%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP003+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 11:27:41 AM UTC 2026
% Result : Theorem 23.17s 4.19s
% Output : Refutation 23.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 20
% Syntax : Number of formulae : 112 ( 33 unt; 4 def)
% Number of atoms : 272 ( 114 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 296 ( 136 ~; 122 |; 26 &)
% ( 11 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 96 ( 0 sgn 88 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
fof(f5,axiom,
! [X0] :
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
fof(f38,axiom,
s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EONE) ).
fof(f39,axiom,
s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ETWO) ).
fof(f40,axiom,
! [X0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD__0) ).
fof(f41,axiom,
! [X0,X1] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X1))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MONO__EQ) ).
fof(f42,axiom,
! [X0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD1) ).
fof(f43,axiom,
! [X0,X1] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,X1))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__COMM) ).
fof(f44,axiom,
! [X0] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0))))
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__ODD) ).
fof(f46,axiom,
! [X0] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0))))
<=> ? [X1] : s(tyop_2Enum_2Enum,X0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__EXISTS) ).
fof(f47,axiom,
! [X0] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0))))
<=> ? [X1] : s(tyop_2Enum_2Enum,X0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X1))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EODD__EXISTS) ).
fof(f48,axiom,
! [X0,X1,X2] :
( ? [X3] :
( s(tyop_2Enum_2Enum,X1) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X3),s(tyop_2Enum_2Enum,X0))),s(tyop_2Enum_2Enum,X2)))
& p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X0)))) )
=> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X0))) = s(tyop_2Enum_2Enum,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__UNIQUE) ).
fof(f62,axiom,
! [X0] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0)
<=> p(s(tyop_2Emin_2Ebool,X0)) )
& ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
<=> p(s(tyop_2Emin_2Ebool,X0)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0)
<=> ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
<=> ~ p(s(tyop_2Emin_2Ebool,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
fof(f63,axiom,
! [X0,X1,X2] :
( s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X0,X1),s(X0,X2))) = s(X0,X1)
& s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X0,X1),s(X0,X2))) = s(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).
fof(f79,axiom,
! [X0] : p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ELESS__0) ).
fof(f95,conjecture,
! [X0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__2) ).
fof(f96,negated_conjecture,
~ ! [X0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f97,plain,
? [X0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) != s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
inference(ennf_transformation,[],[f96]) ).
fof(f101,plain,
! [X0,X1,X2] :
( s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X0))) = s(tyop_2Enum_2Enum,X2)
| ! [X3] :
( s(tyop_2Enum_2Enum,X1) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X3),s(tyop_2Enum_2Enum,X0))),s(tyop_2Enum_2Enum,X2)))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X0)))) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f146,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,sK12),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) != s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,sK12))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f97]) ).
fof(f161,plain,
! [X0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0))))
| ! [X1] : s(tyop_2Enum_2Enum,X0) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X1))) )
& ( ? [X1] : s(tyop_2Enum_2Enum,X0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X1)))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0)))) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f162,plain,
! [X0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0))))
| ! [X1] : s(tyop_2Enum_2Enum,X0) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X1))) )
& ( ? [X2] : s(tyop_2Enum_2Enum,X0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X2)))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0)))) ) ),
inference(rectify,[],[f161]) ).
fof(f163,plain,
! [X0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0))))
| ! [X1] : s(tyop_2Enum_2Enum,X0) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X1))) )
& ( s(tyop_2Enum_2Enum,X0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,sK13(X0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X2,sK13(X0))],[f162]) ).
fof(f165,plain,
! [X0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0))))
| p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0)))) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f166,plain,
! [X0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0))))
| ! [X1] : s(tyop_2Enum_2Enum,X0) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X1))))) )
& ( ? [X1] : s(tyop_2Enum_2Enum,X0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X1)))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0)))) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f167,plain,
! [X0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0))))
| ! [X1] : s(tyop_2Enum_2Enum,X0) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X1))))) )
& ( ? [X2] : s(tyop_2Enum_2Enum,X0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X2)))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0)))) ) ),
inference(rectify,[],[f166]) ).
fof(f168,plain,
! [X0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0))))
| ! [X1] : s(tyop_2Enum_2Enum,X0) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,X1))))) )
& ( s(tyop_2Enum_2Enum,X0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,sK14(X0))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X2,sK14(X0))],[f167]) ).
