK148,tyop_2Emin_2Ebool)),sK149) != s(tyop_2Emin_2Efun(sK147,tyop_2Emin_2Efun(sK148,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(sK147,sK148),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(sK147,tyop_2Emin_2Efun(sK148,tyop_2Emin_2Ebool)),sK149))))),
inference(cnf_transformation,[],[f6246]) ).
fof(f10819,plain,
! [X2,X3,X0,X1] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X3))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X3))),
inference(cnf_transformation,[],[f1315]) ).
fof(f11306,plain,
! [X2,X3,X0,X1] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2),X3))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2))),c_2Epair_2ECURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2),X3))),
inference(cnf_transformation,[],[f1314]) ).
fof(f12032,plain,
! [X2,X3,X0,X1] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X3) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),X2),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X3))))),
inference(cnf_transformation,[],[f1401]) ).
fof(f13468,plain,
! [X2,X0,X1] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),X2))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))),c_2Epair_2ECURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),X2))),
inference(forward_demodulation,[],[f8305,f8600]) ).
fof(f13469,plain,
! [X2,X0,X1] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2))),
inference(forward_demodulation,[],[f8304,f8599]) ).
fof(f13731,plain,
! [X2,X0,X1] : s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),X2))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),X2))),
inference(forward_demodulation,[],[f13468,f11306]) ).
fof(f13732,plain,
! [X2,X0,X1] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2))),
inference(forward_demodulation,[],[f13469,f10819]) ).
fof(f14294,plain,
s(tyop_2Emin_2Efun(sK147,tyop_2Emin_2Efun(sK148,tyop_2Emin_2Ebool)),sK149) != s(tyop_2Emin_2Efun(sK147,tyop_2Emin_2Efun(sK148,tyop_2Emin_2Ebool)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(sK147,sK148),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(sK147,tyop_2Emin_2Efun(sK148,tyop_2Emin_2Ebool)),sK149))))),
inference(superposition,[],[f8601,f13731]) ).
fof(f14295,plain,
s(tyop_2Emin_2Efun(sK147,tyop_2Emin_2Efun(sK148,tyop_2Emin_2Ebool)),sK149) != s(tyop_2Emin_2Efun(sK147,tyop_2Emin_2Efun(sK148,tyop_2Emin_2Ebool)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(sK147,sK148),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(sK147,tyop_2Emin_2Efun(sK148,tyop_2Emin_2Ebool)),sK149))))),
inference(forward_demodulation,[],[f14294,f13732]) ).
fof(f14296,plain,
$false,
inference(forward_subsumption_resolution,[],[f14295,f12032]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP005+4 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 % Computer : n004.cluster.edu
% 0.10/0.41 % Model : x86_64 x86_64
% 0.10/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.41 % Memory : 8046.5625MB
% 0.10/0.41 % OS : Linux 6.8.0-71-generic
% 0.10/0.41 % CPULimit : 300
% 0.10/0.41 % WCLimit : 300
% 0.10/0.41 % DateTime : Sun Sep 27 11:50:23 UTC 2026
% 0.10/0.42 % CPUTime :
% 0.10/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.45 Running first-order theorem proving
% 0.10/0.45 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.53/3.02 % (3382721)Detected formulas, will run a generic FOF schedule.
