%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW177+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 : Thu Sep 24 03:10:01 PM UTC 2026
% Result : Theorem 15.92s 2.71s
% Output : CNFRefutation 15.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 23
% Syntax : Number of formulae : 104 ( 54 unt; 0 def)
% Number of atoms : 223 ( 43 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 218 ( 99 ~; 81 |; 15 &)
% ( 6 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 121 ( 2 sgn 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_2,conjecture,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(fact_one__add__one__is__two,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Oone__class_Oone(X5)) = c_Int_Onumber__class_Onumber__of(X5,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).
fof(fact_Bit0__def,axiom,
! [X21] : c_Int_OBit0(X21) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X21] : c_Int_OBit1(X21) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21),X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(fact_min__less__iff__conj,axiom,
! [X9,X10,X25,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X25,c_Orderings_Oord__class_Omin(X5,X10,X9))
<=> ( c_Orderings_Oord__class_Oless(X5,X25,X9)
& c_Orderings_Oord__class_Oless(X5,X25,X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__less__iff__conj) ).
fof(fact_add__Pls__right,axiom,
! [X21] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Int_OPls) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(conj_0,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(fact_add__0__left,axiom,
! [X7,X5] :
( class_Groups_Omonoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X7) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(conj_1,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(fact_gt__half__sum,axiom,
! [X24,X7,X5] :
( class_Fields_Olinordered__field(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X7,X24)
=> c_Orderings_Oord__class_Oless(X5,c_Rings_Oinverse__class_Odivide(X5,c_Groups_Oplus__class_Oplus(X5,X7,X24),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Oone__class_Oone(X5))),X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gt__half__sum) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(fact_zadd__commute,axiom,
! [X27,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X27) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(fact_less__half__sum,axiom,
! [X24,X7,X5] :
( class_Fields_Olinordered__field(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X7,X24)
=> c_Orderings_Oord__class_Oless(X5,X7,c_Rings_Oinverse__class_Odivide(X5,c_Groups_Oplus__class_Oplus(X5,X7,X24),c_Groups_Oplus__class_Oplus(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Oone__class_Oone(X5)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__half__sum) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(fact_min__max_Oinf_Ocommute,axiom,
! [X24,X7,X5] :
( class_Orderings_Olinorder(X5)
=> c_Orderings_Oord__class_Omin(X5,X7,X24) = c_Orderings_Oord__class_Omin(X5,X24,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Ocommute) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X10,X9)
<=> ( X10 = X9
| c_Orderings_Oord__class_Oless(X5,X9,X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X13,X8,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X8 != X13
=> ( ~ c_Orderings_Oord__class_Oless(X5,X8,X13)
=> c_Orderings_Oord__class_Oless(X5,X13,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(fact_real__less__def,axiom,
! [X9,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,X9)
<=> ( X10 != X9
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(fact_half__gt__zero__iff,axiom,
! [X4,X5] :
( ( class_Int_Onumber__ring(X5)
& class_Fields_Olinordered__field__inverse__zero(X5) )
=> ( c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),c_Rings_Oinverse__class_Odivide(X5,X4,c_Int_Onumber__class_Onumber__of(X5,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> c_Orderings_Oord__class_Oless(X5,c_Groups_Ozero__class_Ozero(X5),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(c_0_23,negated_conjecture,
~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(assume_negation,[status(cth)],[conj_2]) ).
fof(c_0_24,plain,
! [X1681] :
( c_Groups_Oplus__class_Oplus(X1681,c_Groups_Oone__class_Oone(X1681),c_Groups_Oone__class_Oone(X1681)) = c_Int_Onumber__class_Onumber__of(X1681,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X1681) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__add__one__is__two])])]) ).
