%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP013+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 : Fri Sep 25 01:47:44 PM UTC 2026
% Result : Theorem 4.34s 1.31s
% Output : CNFRefutation 4.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 73 ( 44 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 71 ( 26 ~; 18 |; 21 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 51 ( 0 sgn 48 !; 3 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f39,axiom,
! [X0] :
( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_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_2ET_2E0)
<=> p(s(tyop_2Emin_2Ebool,X0)) )
& ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0)
<=> p(s(tyop_2Emin_2Ebool,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
fof(f43,axiom,
! [X0] :
( ! [X3,X4] : s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(X0,X3),s(X0,X4))) = s(X0,X4)
& ! [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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
fof(f44,axiom,
! [X0,X1,X2] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X1),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X2))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X1),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X2))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def) ).
fof(f45,axiom,
! [X0,X1] :
( ! [X4,X5] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X4))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X5))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X5),s(tyop_2Enum_2Enum,X4))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X4),s(tyop_2Enum_2Enum,X5))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X5),s(tyop_2Enum_2Enum,X4)))))))))
& ! [X2,X3] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X2))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X3))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X3))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LITERAL__ADD) ).
fof(f46,conjecture,
! [X0,X1,X2] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X1))))
=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X1))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X2))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub) ).
fof(f47,negated_conjecture,
~ ! [X0,X1,X2] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X1))))
=> s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X1))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X2))))) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f48,plain,
? [X0,X1,X2] :
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X1))))
& s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X1))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X2))))) ),
inference(ennf_transformation,[],[f47]) ).
fof(f58,plain,
( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,sK2),s(tyop_2Enum_2Enum,sK1))))
& s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK1),s(tyop_2Enum_2Enum,sK2))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK1))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK2))))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f48]) ).
fof(f66,plain,
! [X0] :
( ( 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) )
& ( 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,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0) )
& ( 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,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,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f67,plain,
! [X0] :
( ( 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) )
& ( 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,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0) )
& ( 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,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,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0) ) ),
inference(flattening,[],[f66]) ).
fof(f71,plain,
p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,sK2),s(tyop_2Enum_2Enum,sK1)))),
inference(cnf_transformation,[],[f58]) ).
fof(f72,plain,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK1),s(tyop_2Enum_2Enum,sK2))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK1))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK2))))),
inference(cnf_transformation,[],[f58]) ).
fof(f92,plain,
! [X1,X4,X5] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X4))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X5))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X5),s(tyop_2Enum_2Enum,X4))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X4),s(tyop_2Enum_2Enum,X5))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X5),s(tyop_2Enum_2Enum,X4))))))))),
inference(cnf_transformation,[],[f45]) ).
fof(f94,plain,
! [X2,X0,X1] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X1),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X2))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X1),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X2))))),
inference(cnf_transformation,[],[f44]) ).
fof(f96,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,[],[f43]) ).
fof(f106,plain,
! [X0] :
( ~ p(s(tyop_2Emin_2Ebool,X0))
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_49,negated_conjecture,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK1))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK2))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK1),s(tyop_2Enum_2Enum,sK2))))),
inference(cnf_transformation,[],[f72]) ).
tcf(c_50,negated_conjecture,
p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,sK2),s(tyop_2Enum_2Enum,sK1)))),
inference(cnf_transformation,[],[f71]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X1))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X2))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X1))))))),
inference(cnf_transformation,[],[f92]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__add_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X1),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X2))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X1),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X2))),
inference(cnf_transformation,[],[f94]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] : s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(X0,X1),s(X0,X2))) = s(X0,X1),
inference(cnf_transformation,[],[f96]) ).
tcf(c_70,plain,
! [X0: $i] :
( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
| ~ p(s(tyop_2Emin_2Ebool,X0)) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i,X2: $i] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X2),s(tyop_2Enum_2Enum,X1))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X1),s(tyop_2Enum_2Enum,X2))))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X2))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X1))))),
inference(demodulation,[status(thm)],[c_61,c_62]) ).
tcf(c_1225,plain,
s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,sK2),s(tyop_2Enum_2Enum,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
inference(superposition,[status(thm)],[c_50,c_70]) ).
tcf(c_1320,plain,
! [X0: $i] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK1),s(tyop_2Enum_2Enum,sK2))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK2),s(tyop_2Enum_2Enum,sK1))))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK1))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK2))))),
inference(superposition,[status(thm)],[c_1225,c_377]) ).
tcf(c_1645,plain,
! [X0: $i] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__sub_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK1))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,sK2))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK1),s(tyop_2Enum_2Enum,sK2))))),
inference(demodulation,[status(thm)],[c_1320,c_63]) ).
tcf(c_1646,plain,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK1),s(tyop_2Enum_2Enum,sK2))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,sK1),s(tyop_2Enum_2Enum,sK2))))),
inference(demodulation,[status(thm)],[c_49,c_1645]) ).
tcf(c_1647,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_1646]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP013+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 17:37:43 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42
% 0.15/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42
% 0.15/0.42 % Detected problem language: tptp
% 0.15/0.43 % Proving...
% 4.34/1.31 % SZS status Started for theBenchmark.p
% 4.34/1.31 % SZS status Theorem for theBenchmark.p
% 4.34/1.31
% 4.34/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.34/1.31
% 4.34/1.31 % ------ iProver source info
% 4.34/1.31
% 4.34/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.34/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.34/1.31 % git: non_committed_changes: false
% 4.34/1.31
% 4.34/1.31 % ------ Parsing...
% 4.34/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.34/1.31
% 4.34/1.31 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.34/1.31
% 4.34/1.31 % ------ Preprocessing... gs_s sp: 8 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.34/1.31
% 4.34/1.31 % ------ Preprocessing... sf_s rm: 7 0s sf_e sf_s rm: 0 0s sf_e
% 4.34/1.31 % ------ Proving...
% 4.34/1.31 % ------ Problem Properties
% 4.34/1.31
% 4.34/1.31 %
% 4.34/1.31 % clauses 29
% 4.34/1.31 % conjectures 2
% 4.34/1.31 % EPR 4
% 4.34/1.31 % Horn 22
% 4.34/1.31 % unary 9
% 4.34/1.31 % binary 11
% 4.34/1.31 % lits 63
% 4.34/1.31 % lits eq 29
% 4.34/1.31 % fd_pure 0
% 4.34/1.31 % fd_pseudo 0
% 4.34/1.31 % fd_cond 0
% 4.34/1.31 % fd_pseudo_cond 0
% 4.34/1.31 % AC symbols 0
% 4.34/1.31
% 4.34/1.31 % ------ Schedule dynamic 5 is on
% 4.34/1.31
% 4.34/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.34/1.31
% 4.34/1.31
% 4.34/1.31 % ------
% 4.34/1.31 % Current options:
% 4.34/1.31 % ------
% 4.34/1.31
% 4.34/1.31
% 4.34/1.31 %
% 4.34/1.31
% 4.34/1.31 % ------ Proving...
% 4.34/1.31 %
% 4.34/1.31
% 4.34/1.31 % SZS status Theorem for theBenchmark.p
% 4.34/1.31
% 4.34/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.34/1.31
% 4.34/1.31
%------------------------------------------------------------------------------