%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV671-1 : 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 : n017.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 09:08:55 AM UTC 2026
% Result : Unsatisfiable 165.28s 22.58s
% Output : CNFRefutation 165.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 18 unt; 0 def)
% Number of atoms : 26 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-5 aty)
% Number of variables : 72 ( 27 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_129,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add]) ).
fof(cls_minus__add__cancel_0,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_1),VAR_2)) = VAR_2
| ~ class_OrderedGroup_Ogroup__add(VAR_0) ),
file('theBenchmark.p',cls_minus__add__cancel_0) ).
cnf(c_150,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),B),C)) = C
| ~ class_OrderedGroup_Ogroup__add(A) ),
inference(clausify,[status(thm)],[cls_minus__add__cancel_0]) ).
fof(cls_class__semiring_Osemiring__rules_I5_J_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_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
cnf(c_186,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I5_J_0]) ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(c_236,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1]) ).
cnf(c_1337,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)) = B,
inference(resolve,[status(thm)],[c_150,c_129]) ).
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_1800,plain,
hAPP(c_Suc,A) != A,
inference(clausify,[status(thm)],[cls_Suc__n__not__n_0]) ).
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_1824,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_1826,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_2038,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A,
inference(resolve,[status(thm)],[c_236,c_186]) ).
cnf(c_5670,plain,
hAPP(c_COMBB(c_Suc,A,B,C,D),E) != hAPP(A,E),
inference(paramod,[status(thm)],[c_1824,c_1800]) ).
cnf(c_8211,plain,
hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A,B,C,D),E) = hAPP(E,hAPP(A,E)),
inference(paramod,[status(thm)],[c_2038,c_1826]) ).
cnf(c_10814,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_1824,c_5670]) ).
cnf(c_22390,plain,
hAPP(c_COMBB(c_Suc,c_COMBB(A,hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)),C,D,E),F,V6,V7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),V8)) != hAPP(A,V8),
inference(paramod,[status(thm)],[c_1337,c_10814]) ).
cnf(c_22392,plain,
hAPP(E,hAPP(A,E)) = hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A,B,C,D),E),
inference(copy,[status(thm)],[c_8211]) ).
cnf(c_22391,plain,
$false,
inference(resolve,[status(thm)],[c_22390,c_22392]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV671-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 14:39:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 968286 was started by sandbox on n017,
% 0.11/0.37 % Sat Sep 26 14:39:33 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.43
% 0.11/0.43 % From the command line: assign(max_seconds, 300).
% 165.28/22.58
% 165.28/22.58 % given #500 (I,wt=34): 1768 -class_Ring__and__Field_Omult__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # tptp_name(cls_mult__zero__right_0) # clausal_fof(1). [assumption].
% 165.28/22.58
% 165.28/22.58 % given #1000 (A,wt=97): 2461 hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C))),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D))). [para(910(a,1),842(a,2,2))].
% 165.28/22.58
% 165.28/22.58 % SZS status Unsatisfiable for theBenchmark
% 165.28/22.58
% 165.28/22.58 % Proof 1 at 5.29 (+ 0.67) seconds.
% 165.28/22.58 % Length of proof is 14.
% 165.28/22.58 % Level of proof is 4.
% 165.28/22.58 % Maximum clause weight is 69.000.
% 165.28/22.58 % Given clauses 1381.
% 165.28/22.58
% 165.28/22.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------