fof(c_0_25,plain,
! [X1739] : c_Int_OBit0(X1739) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1739,X1739),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_26,plain,
! [X1888] : c_Int_OBit1(X1888) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1888),X1888),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_27,plain,
! [X178,X179,X180,X181] :
( ( ~ class_Orderings_Olinorder(X181)
| c_Orderings_Oord__class_Oless(X181,X180,c_Orderings_Oord__class_Omin(X181,X179,X178))
| ~ c_Orderings_Oord__class_Oless(X181,X180,X178)
| ~ c_Orderings_Oord__class_Oless(X181,X180,X179) )
& ( ~ class_Orderings_Olinorder(X181)
| ~ c_Orderings_Oord__class_Oless(X181,X180,c_Orderings_Oord__class_Omin(X181,X179,X178))
| c_Orderings_Oord__class_Oless(X181,X180,X178) )
& ( ~ class_Orderings_Olinorder(X181)
| ~ c_Orderings_Oord__class_Oless(X181,X180,c_Orderings_Oord__class_Omin(X181,X179,X178))
| c_Orderings_Oord__class_Oless(X181,X180,X179) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj])])])]) ).
fof(c_0_28,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
cnf(c_0_29,plain,
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
c_Int_OBit1(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,plain,
! [X1738] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1738,c_Int_OPls) = X1738,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
cnf(c_0_33,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X2,c_Orderings_Oord__class_Omin(X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1),
inference(split_conjunct,[status(thm)],[conj_0]) ).
cnf(c_0_35,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(c_0_36,plain,
! [X892,X893] :
( c_Groups_Oplus__class_Oplus(X893,c_Groups_Ozero__class_Ozero(X893),X892) = X892
| ~ class_Groups_Omonoid__add(X893) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])])]) ).
cnf(c_0_37,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_31]) ).
cnf(c_0_39,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d2),
inference(split_conjunct,[status(thm)],[conj_1]) ).
fof(c_0_41,plain,
! [X1517,X1518,X1519] :
( c_Orderings_Oord__class_Oless(X1519,c_Rings_Oinverse__class_Odivide(X1519,c_Groups_Oplus__class_Oplus(X1519,X1518,X1517),c_Groups_Oplus__class_Oplus(X1519,c_Groups_Oone__class_Oone(X1519),c_Groups_Oone__class_Oone(X1519))),X1517)
| ~ c_Orderings_Oord__class_Oless(X1519,X1518,X1517)
| ~ class_Fields_Olinordered__field(X1519) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gt__half__sum])])]) ).
cnf(c_0_42,hypothesis,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,v_d1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_43,plain,
( ~ class_Groups_Omonoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]) ).
cnf(c_0_45,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_d1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_30]),c_0_30]),c_0_30]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]) ).
fof(c_0_46,plain,
! [X1710,X1711] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1711,X1710) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1710,X1711),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
cnf(c_0_47,plain,
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_39]),c_0_39]),c_0_39]) ).
cnf(c_0_48,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
fof(c_0_49,plain,
! [X1514,X1515,X1516] :
( c_Orderings_Oord__class_Oless(X1516,X1515,c_Rings_Oinverse__class_Odivide(X1516,c_Groups_Oplus__class_Oplus(X1516,X1515,X1514),c_Groups_Oplus__class_Oplus(X1516,c_Groups_Oone__class_Oone(X1516),c_Groups_Oone__class_Oone(X1516))))
| ~ c_Orderings_Oord__class_Oless(X1516,X1515,X1514)
| ~ class_Fields_Olinordered__field(X1516) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__half__sum])])]) ).
cnf(c_0_50,hypothesis,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,v_d2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_40]),c_0_35])]) ).
cnf(c_0_51,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Fields_Olinordered__field(X1)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_52,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d2,v_d1)),
inference(spm,[status(thm)],[c_0_42,c_0_40]) ).
cnf(c_0_53,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = X1,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]) ).
fof(c_0_55,plain,
! [X285,X286,X287] :
( c_Orderings_Oord__class_Omin(X287,X286,X285) = c_Orderings_Oord__class_Omin(X287,X285,X286)
| ~ class_Orderings_Olinorder(X287) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Ocommute])])]) ).
