%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV674-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:23:59 PM UTC 2026
% Result : Unsatisfiable 6.23s 7.27s
% Output : CNFRefutation 6.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 94 ( 38 unt; 7 def)
% Number of atoms : 213 ( 119 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 146 ( 67 ~; 79 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 147 ( 0 sgn 147 !; 0 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
fof(f55,axiom,
! [X2,X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f164,axiom,
! [X2,X0,X1] :
( c_HOL_Oinverse__class_Oinverse(X1,X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Odivision__ring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
fof(f165,axiom,
! [X2,X0,X1] :
( c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X0),X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
fof(f415,axiom,
! [X0,X1] :
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
fof(f416,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(reorient_equations,[],[f415]) ).
fof(f439,axiom,
! [X0,X1] :
( c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
fof(f622,axiom,
! [X0] : c_lessequals(X0,X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
fof(f637,axiom,
! [X2,X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(X0)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X2,X0)
| ~ class_Ring__and__Field_Odivision__ring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
fof(f638,plain,
! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X2,X0)
| ~ class_Ring__and__Field_Odivision__ring(X0) ),
inference(reorient_equations,[],[f637]) ).
fof(f687,axiom,
( v_a != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nz_0) ).
fof(f699,axiom,
! [X0] : c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f700,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X0,tc_nat),
inference(reorient_equations,[],[f699]) ).
fof(f701,axiom,
! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f731,axiom,
! [X2,X3,X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(X0)
| ~ c_lessequals(X3,X2,tc_nat)
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff_0) ).
fof(f732,plain,
! [X2,X3,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(X3,X2,tc_nat)
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(reorient_equations,[],[f731]) ).
fof(f747,negated_conjecture,
class_Ring__and__Field_Ofield(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f749,negated_conjecture,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f753,axiom,
! [X0] :
( class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ocomm__semiring__1) ).
fof(f756,axiom,
! [X0] :
( class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Odivision__ring) ).
tcf(c_763,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_847,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oinverse__class_Oinverse(X0,X2) = X1 )
| ~ class_Ring__and__Field_Odivision__ring(X2)
| ( c_HOL_Otimes__class_Otimes(X0,X1,X2) != c_HOL_Oone__class_Oone(X2) ) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_848,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,X2,X0) )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_899,plain,
! [X0: $i,X1: $i] :
( ( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_HOL_Oone__class_Oone(X0) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f416]) ).
tcf(c_904,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oinverse__class_Oinverse(X1,X0) )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f439]) ).
tcf(c_1024,plain,
! [X0: $i] : c_lessequals(X0,X0,tc_nat),
inference(cnf_transformation,[],[f622]) ).
tcf(c_1033,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ozero__class_Ozero(X0) = X1 )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X2,X0) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ class_Ring__and__Field_Odivision__ring(X0) ),
inference(cnf_transformation,[],[f638]) ).
tcf(c_1053,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Ozero__class_Ozero(t_a) != v_a ) ),
inference(cnf_transformation,[],[f687]) ).
tcf(c_1060,plain,
! [X0: $i] : c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnf_transformation,[],[f700]) ).
tcf(c_1061,plain,
! [X0: $i] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0,
inference(cnf_transformation,[],[f701]) ).
tcf(c_1077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_HOL_Ozero__class_Ozero(X2) = X3 )
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X3,X1,X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) = c_Power_Opower__class_Opower(X3,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2) )
| ~ class_Ring__and__Field_Ofield(X2)
| ~ c_lessequals(X0,X1,tc_nat) ),
inference(cnf_transformation,[],[f732]) ).
tcf(c_1082,negated_conjecture,
class_Ring__and__Field_Ofield(t_a),
inference(cnf_transformation,[],[f747]) ).
tcf(c_1084,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a),
inference(cnf_transformation,[],[f749]) ).
tcf(c_1088,plain,
! [X0: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f753]) ).
tcf(c_1091,plain,
! [X0: $i] :
( class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f756]) ).
tcf(c_1342,plain,
c_HOL_Ozero__class_Ozero(t_a) != v_a,
inference(global_subsumption_just,[status(thm)],[c_1053,c_1082,c_1053]) ).
tcf(c_1383,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_763]) ).