% 8.53/3.02 % (3382747)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3760091202:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2992 on theBenchmark for (2992ds/134677Mi)
% 8.53/3.02 % (3382750)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2042293528:i=119:av=off:ss=axioms_2992 on theBenchmark for (2992ds/119Mi)
% 8.53/3.02 % (3382751)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3536562386:s2a=on:i=139:gtg=position_2992 on theBenchmark for (2992ds/139Mi)
% 8.53/3.02 % (3382752)dis-21_1_sil=8000:lcm=predicate:random_seed=1566236111:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2992 on theBenchmark for (2992ds/129Mi)
% 8.53/3.02 % (3382746)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=877143626:i=141193_2992 on theBenchmark for (2992ds/141193Mi)
% 8.53/3.02 % (3382748)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4226904839:i=141695:sd=1:nm=32:gsp=on:ss=included_2992 on theBenchmark for (2992ds/141695Mi)
% 8.53/3.02 % (3382749)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1638750884:i=109:sd=1:ins=1:gsp=on:ss=axioms_2992 on theBenchmark for (2992ds/109Mi)
% 8.53/3.02 % (3382749)Refutation not found, incomplete strategy
% 8.53/3.02 % (3382749)------------------------------
% 8.53/3.02 % (3382749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/3.02 % (3382749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/3.02 % (3382749)CaDiCaL version: 2.1.3
% 8.53/3.02 % (3382749)Termination reason: Refutation not found, incomplete strategy
% 8.53/3.02 % (3382749)Time elapsed: 0.031 s
% 8.53/3.02 % (3382749)Peak memory usage: 94 MB
% 8.53/3.02 % (3382749)Instructions burned: 49 (million)
% 8.53/3.02 % (3382751)Instruction limit reached!
% 8.53/3.02 % (3382751)------------------------------
% 8.53/3.02 % (3382751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/3.02 % (3382751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/3.02 % (3382751)CaDiCaL version: 2.1.3
% 8.53/3.02 % (3382751)Termination reason: Instruction limit
% 8.53/3.02 % (3382751)Termination phase: Property scanning
% 8.53/3.02 % (3382751)Time elapsed: 0.050 s
% 8.53/3.02 % (3382751)Peak memory usage: 90 MB
% 8.53/3.02 % (3382751)Instructions burned: 142 (million)
% 8.53/3.02 % (3382750)Instruction limit reached!
% 8.53/3.02 % (3382750)------------------------------
% 8.53/3.02 % (3382750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/3.02 % (3382750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/3.02 % (3382750)CaDiCaL version: 2.1.3
% 8.53/3.02 % (3382750)Termination reason: Instruction limit
% 8.53/3.02 % (3382750)Termination phase: Property scanning
% 8.53/3.02 % (3382750)Time elapsed: 0.066 s
% 8.53/3.02 % (3382750)Peak memory usage: 93 MB
% 8.53/3.02 % (3382750)Instructions burned: 121 (million)
% 8.53/3.02 % (3382752)Instruction limit reached!
% 8.53/3.02 % (3382752)------------------------------
% 8.53/3.02 % (3382752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/3.02 % (3382752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/3.02 % (3382752)CaDiCaL version: 2.1.3
% 8.53/3.02 % (3382752)Termination reason: Instruction limit
% 8.53/3.02 % (3382752)Termination phase: Unused predicate definition removal
% 8.53/3.02 % (3382752)Time elapsed: 0.075 s
% 8.53/3.02 % (3382752)Peak memory usage: 92 MB
% 8.53/3.02 % (3382752)Instructions burned: 129 (million)
% 8.53/3.02 % (3382760)lrs+10_1_sil=8000:sp=occurrence:random_seed=3097497874:i=285:sd=3:ss=axioms:sgt=8_2990 on theBenchmark for (2990ds/285Mi)
% 8.53/3.02 % (3382761)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3236005744:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2990 on theBenchmark for (2990ds/157Mi)
% 8.53/3.02 % (3382762)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2029060135:i=325:sd=1:ss=axioms:sgt=32_2990 on theBenchmark for (2990ds/325Mi)
% 8.53/3.02 % (3382762)Refutation not found, incomplete strategy
% 8.53/3.02 % (3382762)------------------------------
% 8.53/3.02 % (3382762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/3.02 % (3382762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/3.02 % (3382762)CaDiCaL version: 2.1.3
% 8.53/3.02 % (3382762)Termination reason: Refutation not found, incomplete strategy
% 8.53/3.02 % (3382762)Time elapsed: 0.037 s
% 8.53/3.02 % (3382762)Peak memory usage: 94 MB
% 8.53/3.02 % (3382762)Instructions burned: 52 (million)
% 8.53/3.02 % (3382749)------------------------------
% 8.53/3.02 % (3382749)------------------------------
% 8.53/3.02 % (3382761)Instruction limit reached!
