%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV680-1 : 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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:24:00 PM UTC 2026
% Result : Unsatisfiable 170.40s 26.96s
% Output : CNFRefutation 170.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 27
% Syntax : Number of formulae : 105 ( 43 unt; 10 def)
% Number of atoms : 294 ( 147 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 223 ( 112 ~; 111 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 20 ( 18 usr; 12 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 151 ( 0 sgn 151 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
fof(f50,axiom,
! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f138,axiom,
! [X0] :
( c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f139,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(reorient_equations,[],[f138]) ).
fof(f663,axiom,
! [X2,X3,X0,X1] :
( c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X0) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult_0) ).
fof(f669,axiom,
! [X2,X3,X0,X1] :
( X2 = c_HOL_Ozero__class_Ozero(X0)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X2,X3,X0),X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
fof(f670,plain,
! [X2,X3,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X2
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X2,X3,X0),X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(reorient_equations,[],[f669]) ).
fof(f714,axiom,
! [X2,X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(X0)
| c_Power_Opower__class_Opower(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f715,plain,
! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0) ),
inference(reorient_equations,[],[f714]) ).
fof(f716,axiom,
! [X2,X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(X0)
| c_Power_Opower__class_Opower(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f717,plain,
! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X2,X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(reorient_equations,[],[f716]) ).
fof(f735,axiom,
! [X2,X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(X0)
| X2 = c_HOL_Ozero__class_Ozero(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
fof(f736,plain,
! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X1,X2,X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0) ),
inference(reorient_equations,[],[f735]) ).
fof(f742,axiom,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f757,negated_conjecture,
class_Ring__and__Field_Ofield(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f758,negated_conjecture,
v_a != c_HOL_Ozero__class_Ozero(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f759,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f760,axiom,
! [X0] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f764,axiom,
! [X0] :
( class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ono__zero__divisors) ).
fof(f772,axiom,
! [X0] :
( class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ozero__neq__one) ).
fof(f776,axiom,
! [X0] :
( class_OrderedGroup_Omonoid__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Omonoid__mult) ).
fof(f782,axiom,
! [X0] :
( class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Power_Opower) ).
tcf(c_789,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 )
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_847,plain,
! [X0: $i] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_1095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X0) )
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f663]) ).
tcf(c_1098,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(X1,X2,X0),c_Power_Opower__class_Opower(X3,X2,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X3,X0),X2,X0) )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f670]) ).
tcf(c_1116,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ozero__class_Ozero(X2) = X0 )
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2)
| ( c_Power_Opower__class_Opower(X0,X1,X2) != c_HOL_Ozero__class_Ozero(X2) ) ),
inference(cnf_transformation,[],[f715]) ).
tcf(c_1117,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ozero__class_Ozero(X2) = X0 )
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ( c_Power_Opower__class_Opower(X0,X1,X2) != c_HOL_Ozero__class_Ozero(X2) ) ),
inference(cnf_transformation,[],[f717]) ).
tcf(c_1124,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ozero__class_Ozero(X2) = X1 )
| ( c_HOL_Ozero__class_Ozero(X2) = X0 )
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ( c_HOL_Otimes__class_Otimes(X0,X1,X2) != c_HOL_Ozero__class_Ozero(X2) ) ),
inference(cnf_transformation,[],[f736]) ).
tcf(c_1128,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),
inference(cnf_transformation,[],[f742]) ).
tcf(c_1131,negated_conjecture,
class_Ring__and__Field_Ofield(t_a),
inference(cnf_transformation,[],[f757]) ).
tcf(c_1132,negated_conjecture,
c_HOL_Ozero__class_Ozero(t_a) != v_a,
inference(cnf_transformation,[],[f758]) ).
tcf(c_1133,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),
inference(cnf_transformation,[],[f759]) ).
tcf(c_1134,plain,
! [X0: $i] :
( class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f760]) ).
tcf(c_1138,plain,
! [X0: $i] :
( class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f764]) ).
tcf(c_1146,plain,
! [X0: $i] :
( class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f772]) ).
tcf(c_1150,plain,
! [X0: $i] :
( class_OrderedGroup_Omonoid__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f776]) ).