tcf(c_1401,plain,
! [X0: $i,X1: $i] :
( ( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_HOL_Oone__class_Oone(X0) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_899]) ).
tcf(c_1403,plain,
! [X0: $i] :
( ~ class_Ring__and__Field_Ofield(X0)
| class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_1088]) ).
tcf(c_1404,plain,
! [X0: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(renaming,[status(thm)],[c_1403]) ).
tcf(c_1447,plain,
! [X0: $i] :
( class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(prop_impl_just,[status(thm)],[c_1091]) ).
tcf(c_1449,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,X2,X0) )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(prop_impl_just,[status(thm)],[c_848]) ).
tcf(c_1457,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oinverse__class_Oinverse(X1,X0) )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(prop_impl_just,[status(thm)],[c_904]) ).
tcf(c_5310,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_x,t_a),
inference(demodulation,[status(thm)],[c_1084,c_1061]) ).
tcf(c_7299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_HOL_Ozero__class_Ozero(X1) = X2 )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X2,X1),X3,X1) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X2,X3,X1),X1) )
| ~ class_Ring__and__Field_Ofield(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1447,c_1033]) ).
tcf(c_7300,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ozero__class_Ozero(X0) = X1 )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X2,X0) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(unflattening,[status(thm)],[c_7299]) ).
tcf(c_7364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_HOL_Oinverse__class_Oinverse(X0,X2) = X1 )
| ~ class_Ring__and__Field_Ofield(X3)
| ( X2 != X3 )
| ( c_HOL_Otimes__class_Otimes(X0,X1,X2) != c_HOL_Oone__class_Oone(X2) ) ),
inference(resolution_lifted,[status(thm)],[c_1447,c_847]) ).
tcf(c_7365,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oinverse__class_Oinverse(X0,X2) = X1 )
| ~ class_Ring__and__Field_Ofield(X2)
| ( c_HOL_Otimes__class_Otimes(X0,X1,X2) != c_HOL_Oone__class_Oone(X2) ) ),
inference(unflattening,[status(thm)],[c_7364]) ).
tcf(c_7940,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ozero__class_Ozero(X0) = X1 )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X2,X0) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_7300,c_1082]) ).
tcf(c_7941,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X0,X1,t_a),t_a) ) ),
inference(unflattening,[status(thm)],[c_7940]) ).
tcf(c_8021,plain,
! [X0: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_1404,c_1082]) ).
tcf(c_8022,plain,
class_Ring__and__Field_Ocomm__semiring__1(t_a),
inference(unflattening,[status(thm)],[c_8021]) ).
tcf(c_8068,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oinverse__class_Oinverse(X1,X0) )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_1457,c_1082]) ).
tcf(c_8069,plain,
! [X0: $i] : c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),X0,t_a) = c_HOL_Oinverse__class_Oinverse(X0,t_a),
inference(unflattening,[status(thm)],[c_8068]) ).
tcf(c_8104,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,X2,X0) )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_1449,c_1082]) ).
tcf(c_8105,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,t_a),t_a) = c_HOL_Oinverse__class_Odivide(X0,X1,t_a),
inference(unflattening,[status(thm)],[c_8104]) ).
tcf(c_8119,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oinverse__class_Oinverse(X0,X2) = X1 )
| ( X2 != t_a )
| ( c_HOL_Otimes__class_Otimes(X0,X1,X2) != c_HOL_Oone__class_Oone(X2) ) ),
inference(resolution_lifted,[status(thm)],[c_7365,c_1082]) ).
tcf(c_8120,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oinverse__class_Oinverse(X0,t_a) = X1 )
| ( c_HOL_Otimes__class_Otimes(X0,X1,t_a) != c_HOL_Oone__class_Oone(t_a) ) ),
inference(unflattening,[status(thm)],[c_8119]) ).
tcf(c_8128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_HOL_Ozero__class_Ozero(X0) = X3 )
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X3,X2,X0),c_Power_Opower__class_Opower(X3,X1,X0),X0) = c_Power_Opower__class_Opower(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X0) )
| ~ c_lessequals(X1,X2,tc_nat)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_1077,c_1082]) ).
