%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG363-1 : 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 : n003.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 06:50:04 AM UTC 2026
% Result : Unsatisfiable 12.01s 2.04s
% Output : CNFRefutation 12.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 16 unt; 0 def)
% Number of atoms : 32 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 17 ( 2 sgn 7 !; 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_274,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_284,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(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_311,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_abs__of__nonneg_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(VAR_0),VAR_1,VAR_0)
| c_HOL_Oabs__class_Oabs(VAR_1,VAR_0) = VAR_1
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(VAR_0) ),
file('theBenchmark.p',cls_abs__of__nonneg_0) ).
cnf(c_317,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A)
| c_HOL_Oabs__class_Oabs(B,A) = B
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(A) ),
inference(clausify,[status(thm)],[cls_abs__of__nonneg_0]) ).
fof(cls_abs__add__one__gt__zero_0,axiom,
! [VAR_0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(VAR_0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_abs__add__one__gt__zero_0) ).
cnf(c_899,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_abs__add__one__gt__zero_0]) ).
fof(cls_rp_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('theBenchmark.p',cls_rp_0) ).
cnf(c_908,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_rp_0]) ).
fof(cls_th_0,axiom,
! [VAR_0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(VAR_0)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_th_0) ).
cnf(c_909,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(A)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_th_0]) ).
fof(cls_conjecture_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(v_f____(v_x))),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_917,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(v_f____(v_x))),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_918,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_909,c_917]) ).
cnf(c_1095,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_274,c_284]) ).
cnf(c_1133,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = A ),
inference(resolve,[status(thm)],[c_311,c_317]) ).
cnf(c_3329,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_1095,c_918]) ).
cnf(c_3824,plain,
c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r,
inference(resolve,[status(thm)],[c_1133,c_908]) ).
cnf(c_5459,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_3824,c_899]) ).
cnf(c_5458,plain,
$false,
inference(resolve,[status(thm)],[c_3329,c_5459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG363-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 21:56:55 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3845871 was started by sandbox2 on n003,
% 0.10/0.37 % Sat Sep 26 21:56:55 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 12.01/2.04
% 12.01/2.04 % given #500 (I,wt=31): 1259 c_lessequals(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [factor(705,c,e)].
% 12.01/2.04
% 12.01/2.04 % SZS status Unsatisfiable for theBenchmark
% 12.01/2.04
% 12.01/2.04 % Proof 1 at 1.49 (+ 0.13) seconds.
% 12.01/2.04 % Length of proof is 14.
% 12.01/2.04 % Level of proof is 3.
% 12.01/2.04 % Maximum clause weight is 20.000.
% 12.01/2.04 % Given clauses 572.
% 12.01/2.04
% 12.01/2.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------