%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV656-1 : 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 : n010.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 09:08:53 AM UTC 2026
% Result : Unsatisfiable 53.02s 7.30s
% Output : CNFRefutation 53.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 18 unt; 0 def)
% Number of atoms : 22 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 7 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-5 aty)
% Number of variables : 66 ( 27 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_equation__minus__iff_1,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = hAPP(c_HOL_Ouminus__class_Ouminus(VAR_0),hAPP(c_HOL_Ouminus__class_Ouminus(VAR_0),VAR_1))
| ~ class_OrderedGroup_Ogroup__add(VAR_0) ),
file('theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(c_23,plain,
( B = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))
| ~ class_OrderedGroup_Ogroup__add(A) ),
inference(clausify,[status(thm)],[cls_equation__minus__iff_1]) ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(c_28,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add]) ).
cnf(c_917,plain,
A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),
inference(resolve,[status(thm)],[c_28,c_23]) ).
cnf(c_918,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)) = A,
inference(copy,[status(thm)],[c_917]) ).
fof(cls_ATP__Linkup_OCOMBB__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_COMBB(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(VAR_0,hAPP(VAR_1,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
cnf(c_972,plain,
hAPP(c_COMBB(A,B,C,D,E),F) = hAPP(A,hAPP(B,F)),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBB__def_0]) ).
fof(cls_ATP__Linkup_OCOMBS__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_COMBS(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),hAPP(VAR_1,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
cnf(c_974,plain,
hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(A,F),hAPP(B,F)),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBS__def_0]) ).
fof(cls_nat__mult__1_0,axiom,
! [VAR_0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),VAR_0) = VAR_0,
file('theBenchmark.p',cls_nat__mult__1_0) ).
cnf(c_1106,plain,
hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A,
inference(clausify,[status(thm)],[cls_nat__mult__1_0]) ).
fof(cls_Suc__n__not__n_0,axiom,
! [VAR_0] : hAPP(c_Suc,VAR_0) != VAR_0,
file('theBenchmark.p',cls_Suc__n__not__n_0) ).
cnf(c_1402,plain,
hAPP(c_Suc,A) != A,
inference(clausify,[status(thm)],[cls_Suc__n__not__n_0]) ).
cnf(c_3816,plain,
hAPP(c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A,B,C,D),E) = hAPP(E,hAPP(A,E)),
inference(paramod,[status(thm)],[c_1106,c_974]) ).
cnf(c_4733,plain,
hAPP(c_COMBB(c_Suc,A,B,C,D),E) != hAPP(A,E),
inference(paramod,[status(thm)],[c_972,c_1402]) ).
cnf(c_6713,plain,
hAPP(c_COMBB(c_Suc,c_COMBB(A,B,C,D,E),F,V6,V7),V8) != hAPP(A,hAPP(B,V8)),
inference(paramod,[status(thm)],[c_972,c_4733]) ).
cnf(c_12509,plain,
hAPP(c_COMBB(c_Suc,c_COMBB(A,c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B,C,D),E,F,V6),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),V7)) != hAPP(A,V7),
inference(paramod,[status(thm)],[c_918,c_6713]) ).
cnf(c_12511,plain,
hAPP(E,hAPP(A,E)) = hAPP(c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A,B,C,D),E),
inference(copy,[status(thm)],[c_3816]) ).
cnf(c_12510,plain,
$false,
inference(resolve,[status(thm)],[c_12509,c_12511]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV656-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n010.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 14:42:15 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3553103 was started by sandbox2 on n010,
% 0.19/0.45 % Sat Sep 26 14:42:15 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.27/0.53
% 0.27/0.53 % From the command line: assign(max_seconds, 300).
% 53.02/7.30
% 53.02/7.30 % given #500 (I,wt=44): 1215 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | c_HOL_Ozero__class_Ozero(tc_nat) = B. [copy(1214),flip(f)].
% 53.02/7.30
% 53.02/7.30 % SZS status Unsatisfiable for theBenchmark
% 53.02/7.30
% 53.02/7.30 % Proof 1 at 5.94 (+ 0.76) seconds.
% 53.02/7.30 % Length of proof is 13.
% 53.02/7.30 % Level of proof is 4.
% 53.02/7.30 % Maximum clause weight is 48.000.
% 53.02/7.30 % Given clauses 976.
% 53.02/7.30
% 53.02/7.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------