tcf(c_8129,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ozero__class_Ozero(t_a) = X2 )
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X1,t_a),c_Power_Opower__class_Opower(X2,X0,t_a),t_a) = c_Power_Opower__class_Opower(X2,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),t_a) )
| ~ c_lessequals(X0,X1,tc_nat) ),
inference(unflattening,[status(thm)],[c_8128]) ).
tcf(c_8715,plain,
! [X0: $i,X1: $i] :
( ( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_HOL_Oone__class_Oone(X0) )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_1401,c_8022]) ).
tcf(c_8716,plain,
! [X0: $i] : c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a),
inference(unflattening,[status(thm)],[c_8715]) ).
tcf(c_8745,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_1383,c_8022]) ).
tcf(c_8746,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(X1,X0,t_a),
inference(unflattening,[status(thm)],[c_8745]) ).
tcf(c_13451,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_x,t_a) != c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),
inference(demodulation,[status(thm)],[c_5310,c_8069,c_8716]) ).
tcf(c_17433,plain,
! [X0: $i,X1: $i] :
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X0,X1,t_a),t_a) )
| ( c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_7941]) ).
tcf(c_17434,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X0,X1,t_a),t_a) ) ),
inference(renaming,[status(thm)],[c_17433]) ).
tcf(c_17461,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oinverse__class_Oinverse(X0,t_a) = X1 )
| ( c_HOL_Otimes__class_Otimes(X0,X1,t_a) != c_HOL_Oone__class_Oone(t_a) ) ),
inference(prop_impl_just,[status(thm)],[c_8120]) ).
tcf(c_20465,definition,
iPr_def_10 = c_HOL_Ozero__class_Ozero(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_20466,definition,
iPr_def_11 = c_HOL_Oinverse__class_Oinverse(v_a,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_20467,definition,
iPr_def_12 = c_Power_Opower__class_Opower(iPr_def_11,v_x,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_20468,definition,
iPr_def_13 = c_Power_Opower__class_Opower(v_a,v_x,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_20469,definition,
iPr_def_14 = c_HOL_Oinverse__class_Oinverse(iPr_def_13,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_20470,definition,
iPr_def_15 = c_HOL_Oone__class_Oone(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_20471,definition,
iPr_def_16 = c_HOL_Ozero__class_Ozero(tc_nat),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_20476,plain,
iPr_def_12 != iPr_def_14,
inference(demodulation,[status(thm)],[c_13451,c_20468,c_20469,c_20466,c_20467]) ).
tcf(c_20479,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(X0,X1,t_a) = c_HOL_Otimes__class_Otimes(X1,X0,t_a),
inference(demodulation,[status(thm)],[c_8746]) ).
tcf(c_20481,plain,
! [X0: $i] : c_Power_Opower__class_Opower(X0,iPr_def_16,t_a) = iPr_def_15,
inference(demodulation,[status(thm)],[c_8716,c_20471]) ).
tcf(c_20497,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( iPr_def_10 = X2 )
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X1,t_a),c_Power_Opower__class_Opower(X2,X0,t_a),t_a) = c_Power_Opower__class_Opower(X2,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),t_a) )
| ~ c_lessequals(X0,X1,tc_nat) ),
inference(demodulation,[status(thm)],[c_8129]) ).
tcf(c_20498,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,t_a),t_a) = c_HOL_Oinverse__class_Odivide(X0,X1,t_a),
inference(demodulation,[status(thm)],[c_8105]) ).
tcf(c_24837,plain,
v_a != iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1342,c_20465]) ).
tcf(c_24856,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_10 )
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a) = c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),t_a) ) ),
inference(superposition,[status(thm)],[c_1024,c_20497]) ).
tcf(c_25102,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a) = c_HOL_Oinverse__class_Odivide(X1,X0,t_a),
inference(superposition,[status(thm)],[c_20479,c_20498]) ).
tcf(c_25177,plain,
! [X0: $i] : c_HOL_Otimes__class_Otimes(iPr_def_14,X0,t_a) = c_HOL_Oinverse__class_Odivide(X0,iPr_def_13,t_a),
inference(superposition,[status(thm)],[c_20469,c_25102]) ).
tcf(c_25378,plain,
! [X0: $i] : c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_1060,c_20471]) ).
tcf(c_26161,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_10 )
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a) = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_24856,c_20481,c_25378]) ).