fof(f240,plain,
! [X0] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0)
| p(s(tyop_2Emin_2Ebool,X0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
& ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| p(s(tyop_2Emin_2Ebool,X0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f241,plain,
! [X0] :
( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) )
& ( p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0)
| p(s(tyop_2Emin_2Ebool,X0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
& ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| p(s(tyop_2Emin_2Ebool,X0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
inference(flattening,[],[f240]) ).
fof(f258,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,sK12),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) != s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,sK12))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
inference(cnf_transformation,[],[f146]) ).
fof(f290,plain,
! [X0] :
( s(tyop_2Enum_2Enum,X0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,sK13(X0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0)))) ),
inference(cnf_transformation,[],[f163]) ).
fof(f295,plain,
! [X0] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0))))
| p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0)))) ),
inference(cnf_transformation,[],[f165]) ).
fof(f297,plain,
! [X0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
inference(cnf_transformation,[],[f42]) ).
fof(f298,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
inference(cnf_transformation,[],[f39]) ).
fof(f299,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
inference(cnf_transformation,[],[f38]) ).
fof(f301,plain,
! [X0] :
( s(tyop_2Enum_2Enum,X0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,sK14(X0))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0)))) ),
inference(cnf_transformation,[],[f168]) ).
fof(f313,plain,
! [X2,X0,X1] : s(X0,X2) = s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X0,X1),s(X0,X2))),
inference(cnf_transformation,[],[f63]) ).
fof(f314,plain,
! [X2,X0,X1] : s(X0,X1) = s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X0,X1),s(X0,X2))),
inference(cnf_transformation,[],[f63]) ).
fof(f320,plain,
! [X2,X3,X0,X1] :
( s(tyop_2Enum_2Enum,X1) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X3),s(tyop_2Enum_2Enum,X0))),s(tyop_2Enum_2Enum,X2)))
| s(tyop_2Enum_2Enum,X2) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X0)))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X0)))) ),
inference(cnf_transformation,[],[f101]) ).
fof(f322,plain,
! [X0] : p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0)))))),
inference(cnf_transformation,[],[f79]) ).
fof(f323,plain,
! [X0] : s(tyop_2Enum_2Enum,X0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),
inference(cnf_transformation,[],[f40]) ).
fof(f411,plain,
! [X0,X1] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,X1))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X0))),
inference(cnf_transformation,[],[f43]) ).
fof(f447,plain,
! [X0,X1] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,X1))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X1))))),
inference(cnf_transformation,[],[f41]) ).
fof(f455,plain,
! [X0] :
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ p(s(tyop_2Emin_2Ebool,X0)) ),
inference(cnf_transformation,[],[f241]) ).
fof(f513,plain,
! [X0] :
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(cnf_transformation,[],[f5]) ).
fof(f514,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(cnf_transformation,[],[f3]) ).
fof(f585,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),
inference(forward_demodulation,[],[f298,f299]) ).
fof(f586,plain,
! [X0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),
inference(forward_demodulation,[],[f297,f299]) ).
fof(f590,plain,
s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,sK12),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) != s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,sK12))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),
inference(forward_demodulation,[],[f258,f299]) ).
fof(f592,plain,
( s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,sK12),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) != s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,sK12))) ),
inference(superposition,[],[f590,f513]) ).
fof(f602,plain,
( s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) != s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,sK12),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
| s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,sK12))) ),
inference(forward_demodulation,[],[f592,f313]) ).
fof(f604,definition,
( spl37_11
<=> s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,sK12))) ),
introduced(definition,[new_symbols(definition,[spl37_11])],[avatar_definition]) ).
fof(f605,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,sK12)))
| spl37_11 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f606,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,sK12)))
| ~ spl37_11 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f608,definition,
( spl37_12
<=> s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,sK12),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) ),
introduced(definition,[new_symbols(definition,[spl37_12])],[avatar_definition]) ).
fof(f609,plain,
( s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,sK12),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
| ~ spl37_12 ),
inference(avatar_component_clause,[],[f608]) ).
fof(f610,plain,
( s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) != s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,sK12),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
| spl37_12 ),
inference(avatar_component_clause,[],[f608]) ).
fof(f611,plain,
( spl37_11
| ~ spl37_12 ),
inference(avatar_split_clause,[],[f602,f608,f604]) ).