% 8.53/3.02 % (3382761)------------------------------
% 8.53/3.02 % (3382761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/3.02 % (3382761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/3.02 % (3382761)CaDiCaL version: 2.1.3
% 8.53/3.02 % (3382761)Termination reason: Instruction limit
% 8.53/3.02 % (3382761)Termination phase: Property scanning
% 8.53/3.02 % (3382761)Time elapsed: 0.108 s
% 8.53/3.02 % (3382761)Peak memory usage: 90 MB
% 8.53/3.02 % (3382761)Instructions burned: 159 (million)
% 8.53/3.02 % (3382760)Instruction limit reached!
% 8.53/3.02 % (3382760)------------------------------
% 8.53/3.02 % (3382760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/3.02 % (3382760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/3.02 % (3382760)CaDiCaL version: 2.1.3
% 8.53/3.02 % (3382760)Termination reason: Instruction limit
% 8.53/3.02 % (3382760)Termination phase: Saturation
% 8.53/3.02 % (3382760)Time elapsed: 0.160 s
% 8.53/3.02 % (3382760)Peak memory usage: 97 MB
% 8.53/3.02 % (3382760)Instructions burned: 285 (million)
% 8.53/3.02 % (3382766)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2988204503:s2a=on:i=248:s2at=1.23:gtg=position_2988 on theBenchmark for (2988ds/248Mi)
% 8.53/3.02 % (3382767)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2651185242:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2987 on theBenchmark for (2987ds/294Mi)
% 8.53/3.02 % (3382762)------------------------------
% 8.53/3.02 % (3382762)------------------------------
% 8.53/3.02 % (3382768)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3365797911:i=2350_2987 on theBenchmark for (2987ds/2350Mi)
% 8.53/3.02 % (3382766)Instruction limit reached!
% 8.53/3.02 % (3382766)------------------------------
% 8.53/3.02 % (3382766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/3.02 % (3382766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/3.02 % (3382766)CaDiCaL version: 2.1.3
% 8.53/3.02 % (3382766)Termination reason: Instruction limit
% 8.53/3.02 % (3382766)Termination phase: SInE selection
% 8.53/3.02 % (3382766)Time elapsed: 0.094 s
% 8.53/3.02 % (3382766)Peak memory usage: 91 MB
% 8.53/3.02 % (3382766)Instructions burned: 249 (million)
% 8.53/3.02 % (3382767)Instruction limit reached!
% 8.53/3.02 % (3382767)------------------------------
% 8.53/3.02 % (3382767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/3.02 % (3382767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/3.02 % (3382767)CaDiCaL version: 2.1.3
% 8.53/3.02 % (3382767)Termination reason: Instruction limit
% 8.53/3.02 % (3382767)Termination phase: Saturation
% 8.53/3.02 % (3382767)Time elapsed: 0.149 s
% 8.53/3.02 % (3382767)Peak memory usage: 97 MB
% 8.53/3.02 % (3382767)Instructions burned: 294 (million)
% 8.53/3.02 % (3382772)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=803794810:cts=off:i=113:fsr=off:ss=included:sgt=4_2986 on theBenchmark for (2986ds/113Mi)
% 8.53/3.02 % (3382773)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3944642037:i=127:av=off:fsr=off:sup=off_2985 on theBenchmark for (2985ds/127Mi)
% 8.53/3.02 % (3382772)Instruction limit reached!
