%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV687-1 : 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 : n005.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 09:08:57 AM UTC 2026
% Result : Unsatisfiable 22.26s 3.71s
% Output : CNFRefutation 22.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 14 unt; 0 def)
% Number of atoms : 18 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 7 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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; 0-5 aty)
% Number of variables : 47 ( 15 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_51,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1]) ).
fof(cls_class__semiring_Osemiring__rules_I11_J_0,axiom,
! [VAR_0,VAR_1] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(VAR_0),c_HOL_Oone__class_Oone(VAR_0)),VAR_1) = VAR_1
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
cnf(c_53,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I11_J_0]) ).
cnf(c_670,plain,
hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A,
inference(resolve,[status(thm)],[c_53,c_51]) ).
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_898,plain,
A != hAPP(c_Suc,A),
inference(clausify,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(c_899,plain,
hAPP(c_Suc,A) != A,
inference(copy,[status(thm)],[c_898]) ).
fof(cls_COMBB__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(c_COMBB(VAR_0,VAR_1,VAR_2,VAR_3),VAR_4),VAR_5) = hAPP(VAR_0,hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_COMBB__def_0) ).
cnf(c_1406,plain,
hAPP(hAPP(c_COMBB(A,B,C,D),E),F) = hAPP(A,hAPP(E,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_1408,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_2442,plain,
hAPP(hAPP(c_COMBB(c_Suc,A,B,C),D),E) != hAPP(D,E),
inference(paramod,[status(thm)],[c_1406,c_899]) ).
cnf(c_2558,plain,
hAPP(c_COMBS(A,hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),B,C,D),E) = hAPP(hAPP(A,E),E),
inference(paramod,[status(thm)],[c_670,c_1408]) ).
cnf(c_2560,plain,
hAPP(D,E) != hAPP(hAPP(c_COMBB(c_Suc,A,B,C),D),E),
inference(copy,[status(thm)],[c_2442]) ).
cnf(c_2559,plain,
$false,
inference(resolve,[status(thm)],[c_2558,c_2560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV687-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 14:46:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2378783 was started by sandbox on n005,
% 0.10/0.37 % Sat Sep 26 14:46:32 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.43
% 0.10/0.43 % From the command line: assign(max_seconds, 300).
% 22.26/3.71
% 22.26/3.71 % given #500 (I,wt=27): 1054 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) # tptp_name(cls_of__nat__0__less__iff_1) # clausal_fof(1). [assumption].
% 22.26/3.71
% 22.26/3.71 % SZS status Unsatisfiable for theBenchmark
% 22.26/3.71
% 22.26/3.71 % Proof 1 at 2.76 (+ 0.18) seconds.
% 22.26/3.71 % Length of proof is 10.
% 22.26/3.71 % Level of proof is 3.
% 22.26/3.71 % Maximum clause weight is 28.000.
% 22.26/3.71 % Given clauses 769.
% 22.26/3.71
% 22.26/3.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------