%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV603-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 09:08:48 AM UTC 2026
% Result : Unsatisfiable 17.50s 2.61s
% Output : CNFRefutation 17.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 17 unt; 0 def)
% Number of atoms : 21 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_abs__eq__0_1,axiom,
! [VAR_0] :
( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(VAR_0),VAR_0) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(VAR_0) ),
file('theBenchmark.p',cls_abs__eq__0_1) ).
cnf(c_398,plain,
( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(A) ),
inference(clausify,[status(thm)],[cls_abs__eq__0_1]) ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(c_426,plain,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs]) ).
fof(cls_real__zero__not__eq__one_0,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',cls_real__zero__not__eq__one_0) ).
cnf(c_917,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_real__zero__not__eq__one_0]) ).
cnf(c_918,plain,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(copy,[status(thm)],[c_917]) ).
fof(cls_real__mult__commute_0,axiom,
! [VAR_0,VAR_1] : c_HOL_Otimes__class_Otimes(VAR_0,VAR_1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(VAR_1,VAR_0,tc_RealDef_Oreal),
file('theBenchmark.p',cls_real__mult__commute_0) ).
cnf(c_975,plain,
c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_real__mult__commute_0]) ).
fof(cls_conjecture_0,axiom,
c_Transcendental_Ocos(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)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_990,plain,
c_Transcendental_Ocos(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)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_991,plain,
c_Transcendental_Ocos(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)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_975,c_990]) ).
fof(cls_conjecture_1,axiom,
c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(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_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_992,plain,
c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(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_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_1600,plain,
c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(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) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_975,c_992]) ).
cnf(c_993,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_991,c_1600]) ).
cnf(c_1598,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_426,c_398]) ).
cnf(c_1601,plain,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_993,c_1598]) ).
cnf(c_1599,plain,
$false,
inference(resolve,[status(thm)],[c_918,c_1601]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV603-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 14:35:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2361988 was started by sandbox2 on n005,
% 0.09/0.36 % Sat Sep 26 14:35:48 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.40
% 0.09/0.40 % From the command line: assign(max_seconds, 300).
% 17.50/2.61
% 17.50/2.61 % SZS status Unsatisfiable for theBenchmark
% 17.50/2.61
% 17.50/2.61 % Proof 1 at 2.16 (+ 0.01) seconds.
% 17.50/2.61 % Length of proof is 11.
% 17.50/2.61 % Level of proof is 3.
% 17.50/2.61 % Maximum clause weight is 52.000.
% 17.50/2.61 % Given clauses 0.
% 17.50/2.61
% 17.50/2.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------