%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV620-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Thu Sep 24 02:59:39 PM UTC 2026
% Result : Unsatisfiable 1.49s 0.68s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of clauses : 53 ( 33 unt; 6 nHn; 46 RR)
% Number of literals : 103 ( 7 equ; 58 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 51 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_mult__eq__0__iff_2,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
cnf(cls_CHAINED_0,axiom,
( ~ c_HOL_Oord__class_Oless(v_k,v_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_real__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(cls_CHAINED_0_01,axiom,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_mult__imp__less__div__pos_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
cnf(cls_real__mult__order_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__order_0) ).
cnf(cls_zero__less__divide__iff_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
cnf(cls_pi__not__less__zero_0,axiom,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__not__less__zero_0) ).
cnf(cls_pi__gt__zero_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__gt__zero_0) ).
cnf(cls_pi__half__gt__zero_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__gt__zero_0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
cnf(cls_zero__less__divide__iff_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
cnf(cls_real0_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real0_0) ).
cnf(cls_not__real__of__nat__less__zero_0,axiom,
~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__real__of__nat__less__zero_0) ).
cnf(c_0_17,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_18,plain,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_mult__eq__0__iff_2]) ).
cnf(c_0_19,plain,
( ~ c_HOL_Oord__class_Oless(v_k,v_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_CHAINED_0]) ).
cnf(c_0_20,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
c_0_17 ).
cnf(c_0_21,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),
cls_real__mult__commute_0 ).
cnf(c_0_22,plain,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_18 ).
cnf(c_0_23,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors ).
cnf(c_0_24,plain,
( ~ c_HOL_Oord__class_Oless(v_k,v_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
c_0_19 ).
cnf(c_0_25,axiom,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
cls_CHAINED_0_01 ).
cnf(c_0_26,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
cnf(c_0_27,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_mult__imp__less__div__pos_0]) ).
cnf(c_0_28,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_21]),c_0_21]),c_0_25]),c_0_21])]),c_0_26]) ).
cnf(c_0_30,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
c_0_27 ).
cnf(c_0_31,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field ).
cnf(c_0_32,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_33,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__mult__order_0]) ).
cnf(c_0_34,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_zero__less__divide__iff_2]) ).
cnf(c_0_35,plain,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[cls_pi__not__less__zero_0]) ).
cnf(c_0_36,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_37,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
c_0_33 ).
cnf(c_0_38,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
cls_pi__gt__zero_0 ).
cnf(c_0_39,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
c_0_34 ).
cnf(c_0_40,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_pi__half__gt__zero_0 ).
cnf(c_0_41,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_42,plain,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
c_0_35 ).
cnf(c_0_43,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_zero__less__divide__iff_3]) ).
cnf(c_0_44,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real0_0 ).
cnf(c_0_45,plain,
~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[cls_not__real__of__nat__less__zero_0]) ).
cnf(c_0_46,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_47,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_31])]),c_0_42]) ).
cnf(c_0_48,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
c_0_43 ).
cnf(c_0_49,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_50,plain,
~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
c_0_45 ).
cnf(c_0_51,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_52,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_41]),c_0_31])]),c_0_50]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV620-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 09:17:16 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 1.49/0.68 % Version: 3.5.1
% 1.49/0.68 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.49/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.49/0.68 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.49/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.49/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.49/0.68 % Starting sh5l with 300s (1) cores
% 1.49/0.68 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2953549 completed with status 0
% 1.49/0.68 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.49/0.68 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.49/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.49/0.68 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.49/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.49/0.68 % No SInE strategy applied
% 1.49/0.68 % Search class: FGHSM-FSLM31-DFFFFFNN
% 1.49/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.49/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.49/0.68 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.49/0.68 % Starting C07_19_nc_SAT001_MinMin_p005000_rr with 354s (1) cores
% 1.49/0.68 % Starting U----_206c_10_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.49/0.68 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 1.49/0.68 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2953556 completed with status 0
% 1.49/0.68 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.49/0.68 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.49/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.49/0.68 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.49/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.49/0.68 % No SInE strategy applied
% 1.49/0.68 % Search class: FGHSM-FSLM31-DFFFFFNN
% 1.49/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.49/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.49/0.68 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.49/0.68 % Preprocessing time : 0.012 s
% 1.49/0.68 % Presaturation interreduction done
% 1.49/0.68
% 1.49/0.68 % Proof found!