tcf(c_26173,plain,
( ( v_a = iPr_def_10 )
| ( c_HOL_Oinverse__class_Odivide(iPr_def_13,iPr_def_13,t_a) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_20468,c_26161]) ).
tcf(c_26192,plain,
c_HOL_Oinverse__class_Odivide(iPr_def_13,iPr_def_13,t_a) = iPr_def_15,
inference(forward_subsumption_resolution,[status(thm)],[c_26173,c_24837]) ).
tcf(c_26295,plain,
c_HOL_Otimes__class_Otimes(iPr_def_13,iPr_def_14,t_a) = iPr_def_15,
inference(demodulation,[status(thm)],[c_26192,c_20479,c_25177]) ).
tcf(c_29174,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oinverse__class_Oinverse(X0,t_a) = X1 )
| ( c_HOL_Otimes__class_Otimes(X0,X1,t_a) != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_17461,c_20470]) ).
tcf(c_29195,plain,
c_HOL_Oinverse__class_Oinverse(iPr_def_13,t_a) = iPr_def_14,
inference(superposition,[status(thm)],[c_26295,c_29174]) ).
tcf(c_30074,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_10 )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X0,X1,t_a),t_a) ) ),
inference(light_normalisation,[status(thm)],[c_17434,c_20465]) ).
tcf(c_30081,plain,
( ( v_a = iPr_def_10 )
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_x,t_a) = c_HOL_Oinverse__class_Oinverse(iPr_def_13,t_a) ) ),
inference(superposition,[status(thm)],[c_20468,c_30074]) ).
tcf(c_30117,plain,
( ( iPr_def_12 = iPr_def_14 )
| ( v_a = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_30081,c_20466,c_20467,c_29195]) ).
tcf(c_30118,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_30117,c_20476,c_24837]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV674-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.37 % Computer : n014.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Thu Sep 24 20:52:54 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 6.23/7.27 % SZS status Started for theBenchmark.p
% 6.23/7.27 % SZS status Unsatisfiable for theBenchmark.p
% 6.23/7.27
% 6.23/7.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.23/7.27
% 6.23/7.27 % ------ iProver source info
% 6.23/7.27
% 6.23/7.27 % git: date: 2026-07-19 20:42:38 +0200
% 6.23/7.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.23/7.27 % git: non_committed_changes: false
% 6.23/7.27
% 6.23/7.27 % ------ Parsing...% successful
% 6.23/7.27
% 6.23/7.27
% 6.23/7.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.23/7.27
% 6.23/7.27 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe_e sup_sim: 22 sf_s rm: 34 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 34 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 34 0s sf_e pe_s pe_e %
% 6.23/7.27
% 6.23/7.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.23/7.27
% 6.23/7.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.23/7.27 % ------ Proving...
% 6.23/7.27 % ------ Problem Properties
% 6.23/7.27
% 6.23/7.27 %
% 6.23/7.27 % clauses 296
% 6.23/7.27 % conjectures 0
% 6.23/7.27 % EPR 25
% 6.23/7.27 % Horn 227
% 6.23/7.27 % unary 83
% 6.23/7.27 % binary 76
% 6.23/7.27 % lits 678
% 6.23/7.27 % lits eq 189
% 6.23/7.27 % fd_pure 0
% 6.23/7.27 % fd_pseudo 0
% 6.23/7.27 % fd_cond 28
% 6.23/7.27 % fd_pseudo_cond 13
% 6.23/7.27 % AC symbols 0
% 6.23/7.27
% 6.23/7.27 % ------ Schedule dynamic 5 is on
% 6.23/7.27
% 6.23/7.27 % ------ no conjectures: strip conj schedule
% 6.23/7.27
% 6.23/7.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 6.23/7.27
% 6.23/7.27
% 6.23/7.27 % ------
% 6.23/7.27 % Current options:
% 6.23/7.27 % ------
% 6.23/7.27
% 6.23/7.27
% 6.23/7.27 %
% 6.23/7.27
% 6.23/7.27 % ------ Proving...
% 6.23/7.27 %
% 6.23/7.27
% 6.23/7.27 % SZS status Unsatisfiable for theBenchmark.p
% 6.23/7.27
% 6.23/7.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.23/7.28
% 6.23/7.28
%------------------------------------------------------------------------------