tcf(c_1156,plain,
! [X0: $i] :
( class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f782]) ).
tcf(c_5450,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_k,tc_nat),t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),
inference(demodulation,[status(thm)],[c_1133,c_1128]) ).
tcf(c_5854,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_HOL_Ozero__class_Ozero(X2) = X0 )
| ~ class_Ring__and__Field_Ofield(X3)
| ( X2 != X3 )
| ( c_Power_Opower__class_Opower(X0,X1,X2) != c_HOL_Ozero__class_Ozero(X2) ) ),
inference(resolution_lifted,[status(thm)],[c_1134,c_1116]) ).
tcf(c_5855,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ozero__class_Ozero(X2) = X0 )
| ~ class_Ring__and__Field_Ofield(X2)
| ( c_Power_Opower__class_Opower(X0,X1,X2) != c_HOL_Ozero__class_Ozero(X2) ) ),
inference(unflattening,[status(thm)],[c_5854]) ).
tcf(c_6482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_HOL_Ozero__class_Ozero(X2) = X0 )
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Ring__and__Field_Ofield(X3)
| ( X2 != X3 )
| ( c_Power_Opower__class_Opower(X0,X1,X2) != c_HOL_Ozero__class_Ozero(X2) ) ),
inference(resolution_lifted,[status(thm)],[c_1156,c_1117]) ).
tcf(c_6483,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ozero__class_Ozero(X2) = X0 )
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Ring__and__Field_Ofield(X2)
| ( c_Power_Opower__class_Opower(X0,X1,X2) != c_HOL_Ozero__class_Ozero(X2) ) ),
inference(unflattening,[status(thm)],[c_6482]) ).
tcf(c_6484,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ozero__class_Ozero(X2) = X0 )
| ( c_Power_Opower__class_Opower(X0,X1,X2) != c_HOL_Ozero__class_Ozero(X2) )
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(global_subsumption_just,[status(thm)],[c_6483,c_5855]) ).
tcf(c_6485,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ozero__class_Ozero(X2) = X0 )
| ~ class_Ring__and__Field_Ofield(X2)
| ( c_Power_Opower__class_Opower(X0,X1,X2) != c_HOL_Ozero__class_Ozero(X2) ) ),
inference(renaming,[status(thm)],[c_6484]) ).
tcf(c_6524,plain,
! [X0: $i,X1: $i] :
( ~ class_Ring__and__Field_Ofield(X1)
| ( X0 != X1 )
| ( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_1146,c_847]) ).
tcf(c_6525,plain,
! [X0: $i] :
( ~ class_Ring__and__Field_Ofield(X0)
| ( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
inference(unflattening,[status(thm)],[c_6524]) ).
tcf(c_9511,plain,
! [X0: $i] :
( ( X0 != t_a )
| ( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_6525,c_1131]) ).
tcf(c_9512,plain,
c_HOL_Ozero__class_Ozero(t_a) != c_HOL_Oone__class_Oone(t_a),
inference(unflattening,[status(thm)],[c_9511]) ).
tcf(c_9536,plain,
! [X0: $i] :
( class_OrderedGroup_Omonoid__mult(X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_1150,c_1131]) ).
tcf(c_9537,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(unflattening,[status(thm)],[c_9536]) ).
tcf(c_9586,plain,
! [X0: $i] :
( class_Ring__and__Field_Ono__zero__divisors(X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_1138,c_1131]) ).
tcf(c_9587,plain,
class_Ring__and__Field_Ono__zero__divisors(t_a),
inference(unflattening,[status(thm)],[c_9586]) ).
tcf(c_9626,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(X1,X2,X0),c_Power_Opower__class_Opower(X3,X2,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X3,X0),X2,X0) )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_1098,c_1131]) ).
tcf(c_9627,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(X0,X1,t_a),c_Power_Opower__class_Opower(X2,X1,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X2,t_a),X1,t_a) ) ),
inference(unflattening,[status(thm)],[c_9626]) ).
