%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV684-1 : 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 : n007.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 09:08:56 AM UTC 2026
% Result : Unsatisfiable 64.31s 9.48s
% Output : CNFRefutation 64.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 13 unt; 0 def)
% Number of atoms : 17 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 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 : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 46 ( 15 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
cnf(c_200,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add]) ).
fof(cls_add__0__left_0,axiom,
! [VAR_0,VAR_1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),c_HOL_Ozero__class_Ozero(VAR_0)),VAR_1) = VAR_1
| ~ class_OrderedGroup_Omonoid__add(VAR_0) ),
file('theBenchmark.p',cls_add__0__left_0) ).
cnf(c_202,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B
| ~ class_OrderedGroup_Omonoid__add(A) ),
inference(clausify,[status(thm)],[cls_add__0__left_0]) ).
cnf(c_359,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A,
inference(resolve,[status(thm)],[c_200,c_202]) ).
fof(cls_ATP__Linkup_OCOMBB__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(hAPP(c_COMBB(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(VAR_3,hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
cnf(c_445,plain,
hAPP(hAPP(hAPP(c_COMBB(A,B,C),D),E),F) = hAPP(D,hAPP(E,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(hAPP(hAPP(c_COMBS(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_3,VAR_5),hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
cnf(c_447,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F) = hAPP(hAPP(D,F),hAPP(E,F)),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBS__def_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_540,plain,
hAPP(c_Suc,A) != A,
inference(clausify,[status(thm)],[cls_Suc__n__not__n_0]) ).
cnf(c_890,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))),E) = hAPP(hAPP(D,E),E),
inference(paramod,[status(thm)],[c_359,c_447]) ).
cnf(c_987,plain,
hAPP(hAPP(hAPP(c_COMBB(A,B,C),c_Suc),D),E) != hAPP(D,E),
inference(paramod,[status(thm)],[c_445,c_540]) ).
cnf(c_989,plain,
hAPP(hAPP(D,E),E) = hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))),E),
inference(copy,[status(thm)],[c_890]) ).
cnf(c_988,plain,
$false,
inference(resolve,[status(thm)],[c_987,c_989]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV684-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.65 % Computer : n007.cluster.edu
% 0.19/0.65 % Model : x86_64 x86_64
% 0.19/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.65 % Memory : 8046.5625MB
% 0.19/0.65 % OS : Linux 6.8.0-71-generic
% 0.19/0.65 % CPULimit : 300
% 0.19/0.65 % WCLimit : 300
% 0.19/0.65 % DateTime : Sat Sep 26 14:44:10 UTC 2026
% 0.19/0.66 % CPUTime :
% 0.22/0.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.22/0.66 % Process 3977998 was started by sandbox2 on n007,
% 0.22/0.66 % Sat Sep 26 14:44:10 2026
% 0.22/0.66 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.22/0.70
% 0.22/0.70 % From the command line: assign(max_seconds, 300).
% 64.31/9.48
% 64.31/9.48 % SZS status Unsatisfiable for theBenchmark
% 64.31/9.48
% 64.31/9.48 % Proof 1 at 0.66 (+ 0.05) seconds.
% 64.31/9.48 % Length of proof is 9.
% 64.31/9.48 % Level of proof is 3.
% 64.31/9.48 % Maximum clause weight is 30.000.
% 64.31/9.48 % Given clauses 170.
% 64.31/9.48
% 64.31/9.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------