fof(f670,plain,
! [X0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),
inference(superposition,[],[f447,f585]) ).
fof(f701,plain,
! [X2,X0,X1] :
( s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X1)))
| s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,X1))) != s(tyop_2Enum_2Enum,X2)
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,X1)))) ),
inference(superposition,[],[f320,f323]) ).
fof(f714,plain,
! [X2,X0,X1] :
( s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X1)))
| s(tyop_2Enum_2Enum,X2) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,X1)))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Enum_2Enum,X1)))) ),
inference(superposition,[],[f320,f586]) ).
fof(f761,plain,
! [X0] :
( s(tyop_2Enum_2Enum,X0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,sK13(X0)),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0)))) ),
inference(superposition,[],[f290,f411]) ).
fof(f845,plain,
! [X0] :
( s(tyop_2Enum_2Enum,X0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,sK14(X0)),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0)))) ),
inference(superposition,[],[f301,f411]) ).
fof(f1641,plain,
( s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,sK12),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) != s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))
| ~ spl37_11 ),
inference(superposition,[],[f590,f606]) ).
fof(f1647,plain,
( s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,sK12),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
| ~ spl37_11 ),
inference(forward_demodulation,[],[f1641,f314]) ).
fof(f2031,plain,
( s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
| ~ spl37_11
| ~ spl37_12 ),
inference(forward_demodulation,[],[f1647,f609]) ).
fof(f2565,plain,
p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))),
inference(superposition,[],[f322,f585]) ).
fof(f2804,plain,
( ! [X0] :
( s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
| s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) )
| ~ spl37_12 ),
inference(superposition,[],[f609,f701]) ).
fof(f2844,plain,
( ! [X0] :
( s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) )
| ~ spl37_11
| ~ spl37_12 ),
inference(forward_subsumption_resolution,[],[f2804,f2031]) ).
fof(f2847,plain,
( ! [X0] : s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
| ~ spl37_11
| ~ spl37_12 ),
inference(forward_subsumption_resolution,[],[f2844,f2565]) ).
fof(f2872,plain,
( ! [X0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0))))
| s(tyop_2Enum_2Enum,X0) != s(tyop_2Enum_2Enum,sK12) )
| ~ spl37_11
| ~ spl37_12 ),
inference(superposition,[],[f2847,f761]) ).
fof(f2895,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,sK12)
| ~ spl37_11
| ~ spl37_12 ),
inference(superposition,[],[f2872,f606]) ).
fof(f2900,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ~ spl37_11
| ~ spl37_12 ),
inference(trivial_inequality_removal,[],[f2895]) ).
fof(f2903,plain,
( $false
| ~ spl37_11
| ~ spl37_12 ),
inference(forward_subsumption_resolution,[],[f2900,f514]) ).
fof(f2904,plain,
( ~ spl37_11
| ~ spl37_12 ),
inference(avatar_contradiction_clause,[],[f2903]) ).
fof(f2915,plain,
( ! [X0] :
( s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))
| s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) )
| spl37_12 ),
inference(superposition,[],[f610,f714]) ).
fof(f2916,plain,
( ! [X0] :
( s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) )
| spl37_12 ),
inference(trivial_inequality_removal,[],[f2915]) ).
fof(f2917,plain,
( ! [X0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))
| s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) )
| spl37_12 ),
inference(forward_demodulation,[],[f2916,f670]) ).
fof(f2919,plain,
( ! [X0] : s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))
| spl37_12 ),
inference(forward_subsumption_resolution,[],[f2917,f322]) ).
fof(f2921,definition,
( spl37_15
<=> ! [X0] : s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) ),
introduced(definition,[new_symbols(definition,[spl37_15])],[avatar_definition]) ).
fof(f2922,plain,
( ! [X0] : s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
| ~ spl37_15 ),
inference(avatar_component_clause,[],[f2921]) ).
fof(f2924,plain,
( ! [X0] :
( s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
| s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) )
| ~ spl37_11 ),
inference(superposition,[],[f1647,f701]) ).
fof(f2926,plain,
( ! [X0] :
( s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) )
| ~ spl37_11 ),
inference(trivial_inequality_removal,[],[f2924]) ).
fof(f2927,plain,
( ! [X0] : s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))
| ~ spl37_11 ),
inference(forward_subsumption_resolution,[],[f2926,f2565]) ).