% 8.53/3.02 % (3382772)------------------------------
% 8.53/3.02 % (3382772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/3.02 % (3382772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/3.02 % (3382772)CaDiCaL version: 2.1.3
% 8.53/3.02 % (3382772)Termination reason: Instruction limit
% 8.53/3.02 % (3382772)Termination phase: Preprocessing 3
% 8.53/3.02 % (3382772)Time elapsed: 0.069 s
% 8.53/3.02 % (3382772)Peak memory usage: 93 MB
% 8.53/3.02 % (3382772)Instructions burned: 113 (million)
% 8.53/3.02 % (3382773)Instruction limit reached!
% 8.53/3.02 % (3382773)------------------------------
% 8.53/3.02 % (3382773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/3.02 % (3382773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/3.02 % (3382773)CaDiCaL version: 2.1.3
% 8.53/3.02 % (3382773)Termination reason: Instruction limit
% 8.53/3.02 % (3382773)Termination phase: Preprocessing 3
% 8.53/3.02 % (3382773)Time elapsed: 0.075 s
% 8.53/3.02 % (3382773)Peak memory usage: 94 MB
% 8.53/3.02 % (3382773)Instructions burned: 129 (million)
% 8.53/3.02 % (3382774)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2278124033:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2984 on theBenchmark for (2984ds/114Mi)
% 8.53/3.02 % (3382774)Instruction limit reached!
% 8.53/3.02 % (3382774)------------------------------
% 8.53/3.02 % (3382774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/3.02 % (3382774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/3.02 % (3382774)CaDiCaL version: 2.1.3
% 8.53/3.02 % (3382774)Termination reason: Instruction limit
% 8.53/3.02 % (3382774)Termination phase: Property scanning
% 8.53/3.02 % (3382774)Time elapsed: 0.042 s
% 8.53/3.02 % (3382774)Peak memory usage: 90 MB
% 8.53/3.02 % (3382774)Instructions burned: 117 (million)
% 8.53/3.02 % (3382777)lrs+10_1_sil=8000:sp=occurrence:random_seed=940491930:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2983 on theBenchmark for (2983ds/907Mi)
% 8.53/3.02 % (3382779)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=37308932:i=437:sd=1:aac=none:ss=included_2983 on theBenchmark for (2983ds/437Mi)
% 8.53/3.02 % (3382780)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3794710108:i=5202:ss=axioms:sgt=16_2982 on theBenchmark for (2982ds/5202Mi)
% 8.53/3.02 % (3382747)First to succeed.
% 8.53/3.02 % (3382747)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3382721"
% 8.53/3.02 % (3382779)Refutation not found, incomplete strategy
% 8.53/3.02 % (3382779)------------------------------
% 8.53/3.02 % (3382779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.53/3.02 % (3382779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.53/3.02 % (3382779)CaDiCaL version: 2.1.3
% 8.53/3.02 % (3382779)Termination reason: Refutation not found, incomplete strategy
% 8.53/3.02 % (3382779)Time elapsed: 0.198 s
% 8.53/3.02 % (3382779)Peak memory usage: 100 MB
% 8.53/3.02 % (3382779)Instructions burned: 408 (million)
% 8.53/3.02 % (3382747)Refutation found. Thanks to Tanya!
% 8.53/3.02 % SZS status Theorem for theBenchmark
% 8.53/3.02 % SZS output start Proof for theBenchmark
% See solution above
% 11.07/3.12 % (3382747)------------------------------
% 11.07/3.12 % (3382747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.07/3.12 % (3382747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.07/3.12 % (3382747)CaDiCaL version: 2.1.3
% 11.07/3.12 % (3382747)Termination reason: Refutation
% 11.07/3.12 % (3382747)Time elapsed: 1.132 s
% 11.07/3.12 % (3382747)Peak memory usage: 182 MB
% 11.07/3.12 % (3382747)Instructions burned: 3807 (million)
% 11.07/3.12 % (3382747)------------------------------
% 11.07/3.12 % (3382747)------------------------------
% 11.07/3.12 % (3382721)Success in time 2.128 s
% 11.07/3.12 % Vampire exiting
%------------------------------------------------------------------------------