tcf(c_9752,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ozero__class_Ozero(X2) = X0 )
| ( X2 != t_a )
| ( c_Power_Opower__class_Opower(X0,X1,X2) != c_HOL_Ozero__class_Ozero(X2) ) ),
inference(resolution_lifted,[status(thm)],[c_6485,c_1131]) ).
tcf(c_9753,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ( c_Power_Opower__class_Opower(X0,X1,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(unflattening,[status(thm)],[c_9752]) ).
tcf(c_10133,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Ozero__class_Ozero(X2) = X1 )
| ( c_HOL_Ozero__class_Ozero(X2) = X0 )
| ( X2 != t_a )
| ( c_HOL_Otimes__class_Otimes(X0,X1,X2) != c_HOL_Ozero__class_Ozero(X2) ) ),
inference(resolution_lifted,[status(thm)],[c_1124,c_9587]) ).
tcf(c_10134,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Ozero__class_Ozero(t_a) = X1 )
| ( c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ( c_HOL_Otimes__class_Otimes(X0,X1,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(unflattening,[status(thm)],[c_10133]) ).
tcf(c_10402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X0) )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_1095,c_9537]) ).
tcf(c_10403,plain,
! [X0: $i,X1: $i,X2: $i] : c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X0,X1,t_a),X2,t_a) = c_Power_Opower__class_Opower(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),t_a),
inference(unflattening,[status(thm)],[c_10402]) ).
tcf(c_10414,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_789,c_9537]) ).
tcf(c_10415,plain,
! [X0: $i] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(t_a),t_a) = X0,
inference(unflattening,[status(thm)],[c_10414]) ).
tcf(c_22675,plain,
! [X0: $i,X1: $i] :
( ( c_Power_Opower__class_Opower(X0,X1,t_a) != c_HOL_Ozero__class_Ozero(t_a) )
| ( c_HOL_Ozero__class_Ozero(t_a) = X0 ) ),
inference(prop_impl_just,[status(thm)],[c_9753]) ).
tcf(c_22676,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Ozero__class_Ozero(t_a) = X0 )
| ( c_Power_Opower__class_Opower(X0,X1,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ),
inference(renaming,[status(thm)],[c_22675]) ).
tcf(c_22685,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(X0,X1,t_a),c_Power_Opower__class_Opower(X2,X1,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X2,t_a),X1,t_a) ) ),
inference(prop_impl_just,[status(thm)],[c_9627]) ).
tcf(c_25884,definition,
iPr_def_10 = c_HOL_Ozero__class_Ozero(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_25888,definition,
iPr_def_14 = c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_25889,definition,
iPr_def_15 = c_Power_Opower__class_Opower(v_a,iPr_def_14,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_25890,definition,
iPr_def_16 = c_HOL_Otimes__class_Otimes(v_i,v_k,tc_nat),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_25891,definition,
iPr_def_17 = c_Power_Opower__class_Opower(v_a,iPr_def_16,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_25892,definition,
iPr_def_18 = c_HOL_Oinverse__class_Odivide(iPr_def_15,iPr_def_17,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_25893,definition,
iPr_def_19 = c_Power_Opower__class_Opower(v_a,v_j,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_25894,definition,
iPr_def_20 = c_Power_Opower__class_Opower(v_a,v_k,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_25895,definition,
iPr_def_21 = c_HOL_Oinverse__class_Odivide(iPr_def_19,iPr_def_20,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_25896,definition,
iPr_def_22 = c_Power_Opower__class_Opower(iPr_def_21,v_i,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_25909,plain,
! [X0: $i] : c_HOL_Otimes__class_Otimes(X0,iPr_def_11,t_a) = X0,
inference(demodulation,[status(thm)],[c_10415]) ).
tcf(c_25911,plain,
! [X0: $i,X1: $i,X2: $i] : c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X0,X1,t_a),X2,t_a) = c_Power_Opower__class_Opower(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),t_a),
inference(demodulation,[status(thm)],[c_10403]) ).
tcf(c_25915,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_10 = X1 )
| ( iPr_def_10 = X0 )
| ( c_HOL_Otimes__class_Otimes(X0,X1,t_a) != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_10134]) ).
tcf(c_25939,plain,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_9512]) ).