fof(f2928,plain,
( spl37_15
| ~ spl37_11 ),
inference(avatar_split_clause,[],[f2927,f604,f2921]) ).
fof(f2952,plain,
( ! [X0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0))))
| s(tyop_2Enum_2Enum,X0) != s(tyop_2Enum_2Enum,sK12) )
| spl37_12 ),
inference(superposition,[],[f2919,f845]) ).
fof(f2977,plain,
( ! [X0] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0))))
| s(tyop_2Enum_2Enum,X0) != s(tyop_2Enum_2Enum,sK12) )
| spl37_12 ),
inference(resolution,[],[f2952,f295]) ).
fof(f3061,plain,
( ! [X0] :
( s(tyop_2Enum_2Enum,X0) != s(tyop_2Enum_2Enum,sK12)
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0)))) )
| ~ spl37_15 ),
inference(superposition,[],[f2922,f761]) ).
fof(f3062,plain,
( ! [X0] : s(tyop_2Enum_2Enum,X0) != s(tyop_2Enum_2Enum,sK12)
| spl37_12
| ~ spl37_15 ),
inference(forward_subsumption_resolution,[],[f3061,f2977]) ).
fof(f3083,plain,
( $false
| spl37_12
| ~ spl37_15 ),
inference(equality_resolution,[],[f3062]) ).
fof(f3084,plain,
( spl37_12
| ~ spl37_15 ),
inference(avatar_contradiction_clause,[],[f3083]) ).
fof(f3086,definition,
( spl37_18
<=> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,sK12)))) ),
introduced(definition,[new_symbols(definition,[spl37_18])],[avatar_definition]) ).
fof(f3087,plain,
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,sK12))))
| ~ spl37_18 ),
inference(avatar_component_clause,[],[f3086]) ).
fof(f3088,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,sK12))))
| spl37_18 ),
inference(avatar_component_clause,[],[f3086]) ).
fof(f3094,plain,
( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,sK12))))
| spl37_11 ),
inference(superposition,[],[f605,f455]) ).
fof(f3097,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,sK12))))
| spl37_11 ),
inference(trivial_inequality_removal,[],[f3094]) ).
fof(f3104,plain,
( s(tyop_2Enum_2Enum,sK12) != s(tyop_2Enum_2Enum,sK12)
| spl37_12
| spl37_18 ),
inference(resolution,[],[f2977,f3088]) ).
fof(f3130,plain,
( $false
| spl37_12
| spl37_18 ),
inference(trivial_inequality_removal,[],[f3104]) ).
fof(f3131,plain,
( spl37_12
| spl37_18 ),
inference(avatar_contradiction_clause,[],[f3130]) ).
fof(f3133,plain,
( $false
| spl37_11
| ~ spl37_18 ),
inference(forward_subsumption_resolution,[],[f3097,f3087]) ).
fof(f3134,plain,
( spl37_11
| ~ spl37_18 ),
inference(avatar_contradiction_clause,[],[f3133]) ).
cnf(s8,plain,
( spl37_11
| ~ spl37_12 ),
inference(sat_conversion,[],[f611]) ).
cnf(s12,plain,
( ~ spl37_11
| ~ spl37_12 ),
inference(sat_conversion,[],[f2904]) ).
cnf(s16,plain,
( ~ spl37_11
| spl37_15 ),
inference(sat_conversion,[],[f2928]) ).
cnf(s18,plain,
( spl37_12
| ~ spl37_15 ),
inference(sat_conversion,[],[f3084]) ).
cnf(s20,plain,
( spl37_12
| spl37_18 ),
inference(sat_conversion,[],[f3131]) ).
cnf(s21,plain,
( spl37_11
| ~ spl37_18 ),
inference(sat_conversion,[],[f3134]) ).
cnf(s25,plain,
spl37_11,
inference(rat,[],[s20,s8,s21]) ).
cnf(s26,plain,
spl37_15,
inference(rat,[],[s16,s25]) ).
cnf(s27,plain,
~ spl37_12,
inference(rat,[],[s12,s25]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s18,s26,s27]) ).
fof(f3135,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP003+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 % Computer : n014.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 27 11:48:16 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.47 Running first-order theorem proving
% 0.22/0.47 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.46/3.84 % (666317)Detected formulas, will run a generic FOF schedule.
