%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL752-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 : Sun Sep 27 07:59:38 AM UTC 2026
% Result : Unsatisfiable 57.65s 8.74s
% Output : CNFRefutation 57.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 66 ( 39 unt; 0 def)
% Number of atoms : 117 ( 62 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 110 ( 59 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-5 aty)
% Number of variables : 129 ( 33 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_Int__Oint__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
cnf(c_13,plain,
class_Ring__and__Field_Oidom(tc_Int_Oint),
inference(clausify,[status(thm)],[clsarity_Int__Oint__Ring__and__Field_Oidom]) ).
fof(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( VAR_2 = c_HOL_Ozero__class_Ozero(VAR_0)
| VAR_3 = VAR_4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(VAR_0),VAR_2),VAR_3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(VAR_0),VAR_2),VAR_4))
| ~ class_Int_Onumber__ring(VAR_0)
| ~ class_Ring__and__Field_Oidom(VAR_0) ),
file('theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
cnf(c_15,plain,
( C = c_HOL_Ozero__class_Ozero(A)
| D = E
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E))
| ~ class_Int_Onumber__ring(A)
| ~ class_Ring__and__Field_Oidom(A) ),
inference(clausify,[status(thm)],[cls_class__ringb_Oadd__scale__eq__noteq_0]) ).
fof(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(c_155,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1]) ).
fof(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
! [VAR_0,VAR_1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_1),c_HOL_Ozero__class_Ozero(VAR_0)) = VAR_1
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(c_175,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I6_J_0]) ).
fof(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
! [VAR_0,VAR_1] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(VAR_0),VAR_1),c_HOL_Ozero__class_Ozero(VAR_0)) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
cnf(c_180,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A)
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I10_J_0]) ).
fof(cls_class__semiring_Opwr__0_0,axiom,
! [VAR_0,VAR_1] :
( c_Power_Opower__class_Opower(VAR_1,c_HOL_Ozero__class_Ozero(tc_nat),VAR_0) = c_HOL_Oone__class_Oone(VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
cnf(c_183,plain,
( c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A)
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Opwr__0_0]) ).
fof(cls_class__semiring_Omul__1_0,axiom,
! [VAR_0,VAR_1] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(VAR_0),c_HOL_Oone__class_Oone(VAR_0)),VAR_1) = VAR_1
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Omul__1_0) ).
cnf(c_212,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Omul__1_0]) ).
fof(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
cnf(c_217,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1]) ).
fof(clsarity_Int__Oint__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
cnf(c_339,plain,
class_Power_Opower(tc_Int_Oint),
inference(clausify,[status(thm)],[clsarity_Int__Oint__Power_Opower]) ).
fof(cls_power__eq__0__iff_1,axiom,
! [VAR_0,VAR_1] :
( c_Power_Opower__class_Opower(VAR_1,c_HOL_Ozero__class_Ozero(tc_nat),VAR_0) != c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_Power_Opower(VAR_0)
| ~ class_Ring__and__Field_Omult__zero(VAR_0)
| ~ class_Ring__and__Field_Ono__zero__divisors(VAR_0)
| ~ class_Ring__and__Field_Ozero__neq__one(VAR_0) ),
file('theBenchmark.p',cls_power__eq__0__iff_1) ).
cnf(c_343,plain,
( c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) != c_HOL_Ozero__class_Ozero(A)
| ~ class_Power_Opower(A)
| ~ class_Ring__and__Field_Omult__zero(A)
| ~ class_Ring__and__Field_Ono__zero__divisors(A)
| ~ class_Ring__and__Field_Ozero__neq__one(A) ),
inference(clausify,[status(thm)],[cls_power__eq__0__iff_1]) ).
fof(clsarity_Int__Oint__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
cnf(c_506,plain,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[clsarity_Int__Oint__OrderedGroup_Ogroup__add]) ).
fof(cls_diff__add__cancel_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(VAR_0),VAR_1),VAR_2)),VAR_2) = VAR_1
| ~ class_OrderedGroup_Ogroup__add(VAR_0) ),
file('theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(c_511,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),C) = B
| ~ class_OrderedGroup_Ogroup__add(A) ),
inference(clausify,[status(thm)],[cls_diff__add__cancel_0]) ).
fof(cls_COMBB__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(hAPP(c_COMBB(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(VAR_3,hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_COMBB__def_0) ).
cnf(c_532,plain,
hAPP(hAPP(hAPP(c_COMBB(A,B,C),D),E),F) = hAPP(D,hAPP(E,F)),
inference(clausify,[status(thm)],[cls_COMBB__def_0]) ).
fof(cls_COMBC__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_COMBC(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),VAR_1),
file('theBenchmark.p',cls_COMBC__def_0) ).
cnf(c_533,plain,
hAPP(c_COMBC(A,B,C,D,E),F) = hAPP(hAPP(A,F),B),
inference(clausify,[status(thm)],[cls_COMBC__def_0]) ).
fof(cls_COMBS__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_COMBS(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),hAPP(VAR_1,VAR_5)),
file('theBenchmark.p',cls_COMBS__def_0) ).
cnf(c_534,plain,
hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(A,F),hAPP(B,F)),
inference(clausify,[status(thm)],[cls_COMBS__def_0]) ).
fof(clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
cnf(c_569,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors]) ).
fof(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
cnf(c_571,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
inference(clausify,[status(thm)],[clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one]) ).
fof(clsarity_Int__Oint__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
cnf(c_574,plain,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
inference(clausify,[status(thm)],[clsarity_Int__Oint__Ring__and__Field_Omult__zero]) ).
fof(clsarity_Int__Oint__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
cnf(c_579,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[clsarity_Int__Oint__Int_Onumber__ring]) ).
cnf(c_802,plain,
hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A,
inference(resolve,[status(thm)],[c_155,c_212]) ).