tcf(c_25941,plain,
iPr_def_18 != iPr_def_22,
inference(demodulation,[status(thm)],[c_5450,c_25894,c_25893,c_25895,c_25896,c_25890,c_25891,c_25888,c_25889,c_25892]) ).
tcf(c_25942,negated_conjecture,
iPr_def_10 != v_a,
inference(demodulation,[status(thm)],[c_1132]) ).
tcf(c_25945,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_32151,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( iPr_def_10 = iPr_def_10 )
| ( c_HOL_Otimes__class_Otimes(iPr_def_10,iPr_def_11,t_a) != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_25915]) ).
tcf(c_32152,plain,
c_HOL_Otimes__class_Otimes(iPr_def_10,iPr_def_11,t_a) = iPr_def_10,
inference(instantiation,[status(thm)],[c_25909]) ).
tcf(c_32681,plain,
! [X0: $i] :
( ( iPr_def_10 = v_a )
| ( iPr_def_10 != X0 )
| ( v_a != X0 ) ),
inference(instantiation,[status(thm)],[c_25945]) ).
tcf(c_49464,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_10 )
| ( c_Power_Opower__class_Opower(X0,X1,t_a) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_22676,c_25884]) ).
tcf(c_49472,plain,
( ( v_a = iPr_def_10 )
| ( iPr_def_10 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_25894,c_49464]) ).
tcf(c_86088,plain,
( ( iPr_def_10 = v_a )
| ( iPr_def_10 != iPr_def_10 )
| ( v_a != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_32681]) ).
tcf(c_125862,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_10 )
| ( c_Power_Opower__class_Opower(X0,X1,t_a) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_22676,c_25884]) ).
tcf(c_125870,plain,
( ( v_a = iPr_def_10 )
| ( iPr_def_10 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_25894,c_125862]) ).
tcf(c_128370,plain,
iPr_def_10 != iPr_def_20,
inference(global_subsumption_just,[status(thm)],[c_125870,c_25939,c_25942,c_32151,c_32152,c_49472,c_86088]) ).
tcf(c_142143,plain,
! [X0: $i] : c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_j,X0,tc_nat),t_a) = c_Power_Opower__class_Opower(iPr_def_19,X0,t_a),
inference(superposition,[status(thm)],[c_25893,c_25911]) ).
tcf(c_142144,plain,
! [X0: $i] : c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,X0,tc_nat),t_a) = c_Power_Opower__class_Opower(iPr_def_20,X0,t_a),
inference(superposition,[status(thm)],[c_25894,c_25911]) ).
tcf(c_144278,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = iPr_def_10 )
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,t_a),c_Power_Opower__class_Opower(X2,X1,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X2,t_a),X1,t_a) ) ),
inference(light_normalisation,[status(thm)],[c_22685,c_25884]) ).
tcf(c_150983,plain,
! [X0: $i] : c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(X0,v_j,tc_nat),t_a) = c_Power_Opower__class_Opower(iPr_def_19,X0,t_a),
inference(superposition,[status(thm)],[c_1128,c_142143]) ).
tcf(c_151020,plain,
! [X0: $i] : c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(X0,v_k,tc_nat),t_a) = c_Power_Opower__class_Opower(iPr_def_20,X0,t_a),
inference(superposition,[status(thm)],[c_1128,c_142144]) ).
tcf(c_162793,plain,
c_Power_Opower__class_Opower(v_a,iPr_def_14,t_a) = c_Power_Opower__class_Opower(iPr_def_19,v_i,t_a),
inference(superposition,[status(thm)],[c_25888,c_150983]) ).
tcf(c_162808,plain,
c_Power_Opower__class_Opower(iPr_def_19,v_i,t_a) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_162793,c_25889]) ).
tcf(c_162906,plain,
c_Power_Opower__class_Opower(v_a,iPr_def_16,t_a) = c_Power_Opower__class_Opower(iPr_def_20,v_i,t_a),
inference(superposition,[status(thm)],[c_25890,c_151020]) ).
tcf(c_162920,plain,
c_Power_Opower__class_Opower(iPr_def_20,v_i,t_a) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_162906,c_25891]) ).