% 19.46/3.84 % (666322)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=4250252121:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 19.46/3.84 % (666327)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2234859842:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 19.46/3.84 % (666326)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2018864371:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 19.46/3.84 % (666325)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2676731776:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 19.46/3.84 % (666328)dis-21_1_sil=8000:lcm=predicate:random_seed=1577359480:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 19.46/3.84 % (666323)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=1541805097:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 19.46/3.84 % (666324)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=2896054873:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 19.46/3.84 % (666325)Instruction limit reached!
% 19.46/3.84 % (666325)------------------------------
% 19.46/3.84 % (666325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.46/3.84 % (666325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.46/3.84 % (666325)CaDiCaL version: 2.1.3
% 19.46/3.84 % (666325)Termination reason: Instruction limit
% 19.46/3.84 % (666325)Termination phase: Saturation
% 19.46/3.84 % (666325)Time elapsed: 0.101 s
% 19.46/3.84 % (666325)Peak memory usage: 89 MB
% 19.46/3.84 % (666325)Instructions burned: 110 (million)
% 19.46/3.84 % (666326)Instruction limit reached!
% 19.46/3.84 % (666326)------------------------------
% 19.46/3.84 % (666326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.46/3.84 % (666326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.46/3.84 % (666326)CaDiCaL version: 2.1.3
% 19.46/3.84 % (666326)Termination reason: Instruction limit
% 19.46/3.84 % (666326)Termination phase: Saturation
% 19.46/3.84 % (666326)Time elapsed: 0.101 s
% 19.46/3.84 % (666326)Peak memory usage: 88 MB
% 19.46/3.84 % (666326)Instructions burned: 122 (million)
% 19.46/3.84 % (666328)Instruction limit reached!
% 19.46/3.84 % (666328)------------------------------
% 19.46/3.84 % (666328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.46/3.84 % (666328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.46/3.84 % (666328)CaDiCaL version: 2.1.3
% 19.46/3.84 % (666328)Termination reason: Instruction limit
% 19.46/3.84 % (666328)Termination phase: Saturation
% 19.46/3.84 % (666328)Time elapsed: 0.114 s
% 19.46/3.84 % (666328)Peak memory usage: 90 MB
% 19.46/3.84 % (666328)Instructions burned: 129 (million)
% 19.46/3.84 % (666327)Instruction limit reached!
% 19.46/3.84 % (666327)------------------------------
% 19.46/3.84 % (666327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.46/3.84 % (666327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.46/3.84 % (666327)CaDiCaL version: 2.1.3
% 19.46/3.84 % (666327)Termination reason: Instruction limit
% 19.46/3.84 % (666327)Termination phase: Saturation
% 19.46/3.84 % (666327)Time elapsed: 0.128 s
% 19.46/3.84 % (666327)Peak memory usage: 90 MB
% 19.46/3.84 % (666327)Instructions burned: 139 (million)
% 19.46/3.84 % (666337)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3183553354:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 19.46/3.84 % (666336)lrs+10_1_sil=8000:sp=occurrence:random_seed=2928059911:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 19.46/3.84 % (666339)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=2482041118:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 19.46/3.84 % (666338)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1621280479:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 19.46/3.84 % (666337)Instruction limit reached!
% 19.46/3.84 % (666337)------------------------------
% 19.46/3.84 % (666337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666337)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666337)Termination reason: Instruction limit
% 23.17/4.19 % (666337)Termination phase: Saturation
% 23.17/4.19 % (666337)Time elapsed: 0.143 s
% 23.17/4.19 % (666337)Peak memory usage: 90 MB
% 23.17/4.19 % (666337)Instructions burned: 158 (million)
% 23.17/4.19 % (666339)Instruction limit reached!
% 23.17/4.19 % (666339)------------------------------
% 23.17/4.19 % (666339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666339)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666339)Termination reason: Instruction limit
% 23.17/4.19 % (666339)Termination phase: Saturation
% 23.17/4.19 % (666339)Time elapsed: 0.159 s
% 23.17/4.19 % (666339)Peak memory usage: 91 MB
% 23.17/4.19 % (666339)Instructions burned: 248 (million)
% 23.17/4.19 % (666336)Instruction limit reached!