cnf(c_829,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A,
inference(resolve,[status(thm)],[c_217,c_175]) ).
cnf(c_834,plain,
hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint),
inference(resolve,[status(thm)],[c_217,c_180]) ).
cnf(c_836,plain,
c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint),
inference(resolve,[status(thm)],[c_217,c_183]) ).
cnf(c_863,plain,
hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A) = A,
inference(resolve,[status(thm)],[c_217,c_212]) ).
cnf(c_1712,plain,
( B = c_HOL_Ozero__class_Ozero(tc_Int_Oint)
| C = D
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D))
| ~ class_Int_Onumber__ring(tc_Int_Oint) ),
inference(resolve,[status(thm)],[c_15,c_13]) ).
cnf(c_17576,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = B
| C = D
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D))
| ~ class_Int_Onumber__ring(tc_Int_Oint) ),
inference(copy,[status(thm)],[c_1712]) ).
cnf(c_1713,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = B
| C = D
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)) ),
inference(resolve,[status(thm)],[c_579,c_17576]) ).
cnf(c_2025,plain,
( c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Ring__and__Field_Omult__zero(tc_Int_Oint)
| ~ class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint)
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
inference(resolve,[status(thm)],[c_343,c_339]) ).
cnf(c_17577,plain,
( c_HOL_Oone__class_Oone(tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Ring__and__Field_Omult__zero(tc_Int_Oint)
| ~ class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint)
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
inference(paramod,[status(thm)],[c_836,c_2025]) ).
cnf(c_17578,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint)
| ~ class_Ring__and__Field_Omult__zero(tc_Int_Oint)
| ~ class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint)
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
inference(copy,[status(thm)],[c_17577]) ).
cnf(c_17579,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint)
| ~ class_Ring__and__Field_Omult__zero(tc_Int_Oint)
| ~ class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ),
inference(resolve,[status(thm)],[c_571,c_17578]) ).
cnf(c_17580,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint)
| ~ class_Ring__and__Field_Omult__zero(tc_Int_Oint) ),
inference(resolve,[status(thm)],[c_569,c_17579]) ).
cnf(c_2026,plain,
c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint),
inference(resolve,[status(thm)],[c_574,c_17580]) ).
cnf(c_2124,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),B) = A,
inference(resolve,[status(thm)],[c_511,c_506]) ).
cnf(c_17581,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = B
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)) ),
inference(factor,[status(thm)],[c_1713]) ).
cnf(c_17582,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = B
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)) ),
inference(paramod,[status(thm)],[c_834,c_17581]) ).
cnf(c_17583,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = B
| A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)) ),
inference(paramod,[status(thm)],[c_829,c_17582]) ).
cnf(c_2323,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = B
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)) != A ),
inference(copy,[status(thm)],[c_17583]) ).
cnf(c_2384,plain,
hAPP(c_COMBS(hAPP(c_COMBB(A,B,C),D),E,F,V6,V7),V8) = hAPP(D,hAPP(V8,hAPP(E,V8))),
inference(paramod,[status(thm)],[c_534,c_532]) ).
cnf(c_17584,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)) != A ),
inference(paramod,[status(thm)],[c_863,c_2323]) ).
cnf(c_15091,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)) != A,
inference(resolve,[status(thm)],[c_2026,c_17584]) ).
cnf(c_17585,plain,
A != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)),
inference(paramod,[status(thm)],[c_2124,c_15091]) ).
cnf(c_15296,plain,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)) != A,
inference(copy,[status(thm)],[c_17585]) ).
cnf(c_15845,plain,
hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),A,B,C),D) != D,
inference(paramod,[status(thm)],[c_533,c_15296]) ).
cnf(c_17574,plain,
hAPP(c_COMBS(hAPP(c_COMBB(A,B,C),D),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),E,F,V6),V7) = hAPP(D,hAPP(V7,V7)),
inference(paramod,[status(thm)],[c_802,c_2384]) ).
cnf(c_17586,plain,
D != hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),A,B,C),D),
inference(copy,[status(thm)],[c_15845]) ).
cnf(c_17575,plain,
$false,
inference(resolve,[status(thm)],[c_17574,c_17586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL752-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 23:32:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 254593 was started by sandbox on n002,
% 0.09/0.37 % Fri Sep 25 23:32:04 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.41
% 0.09/0.41 % From the command line: assign(max_seconds, 300).
% 57.65/8.74
% 57.65/8.74 % given #500 (I,wt=21): 1259 hBOOL(hAPP(A,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C))) | -hBOOL(hAPP(A,c_ATP__Linkup_Osko__Nat__Xnat__diff__split__asm__1__1(A,B,C))) | -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))) # tptp_name(cls_nat__diff__split__asm_5) # clausal_fof(1). [assumption].
% 57.65/8.74
% 57.65/8.74 % given #1000 (I,wt=44): 2207 hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(A,hAPP(A,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__iff__1__1(A,tc_nat))),tc_nat),hAPP(A,hAPP(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__iff__1__1(A,tc_nat)))))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(A,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__iff__1__1(A,tc_nat)),tc_nat),hAPP(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__iff__1__1(A,tc_nat))))). [factor(1224,c,d),rewrite([1700(11),1700(28)]),unit_del(a,565)].
% 57.65/8.74
% 57.65/8.74 % SZS status Unsatisfiable for theBenchmark
% 57.65/8.74
% 57.65/8.74 % Proof 1 at 7.41 (+ 0.82) seconds.
% 57.65/8.74 % Length of proof is 36.
% 57.65/8.74 % Level of proof is 7.
% 57.65/8.74 % Maximum clause weight is 30.000.
% 57.65/8.74 % Given clauses 1268.
% 57.65/8.74
% 57.65/8.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------