tcf(c_162965,plain,
! [X0: $i] :
( ( iPr_def_10 = iPr_def_20 )
| ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,v_i,t_a),iPr_def_17,t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,iPr_def_20,t_a),v_i,t_a) ) ),
inference(superposition,[status(thm)],[c_162920,c_144278]) ).
tcf(c_162967,plain,
! [X0: $i] : c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,v_i,t_a),iPr_def_17,t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,iPr_def_20,t_a),v_i,t_a),
inference(forward_subsumption_resolution,[status(thm)],[c_162965,c_128370]) ).
tcf(c_283266,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(iPr_def_19,v_i,t_a),iPr_def_17,t_a) = c_Power_Opower__class_Opower(iPr_def_21,v_i,t_a),
inference(superposition,[status(thm)],[c_25895,c_162967]) ).
tcf(c_283321,plain,
iPr_def_18 = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_283266,c_25892,c_25896,c_162808]) ).
tcf(c_283322,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_283321,c_25941]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV680-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n009.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Thu Sep 24 20:53:29 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.46 Running first-order theorem proving
% 0.13/0.46 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
% 0.13/0.48
% 0.13/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.48
% 0.13/0.48 % Detected problem language: tptp
% 0.20/0.49 % Proving...
% 170.40/26.96 % SZS status Started for theBenchmark.p
% 170.40/26.96 % SZS status Unsatisfiable for theBenchmark.p
% 170.40/26.96
% 170.40/26.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 170.40/26.96
% 170.40/26.96 % ------ iProver source info
% 170.40/26.96
% 170.40/26.96 % git: date: 2026-07-19 20:42:38 +0200
% 170.40/26.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 170.40/26.96 % git: non_committed_changes: false
% 170.40/26.96
% 170.40/26.96 % ------ Parsing...% successful
% 170.40/26.96
% 170.40/26.96
% 170.40/26.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 170.40/26.96
% 170.40/26.96 % ------ 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: 41 sf_s rm: 48 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 48 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 48 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 48 0s sf_e pe_s pe_e %
% 170.40/26.96
% 170.40/26.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 170.40/26.96
% 170.40/26.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 170.40/26.96 % ------ Proving...
% 170.40/26.96 % ------ Problem Properties
% 170.40/26.96
% 170.40/26.96 %
% 170.40/26.96 % clauses 351
% 170.40/26.96 % conjectures 1
% 170.40/26.96 % EPR 20
% 170.40/26.96 % Horn 298
% 170.40/26.96 % unary 124
% 170.40/26.96 % binary 92
% 170.40/26.96 % lits 746
% 170.40/26.96 % lits eq 238
% 170.40/26.96 % fd_pure 0
% 170.40/26.96 % fd_pseudo 0
% 170.40/26.96 % fd_cond 30
% 170.40/26.96 % fd_pseudo_cond 26
% 170.40/26.96 % AC symbols 0
% 170.40/26.96
% 170.40/26.96 % ------ Schedule dynamic 5 is on
% 170.40/26.96
% 170.40/26.96 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 170.40/26.96
% 170.40/26.96
% 170.40/26.96 % ------
% 170.40/26.96 % Current options:
% 170.40/26.96 % ------
% 170.40/26.96
% 170.40/26.96
% 170.40/26.96 %
% 170.40/26.96
% 170.40/26.96 % ------ Proving...
% 170.40/26.96 % Proof_search_loop: time out after: 2239 full_loop iterations
% 170.40/26.96
% 170.40/26.96 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 170.40/26.96
% 170.40/26.96
% 170.40/26.96 % ------
% 170.40/26.96 % Current options:
% 170.40/26.96 % ------
% 170.40/26.96
% 170.40/26.96
% 170.40/26.96 %
% 170.40/26.96
% 170.40/26.96 % ------ Proving...
% 170.40/26.96 %
% 170.40/26.96
% 170.40/26.96 % SZS status Unsatisfiable for theBenchmark.p
% 170.40/26.96
% 170.40/26.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 170.40/26.96
% 170.40/26.96
%------------------------------------------------------------------------------