% 23.17/4.19 % (666336)------------------------------
% 23.17/4.19 % (666336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666336)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666336)Termination reason: Instruction limit
% 23.17/4.19 % (666336)Termination phase: Saturation
% 23.17/4.19 % (666336)Time elapsed: 0.269 s
% 23.17/4.19 % (666336)Peak memory usage: 91 MB
% 23.17/4.19 % (666336)Instructions burned: 285 (million)
% 23.17/4.19 % (666338)Instruction limit reached!
% 23.17/4.19 % (666338)------------------------------
% 23.17/4.19 % (666338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666338)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666338)Termination reason: Instruction limit
% 23.17/4.19 % (666338)Termination phase: Saturation
% 23.17/4.19 % (666338)Time elapsed: 0.294 s
% 23.17/4.19 % (666338)Peak memory usage: 90 MB
% 23.17/4.19 % (666338)Instructions burned: 326 (million)
% 23.17/4.19 % (666344)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3986896573:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 23.17/4.19 % (666345)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3608278555:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 23.17/4.19 % (666346)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=82567434:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 23.17/4.19 % (666347)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1337654971:i=127:av=off:fsr=off:sup=off_2990 on theBenchmark for (2990ds/127Mi)
% 23.17/4.19 % (666347)Refutation not found, incomplete strategy
% 23.17/4.19 % (666347)------------------------------
% 23.17/4.19 % (666347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666347)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666347)Termination reason: Refutation not found, incomplete strategy
% 23.17/4.19 % (666347)Time elapsed: 0.009 s
% 23.17/4.19 % (666347)Peak memory usage: 88 MB
% 23.17/4.19 % (666347)Instructions burned: 20 (million)
% 23.17/4.19 % (666346)Instruction limit reached!
% 23.17/4.19 % (666346)------------------------------
% 23.17/4.19 % (666346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666346)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666346)Termination reason: Instruction limit
% 23.17/4.19 % (666346)Termination phase: Saturation
% 23.17/4.19 % (666346)Time elapsed: 0.100 s
% 23.17/4.19 % (666346)Peak memory usage: 89 MB
% 23.17/4.19 % (666346)Instructions burned: 113 (million)
% 23.17/4.19 % (666344)Instruction limit reached!
% 23.17/4.19 % (666344)------------------------------
% 23.17/4.19 % (666344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666344)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666344)Termination reason: Instruction limit
% 23.17/4.19 % (666344)Termination phase: Saturation
% 23.17/4.19 % (666344)Time elapsed: 0.236 s
% 23.17/4.19 % (666344)Peak memory usage: 89 MB
% 23.17/4.19 % (666344)Instructions burned: 294 (million)
% 23.17/4.19 % (666347)------------------------------
% 23.17/4.19 % (666347)------------------------------
% 23.17/4.19 % (666353)lrs+10_1_sil=8000:sp=occurrence:random_seed=96415827:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2987 on theBenchmark for (2987ds/907Mi)
% 23.17/4.19 % (666352)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1222934216:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2987 on theBenchmark for (2987ds/114Mi)
% 23.17/4.19 % (666352)Instruction limit reached!
% 23.17/4.19 % (666352)------------------------------
% 23.17/4.19 % (666352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666352)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666352)Termination reason: Instruction limit
% 23.17/4.19 % (666352)Termination phase: Saturation
% 23.17/4.19 % (666352)Time elapsed: 0.099 s
% 23.17/4.19 % (666352)Peak memory usage: 89 MB
% 23.17/4.19 % (666352)Instructions burned: 115 (million)
% 23.17/4.19 % (666354)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3724045216:i=437:sd=1:aac=none:ss=included_2985 on theBenchmark for (2985ds/437Mi)
% 23.17/4.19 % (666354)Refutation not found, incomplete strategy
% 23.17/4.19 % (666354)------------------------------
% 23.17/4.19 % (666354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666354)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666354)Termination reason: Refutation not found, incomplete strategy
% 23.17/4.19 % (666354)Time elapsed: 0.050 s
% 23.17/4.19 % (666354)Peak memory usage: 89 MB
% 23.17/4.19 % (666354)Instructions burned: 103 (million)
% 23.17/4.19 % (666354)------------------------------
% 23.17/4.19 % (666354)------------------------------
% 23.17/4.19 % (666358)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3422518281:i=5202:ss=axioms:sgt=16_2983 on theBenchmark for (2983ds/5202Mi)
% 23.17/4.19 % (666361)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1088480519:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2981 on theBenchmark for (2981ds/134Mi)
% 23.17/4.19 % (666361)Instruction limit reached!
