%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV592-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:08:47 AM UTC 2026
% Result : Unsatisfiable 16.29s 7.57s
% Output : CNFRefutation 16.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 42 ( 34 unt; 0 def)
% Number of atoms : 50 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 47 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
cnf(c_197,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1]) ).
fof(cls_class__semiring_Oadd__c_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_HOL_Oplus__class_Oplus(VAR_1,VAR_2,VAR_0) = c_HOL_Oplus__class_Oplus(VAR_2,VAR_1,VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(c_206,plain,
( c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A)
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Oadd__c_0]) ).
fof(cls_mult__eq__0__iff_2,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Otimes__class_Otimes(VAR_1,c_HOL_Ozero__class_Ozero(VAR_0),VAR_0) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(VAR_0) ),
file('theBenchmark.p',cls_mult__eq__0__iff_2) ).
cnf(c_606,plain,
( c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(A) ),
inference(clausify,[status(thm)],[cls_mult__eq__0__iff_2]) ).
fof(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(c_607,plain,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors]) ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(c_701,plain,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add]) ).
fof(cls_diff__0__right_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Ominus__class_Ominus(VAR_1,c_HOL_Ozero__class_Ozero(VAR_0),VAR_0) = VAR_1
| ~ class_OrderedGroup_Ogroup__add(VAR_0) ),
file('theBenchmark.p',cls_diff__0__right_0) ).
cnf(c_721,plain,
( c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A) = B
| ~ class_OrderedGroup_Ogroup__add(A) ),
inference(clausify,[status(thm)],[cls_diff__0__right_0]) ).
fof(cls_add__0__left_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(VAR_0),VAR_1,VAR_0) = VAR_1
| ~ class_OrderedGroup_Omonoid__add(VAR_0) ),
file('theBenchmark.p',cls_add__0__left_0) ).
cnf(c_742,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B
| ~ class_OrderedGroup_Omonoid__add(A) ),
inference(clausify,[status(thm)],[cls_add__0__left_0]) ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
cnf(c_743,plain,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add]) ).
cnf(c_759,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = A,
inference(resolve,[status(thm)],[c_742,c_743]) ).
cnf(c_791,plain,
c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_606,c_607]) ).
fof(cls_sin__add_0,axiom,
! [VAR_0,VAR_1] : c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(VAR_0,VAR_1,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(VAR_0),c_Transcendental_Ocos(VAR_1),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(VAR_0),c_Transcendental_Osin(VAR_1),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_sin__add_0) ).
cnf(c_1141,plain,
c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(A),c_Transcendental_Ocos(B),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(A),c_Transcendental_Osin(B),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_sin__add_0]) ).
cnf(c_1142,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(A),c_Transcendental_Ocos(B),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(A),c_Transcendental_Osin(B),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal)),
inference(copy,[status(thm)],[c_1141]) ).
fof(cls_sin__diff_0,axiom,
! [VAR_0,VAR_1] : c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(VAR_0,VAR_1,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(VAR_0),c_Transcendental_Ocos(VAR_1),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(VAR_0),c_Transcendental_Osin(VAR_1),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_sin__diff_0) ).
cnf(c_1236,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(A),c_Transcendental_Ocos(B),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(A),c_Transcendental_Osin(B),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_sin__diff_0]) ).
cnf(c_1237,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(A),c_Transcendental_Ocos(B),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(A),c_Transcendental_Osin(B),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal)),
inference(copy,[status(thm)],[c_1236]) ).
fof(cls_sin__pi_0,axiom,
c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',cls_sin__pi_0) ).
cnf(c_1249,plain,
c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_sin__pi_0]) ).
fof(cls_sin__periodic__pi_0,axiom,
! [VAR_0] : c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(VAR_0,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(VAR_0),tc_RealDef_Oreal),
file('theBenchmark.p',cls_sin__periodic__pi_0) ).
cnf(c_1251,plain,
c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(A,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(A),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_sin__periodic__pi_0]) ).
fof(cls_conjecture_0,axiom,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) != c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x),tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1253,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) != c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_1355,plain,
c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(B,A,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_197,c_206]) ).
cnf(c_1542,plain,
c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = A,
inference(resolve,[status(thm)],[c_701,c_721]) ).
cnf(c_1665,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(A),c_Transcendental_Osin(B),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(A),c_Transcendental_Ocos(B),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal)),
inference(paramod,[status(thm)],[c_1355,c_1142]) ).
cnf(c_5636,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(A),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(A,c_Transcendental_Opi,tc_RealDef_Oreal)),
inference(paramod,[status(thm)],[c_1249,c_1237]) ).
cnf(c_5637,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(A),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(A,c_Transcendental_Opi,tc_RealDef_Oreal)),
inference(paramod,[status(thm)],[c_791,c_5636]) ).
cnf(c_3377,plain,
c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(A),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(A,c_Transcendental_Opi,tc_RealDef_Oreal)),
inference(paramod,[status(thm)],[c_1542,c_5637]) ).
cnf(c_5638,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(A),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(A,c_Transcendental_Opi,tc_RealDef_Oreal)),
inference(paramod,[status(thm)],[c_1249,c_1665]) ).
cnf(c_5639,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(A),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(A,c_Transcendental_Opi,tc_RealDef_Oreal)),
inference(paramod,[status(thm)],[c_791,c_5638]) ).
cnf(c_5640,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(A,c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(A,c_Transcendental_Opi,tc_RealDef_Oreal)),
inference(paramod,[status(thm)],[c_3377,c_5639]) ).
cnf(c_5641,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(A,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(A,c_Transcendental_Opi,tc_RealDef_Oreal)),
inference(paramod,[status(thm)],[c_759,c_5640]) ).
cnf(c_5634,plain,
c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(A,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(A),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_1251,c_5641]) ).
cnf(c_5635,plain,
$false,
inference(resolve,[status(thm)],[c_5634,c_1253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV592-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n006.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 : Sat Sep 26 14:34:38 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 1471276 was started by sandbox on n006,
% 0.10/5.38 % Sat Sep 26 14:34:38 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.41
% 0.14/5.41 % From the command line: assign(max_seconds, 300).
% 16.29/7.57
% 16.29/7.57 % given #500 (I,wt=36): 1599 c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [back_unit_del(1086),unit_del(a,1255)].
% 16.29/7.57
% 16.29/7.57 % SZS status Unsatisfiable for theBenchmark
% 16.29/7.57
% 16.29/7.57 % Proof 1 at 1.96 (+ 0.15) seconds.
% 16.29/7.57 % Length of proof is 23.
% 16.29/7.57 % Level of proof is 4.
% 16.29/7.57 % Maximum clause weight is 40.000.
% 16.29/7.57 % Given clauses 563.
% 16.29/7.57
% 16.29/7.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------