% 1.49/0.68 % SZS status Unsatisfiable
% 1.49/0.68 % SZS output start CNFRefutation
% See solution above
% 1.49/0.68 % Parsed axioms : 877
% 1.49/0.68 % Removed by relevancy pruning/SinE : 0
% 1.49/0.68 % Initial clauses : 877
% 1.49/0.68 % Removed in clause preprocessing : 0
% 1.49/0.68 % Initial clauses in saturation : 877
% 1.49/0.68 % Processed clauses : 1712
% 1.49/0.68 % ...of these trivial : 43
% 1.49/0.68 % ...subsumed : 340
% 1.49/0.68 % ...remaining for further processing : 1328
% 1.49/0.68 % Other redundant clauses eliminated : 64
% 1.49/0.68 % Clauses deleted for lack of memory : 0
% 1.49/0.68 % Backward-subsumed : 12
% 1.49/0.68 % Backward-rewritten : 10
% 1.49/0.68 % Generated clauses : 4583
% 1.49/0.68 % ...of the previous two non-redundant : 3903
% 1.49/0.68 % ...aggressively subsumed : 0
% 1.49/0.68 % Contextual simplify-reflections : 0
% 1.49/0.68 % Paramodulations : 4511
% 1.49/0.68 % Factorizations : 2
% 1.49/0.68 % NegExts : 0
% 1.49/0.68 % Equation resolutions : 70
% 1.49/0.68 % Disequality decompositions : 0
% 1.49/0.68 % Total rewrite steps : 3437
% 1.49/0.68 % ...of those cached : 3257
% 1.49/0.68 % Propositional unsat checks : 0
% 1.49/0.68 % Propositional check models : 0
% 1.49/0.68 % Propositional check unsatisfiable : 0
% 1.49/0.68 % Propositional clauses : 0
% 1.49/0.68 % Propositional clauses after purity: 0
% 1.49/0.68 % Propositional unsat core size : 0
% 1.49/0.68 % Propositional preprocessing time : 0.000
% 1.49/0.68 % Propositional encoding time : 0.000
% 1.49/0.68 % Propositional solver time : 0.000
% 1.49/0.68 % Success case prop preproc time : 0.000
% 1.49/0.68 % Success case prop encoding time : 0.000
% 1.49/0.68 % Success case prop solver time : 0.000
% 1.49/0.68 % Current number of processed clauses : 611
% 1.49/0.68 % Positive orientable unit clauses : 224
% 1.49/0.68 % Positive unorientable unit clauses: 2
% 1.49/0.68 % Negative unit clauses : 46
% 1.49/0.68 % Non-unit-clauses : 339
% 1.49/0.68 % Current number of unprocessed clauses: 3744
% 1.49/0.68 % ...number of literals in the above : 11030
% 1.49/0.68 % Current number of archived formulas : 0
% 1.49/0.68 % Current number of archived clauses : 717
% 1.49/0.68 % Clause-clause subsumption calls (NU) : 74322
% 1.49/0.68 % Rec. Clause-clause subsumption calls : 27555
% 1.49/0.68 % Non-unit clause-clause subsumptions : 207
% 1.49/0.68 % Unit Clause-clause subsumption calls : 496
% 1.49/0.68 % Rewrite failures with RHS unbound : 0
% 1.49/0.68 % BW rewrite match attempts : 53
% 1.49/0.68 % BW rewrite match successes : 11
% 1.49/0.68 % Condensation attempts : 0
% 1.49/0.68 % Condensation successes : 0
% 1.49/0.68 % Termbank termtop insertions : 119661
% 1.49/0.68 % Search garbage collected termcells : 1926
% 1.49/0.68
% 1.49/0.68 % -------------------------------------------------
% 1.49/0.68 % User time : 0.200 s
% 1.49/0.68 % System time : 0.015 s
% 1.49/0.68 % Total time : 0.215 s
% 1.49/0.68 % Maximum resident set size: 5232 pages
% 1.49/0.68
% 1.49/0.68 % -------------------------------------------------
% 1.49/0.68 % User time : 0.821 s
% 1.49/0.68 % System time : 0.058 s
% 1.49/0.68 % Total time : 0.879 s
% 1.49/0.68 % Maximum resident set size: 5376 pages
% 1.49/0.68 % E exiting
%------------------------------------------------------------------------------