% 23.17/4.19 % (666361)------------------------------
% 23.17/4.19 % (666361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666361)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666361)Termination reason: Instruction limit
% 23.17/4.19 % (666361)Termination phase: Saturation
% 23.17/4.19 % (666361)Time elapsed: 0.122 s
% 23.17/4.19 % (666361)Peak memory usage: 90 MB
% 23.17/4.19 % (666361)Instructions burned: 134 (million)
% 23.17/4.19 % (666353)Instruction limit reached!
% 23.17/4.19 % (666353)------------------------------
% 23.17/4.19 % (666353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666353)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666353)Termination reason: Instruction limit
% 23.17/4.19 % (666353)Termination phase: Saturation
% 23.17/4.19 % (666353)Time elapsed: 0.793 s
% 23.17/4.19 % (666353)Peak memory usage: 94 MB
% 23.17/4.19 % (666353)Instructions burned: 907 (million)
% 23.17/4.19 % (666364)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1982682986:st=8:i=592:sd=3:ep=RST:ss=axioms_2976 on theBenchmark for (2976ds/592Mi)
% 23.17/4.19 % (666365)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2833078622:st=3:i=13193:sd=3:ss=axioms_2976 on theBenchmark for (2976ds/13193Mi)
% 23.17/4.19 % (666345)Instruction limit reached!
% 23.17/4.19 % (666345)------------------------------
% 23.17/4.19 % (666345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666345)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666345)Termination reason: Instruction limit
% 23.17/4.19 % (666345)Termination phase: Saturation
% 23.17/4.19 % (666345)Time elapsed: 1.650 s
% 23.17/4.19 % (666345)Peak memory usage: 143 MB
% 23.17/4.19 % (666345)Instructions burned: 2352 (million)
% 23.17/4.19 % (666368)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=891996150:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2973 on theBenchmark for (2973ds/125Mi)
% 23.17/4.19 % (666358)First to succeed.
% 23.17/4.19 % (666358)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-666317"
% 23.17/4.19 % (666368)Instruction limit reached!
% 23.17/4.19 % (666368)------------------------------
% 23.17/4.19 % (666368)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666368)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666368)Termination reason: Instruction limit
% 23.17/4.19 % (666368)Termination phase: Saturation
% 23.17/4.19 % (666368)Time elapsed: 0.124 s
% 23.17/4.19 % (666368)Peak memory usage: 91 MB
% 23.17/4.19 % (666368)Instructions burned: 125 (million)
% 23.17/4.19 % (666364)Instruction limit reached!
% 23.17/4.19 % (666364)------------------------------
% 23.17/4.19 % (666364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.17/4.19 % (666364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.17/4.19 % (666364)CaDiCaL version: 2.1.3
% 23.17/4.19 % (666364)Termination reason: Instruction limit
% 23.17/4.19 % (666364)Termination phase: Saturation
% 23.17/4.19 % (666364)Time elapsed: 0.488 s
% 23.17/4.19 % (666364)Peak memory usage: 91 MB
% 23.17/4.19 % (666364)Instructions burned: 592 (million)
% 23.17/4.19 % (666358)Refutation found. Thanks to Tanya!
% 23.17/4.19 % SZS status Theorem for theBenchmark
% 23.17/4.19 % SZS output start Proof for theBenchmark
% See solution above
% 23.74/4.42 % (666358)------------------------------
% 23.74/4.42 % (666358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.74/4.42 % (666358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.74/4.42 % (666358)CaDiCaL version: 2.1.3
% 23.74/4.42 % (666358)Termination reason: Refutation
% 23.74/4.42 % (666358)Time elapsed: 1.089 s
% 23.74/4.42 % (666358)Peak memory usage: 132 MB
% 23.74/4.42 % (666358)Instructions burned: 1213 (million)
% 23.74/4.42 % (666358)------------------------------
% 23.74/4.42 % (666358)------------------------------
% 23.74/4.42 % (666317)Success in time 3.265 s
% 23.74/4.42 % Vampire exiting
%------------------------------------------------------------------------------