fof(c_0_56,plain,
! [X9,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X10,X9)
<=> ( X10 = X9
| c_Orderings_Oord__class_Oless(X5,X9,X10) ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
cnf(c_0_57,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]) ).
cnf(c_0_58,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_59,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_60,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Fields_Olinordered__field(X1)
| c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2)),
inference(spm,[status(thm)],[c_0_50,c_0_34]) ).
cnf(c_0_62,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Orderings_Oord__class_Omin(X1,X3,X4))
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_63,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d2,v_d1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d2,v_d1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54])]) ).
cnf(c_0_64,plain,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Omin(X1,X2,X3) = c_Orderings_Oord__class_Omin(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_65,plain,
! [X217,X218,X219] :
( ( ~ class_Orderings_Olinorder(X219)
| ~ c_Orderings_Oord__class_Oless(X219,X218,X217)
| X218 != X217 )
& ( ~ class_Orderings_Olinorder(X219)
| ~ c_Orderings_Oord__class_Oless(X219,X218,X217)
| ~ c_Orderings_Oord__class_Oless(X219,X217,X218) )
& ( ~ class_Orderings_Olinorder(X219)
| X218 = X217
| c_Orderings_Oord__class_Oless(X219,X217,X218)
| c_Orderings_Oord__class_Oless(X219,X218,X217) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])])]) ).
cnf(c_0_66,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Orderings_Oord__class_Omin(X1,X4,X3))
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_67,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_59]),c_0_59]) ).
cnf(c_0_68,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_53]),c_0_54])]) ).
cnf(c_0_69,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d2,v_d1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_35])]) ).
cnf(c_0_70,plain,
c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X1,X2) = c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,X2,X1),
inference(spm,[status(thm)],[c_0_64,c_0_35]) ).
fof(c_0_71,plain,
! [X13,X8,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X8 != X13
=> ( ~ c_Orderings_Oord__class_Oless(X5,X8,X13)
=> c_Orderings_Oord__class_Oless(X5,X13,X8) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
cnf(c_0_72,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_73,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d2,v_d1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_63]),c_0_35])]) ).
cnf(c_0_74,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_75,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d2),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
fof(c_0_76,plain,
! [X229,X230,X231] :
( c_Orderings_Oord__class_Oless(X231,X229,X230)
| c_Orderings_Oord__class_Oless(X231,X230,X229)
| X230 = X229
| ~ class_Rings_Olinordered__idom(X231) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])])]) ).
cnf(c_0_77,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d2,v_d1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_35])]) ).
cnf(c_0_78,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d2,v_d1),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d2,v_d1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_63]),c_0_35])]) ).
cnf(c_0_79,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
cnf(c_0_80,plain,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_81,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(c_0_82,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(spm,[status(thm)],[c_0_77,c_0_70]) ).
fof(c_0_83,plain,
! [X9,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,X9)
<=> ( X10 != X9
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X9) ) ),
inference(fof_simplification,[status(thm)],[fact_real__less__def]) ).
fof(c_0_84,plain,
! [X79,X80] :
( ( ~ class_Int_Onumber__ring(X80)
| ~ class_Fields_Olinordered__field__inverse__zero(X80)
| c_Orderings_Oord__class_Oless(X80,c_Groups_Ozero__class_Ozero(X80),c_Rings_Oinverse__class_Odivide(X80,X79,c_Int_Onumber__class_Onumber__of(X80,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(X80,c_Groups_Ozero__class_Ozero(X80),X79) )
& ( ~ class_Int_Onumber__ring(X80)
| ~ class_Fields_Olinordered__field__inverse__zero(X80)
| c_Orderings_Oord__class_Oless(X80,c_Groups_Ozero__class_Ozero(X80),X79)
| ~ c_Orderings_Oord__class_Oless(X80,c_Groups_Ozero__class_Ozero(X80),c_Rings_Oinverse__class_Odivide(X80,X79,c_Int_Onumber__class_Onumber__of(X80,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff])])])]) ).
