%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV663-1 : 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 : n002.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 09:08:54 AM UTC 2026
% Result : Unsatisfiable 42.72s 11.63s
% Output : CNFRefutation 42.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 28 unt; 0 def)
% Number of atoms : 40 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 12 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-5 aty)
% Number of variables : 91 ( 27 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_Int__Oint__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
cnf(c_28,plain,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[clsarity_Int__Oint__OrderedGroup_Ogroup__add]) ).
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_29,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add]) ).
fof(cls_diff__minus_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(VAR_0),VAR_1),VAR_2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_1),hAPP(c_HOL_Ouminus__class_Ouminus(VAR_0),VAR_2))
| ~ class_OrderedGroup_Ogroup__add(VAR_0) ),
file('theBenchmark.p',cls_diff__minus_0) ).
cnf(c_34,plain,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))
| ~ class_OrderedGroup_Ogroup__add(A) ),
inference(clausify,[status(thm)],[cls_diff__minus_0]) ).
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_50,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_Int__Oint__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
cnf(c_100,plain,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[clsarity_Int__Oint__OrderedGroup_Oab__group__add]) ).
fof(cls_add__cancel__end_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),hAPP(c_HOL_Ouminus__class_Ouminus(VAR_0),VAR_1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_2),VAR_1)) = VAR_2
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_add__cancel__end_1) ).
cnf(c_112,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B)) = C
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_add__cancel__end_1]) ).
cnf(c_658,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),A)) = B,
inference(resolve,[status(thm)],[c_112,c_100]) ).
cnf(c_710,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_50,c_29]) ).
cnf(c_711,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_710]) ).
cnf(c_712,plain,
A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),
inference(resolve,[status(thm)],[c_50,c_28]) ).
cnf(c_713,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)) = A,
inference(copy,[status(thm)],[c_712]) ).
cnf(c_748,plain,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)),
inference(resolve,[status(thm)],[c_34,c_28]) ).
cnf(c_749,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),
inference(copy,[status(thm)],[c_748]) ).
fof(cls_n__not__Suc__n_0,axiom,
! [VAR_0] : VAR_0 != hAPP(c_Suc,VAR_0),
file('theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(c_772,plain,
A != hAPP(c_Suc,A),
inference(clausify,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(c_773,plain,
hAPP(c_Suc,A) != A,
inference(copy,[status(thm)],[c_772]) ).
fof(cls_COMBB__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_COMBB__def_0) ).
cnf(c_1025,plain,
hAPP(c_COMBB(A,B,C,D,E),F) = hAPP(A,hAPP(B,F)),
inference(clausify,[status(thm)],[cls_COMBB__def_0]) ).
fof(cls_COMBS__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_COMBS__def_0) ).
cnf(c_1027,plain,
hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(A,F),hAPP(B,F)),
inference(clausify,[status(thm)],[cls_COMBS__def_0]) ).
cnf(c_14856,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A))) = B,
inference(paramod,[status(thm)],[c_713,c_658]) ).
cnf(c_1944,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),A)) = B,
inference(paramod,[status(thm)],[c_749,c_14856]) ).
cnf(c_2446,plain,
hAPP(c_COMBB(c_Suc,A,B,C,D),E) != hAPP(A,E),
inference(paramod,[status(thm)],[c_1025,c_773]) ).
cnf(c_8323,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_1025,c_2446]) ).
cnf(c_9742,plain,
hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B,C,D,E),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),F),A)) = hAPP(F,hAPP(B,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),F),A))),
inference(paramod,[status(thm)],[c_1944,c_1027]) ).
cnf(c_14854,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_711,c_8323]) ).
cnf(c_14857,plain,
hAPP(F,hAPP(B,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),F),A))) = hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B,C,D,E),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),F),A)),
inference(copy,[status(thm)],[c_9742]) ).
cnf(c_14855,plain,
$false,
inference(resolve,[status(thm)],[c_14854,c_14857]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV663-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n002.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sat Sep 26 14:45:28 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.39 % Process 1972451 was started by sandbox on n002,
% 0.09/5.39 % Sat Sep 26 14:45:28 2026
% 0.09/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.43
% 0.14/5.43 % From the command line: assign(max_seconds, 300).
% 42.72/11.63
% 42.72/11.63 % given #500 (I,wt=37): 1378 c_HOL_Ozero__class_Ozero(tc_nat) = A | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A),tc_Int_Oint). [copy(1377),flip(a),unit_del(c,1264)].
% 42.72/11.63
% 42.72/11.63 % given #1000 (F,wt=39): 8327 hAPP(c_COMBC(A,B,C,D,E),F) != hAPP(c_COMBB(c_Suc,hAPP(A,F),V6,V7,V8),B). [para(1026(a,2),2446(a,2)),flip(a)].
% 42.72/11.63
% 42.72/11.63 % SZS status Unsatisfiable for theBenchmark
% 42.72/11.63
% 42.72/11.63 % Proof 1 at 5.46 (+ 0.69) seconds.
% 42.72/11.63 % Length of proof is 23.
% 42.72/11.63 % Level of proof is 5.
% 42.72/11.63 % Maximum clause weight is 67.000.
% 42.72/11.63 % Given clauses 1041.
% 42.72/11.63
% 42.72/11.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------