cnf(c_0_85,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_70]),c_0_70]) ).
cnf(c_0_86,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]),c_0_82]) ).
fof(c_0_87,plain,
! [X795,X796] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X796,X795)
| X796 = X795
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X796,X795) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X796,X795)
| X796 != X795 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X796,X795)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X796,X795) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])])]) ).
cnf(c_0_88,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_89,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2),v_d1),
inference(rw,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_90,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_91,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_30]),c_0_31]),c_0_31]) ).
cnf(c_0_92,hypothesis,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2))
| c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2) = v_d1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_80]),c_0_81])]) ).
cnf(c_0_93,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(er,[status(thm)],[c_0_90]) ).
cnf(c_0_94,plain,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_39]),c_0_39]),c_0_39]),c_0_39]) ).
cnf(c_0_95,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
cnf(c_0_96,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_34]),c_0_54])]) ).
cnf(c_0_97,hypothesis,
c_Orderings_Oord__class_Omin(tc_RealDef_Oreal,v_d1,v_d2) = v_d1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_92]),c_0_35])]),c_0_93]) ).
cnf(c_0_98,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_34]),c_0_48]),c_0_95])]),c_0_59]) ).
cnf(c_0_99,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d1),
inference(spm,[status(thm)],[c_0_96,c_0_53]) ).
cnf(c_0_100,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),v_d2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_97]),c_0_59]),c_0_98]),c_0_59]),c_0_99]),c_0_59])]) ).
cnf(c_0_101,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_d1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = v_d1,
inference(rw,[status(thm)],[c_0_86,c_0_97]) ).
cnf(c_0_102,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d1,v_d2),
inference(rw,[status(thm)],[c_0_75,c_0_86]) ).
cnf(c_0_103,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101]),c_0_102])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW177+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Mon Sep 21 09:38:52 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.92/2.71 % Version: 3.5.1
% 15.92/2.71 % Preprocessing class: FMLMSMSMSSSNFFN.
% 15.92/2.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.92/2.71 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.92/2.71 % Starting new_bool_3 with 300s (1) cores
% 15.92/2.71 % Starting new_bool_1 with 300s (1) cores
% 15.92/2.71 % Starting sh5l with 300s (1) cores
% 15.92/2.71 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2094073 completed with status 0
% 15.92/2.71 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 15.92/2.71 % Preprocessing class: FMLMSMSMSSSNFFN.
% 15.92/2.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.92/2.71 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.92/2.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.92/2.71 % No SInE strategy applied
% 15.92/2.71 % Search class: FGHSM-SMLM32-DFFFFFNN
% 15.92/2.71 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 15.92/2.71 % Starting SubtermCWHack with 136s (1) cores
% 15.92/2.71 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 15.92/2.71 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 15.92/2.71 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 15.92/2.71 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 15.92/2.71 % G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with pid 2094099 completed with status 0
% 15.92/2.71 % Result found by G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI
% 15.92/2.71 % Preprocessing class: FMLMSMSMSSSNFFN.
% 15.92/2.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.92/2.71 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.92/2.71 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.92/2.71 % No SInE strategy applied
% 15.92/2.71 % Search class: FGHSM-SMLM32-DFFFFFNN
% 15.92/2.71 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 15.92/2.71 % Starting SubtermCWHack with 136s (1) cores
% 15.92/2.71 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 15.92/2.71 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 15.92/2.71 % Preprocessing time : 0.014 s
% 15.92/2.71
% 15.92/2.71 % Proof found!
% 15.92/2.71 % SZS status Theorem
% 15.92/2.71 % SZS output start CNFRefutation
% See solution above
% 15.92/2.71 % Parsed axioms : 1200
% 15.92/2.71 % Removed by relevancy pruning/SinE : 0
% 15.92/2.71 % Initial clauses : 1801
% 15.92/2.71 % Removed in clause preprocessing : 89
% 15.92/2.71 % Initial clauses in saturation : 1712
% 15.92/2.71 % Processed clauses : 9718
% 15.92/2.71 % ...of these trivial : 680
% 15.92/2.71 % ...subsumed : 5037
% 15.92/2.71 % ...remaining for further processing : 4001
% 15.92/2.71 % Other redundant clauses eliminated : 323
% 15.92/2.71 % Clauses deleted for lack of memory : 0
% 15.92/2.71 % Backward-subsumed : 16
% 15.92/2.71 % Backward-rewritten : 1170
% 15.92/2.71 % Generated clauses : 114374
% 15.92/2.71 % ...of the previous two non-redundant : 103311
% 15.92/2.71 % ...aggressively subsumed : 0
% 15.92/2.71 % Contextual simplify-reflections : 2
% 15.92/2.71 % Paramodulations : 114020
% 15.92/2.71 % Factorizations : 17
% 15.92/2.71 % NegExts : 0
% 15.92/2.71 % Equation resolutions : 355
% 15.92/2.71 % Disequality decompositions : 0
% 15.92/2.71 % Total rewrite steps : 134145
% 15.92/2.71 % ...of those cached : 128958
% 15.92/2.71 % Propositional unsat checks : 0
% 15.92/2.71 % Propositional check models : 0
% 15.92/2.71 % Propositional check unsatisfiable : 0
% 15.92/2.71 % Propositional clauses : 0
% 15.92/2.71 % Propositional clauses after purity: 0
% 15.92/2.71 % Propositional unsat core size : 0
% 15.92/2.71 % Propositional preprocessing time : 0.000
% 15.92/2.71 % Propositional encoding time : 0.000
% 15.92/2.71 % Propositional solver time : 0.000
% 15.92/2.71 % Success case prop preproc time : 0.000
% 15.92/2.71 % Success case prop encoding time : 0.000
% 15.92/2.71 % Success case prop solver time : 0.000
% 15.92/2.71 % Current number of processed clauses : 2686
% 15.92/2.71 % Positive orientable unit clauses : 888
% 15.92/2.71 % Positive unorientable unit clauses: 23
% 15.92/2.71 % Negative unit clauses : 638
% 15.92/2.71 % Non-unit-clauses : 1137
% 15.92/2.71 % Current number of unprocessed clauses: 95134
% 15.92/2.71 % ...number of literals in the above : 189500
% 15.92/2.71 % Current number of archived formulas : 0
% 15.92/2.71 % Current number of archived clauses : 1190
% 15.92/2.71 % Clause-clause subsumption calls (NU) : 91079
% 15.92/2.71 % Rec. Clause-clause subsumption calls : 39109
% 15.92/2.71 % Non-unit clause-clause subsumptions : 597
% 15.92/2.71 % Unit Clause-clause subsumption calls : 128917
% 15.92/2.71 % Rewrite failures with RHS unbound : 0
% 15.92/2.71 % BW rewrite match attempts : 241132
% 15.92/2.71 % BW rewrite match successes : 1478
% 15.92/2.71 % Condensation attempts : 0
% 15.92/2.71 % Condensation successes : 0
% 15.92/2.71 % Termbank termtop insertions : 3763339
% 15.92/2.71 % Search garbage collected termcells : 20661
% 15.92/2.71
% 15.92/2.71 % -------------------------------------------------
% 15.92/2.71 % User time : 2.196 s
% 15.92/2.71 % System time : 0.092 s
% 15.92/2.71 % Total time : 2.289 s
% 15.92/2.71 % Maximum resident set size: 9552 pages
% 15.92/2.71
% 15.92/2.71 % -------------------------------------------------
% 15.92/2.71 % User time : 10.744 s
% 15.92/2.71 % System time : 0.416 s
% 15.92/2.71 % Total time : 11.160 s
% 15.92/2.71 % Maximum resident set size: 5888 pages
% 15.92/2.71 % E exiting
%------------------------------------------------------------------------------