%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV650-1 : 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 : n004.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 33.14s 4.66s
% Output : CNFRefutation 33.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-5 aty)
% Number of variables : 48 ( 18 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_plus__nat_Oadd__0_0,axiom,
! [VAR_0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),VAR_0) = VAR_0,
file('theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
cnf(c_445,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A,
inference(clausify,[status(thm)],[cls_plus__nat_Oadd__0_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_482,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]) ).
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_483,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_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_572,plain,
A != hAPP(c_Suc,A),
inference(clausify,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(c_573,plain,
hAPP(c_Suc,A) != A,
inference(copy,[status(thm)],[c_572]) ).
cnf(c_2675,plain,
hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C,D),E) = hAPP(E,hAPP(A,E)),
inference(paramod,[status(thm)],[c_445,c_482]) ).
cnf(c_2695,plain,
hAPP(c_COMBB(c_Suc,A,B,C,D),E) != hAPP(A,E),
inference(paramod,[status(thm)],[c_483,c_573]) ).
cnf(c_5750,plain,
hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C),D) = hAPP(D,D),
inference(paramod,[status(thm)],[c_445,c_2675]) ).
cnf(c_5752,plain,
hAPP(A,E) != hAPP(c_COMBB(c_Suc,A,B,C,D),E),
inference(copy,[status(thm)],[c_2695]) ).
cnf(c_5751,plain,
$false,
inference(resolve,[status(thm)],[c_5750,c_5752]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV650-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 14:41:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1960761 was started by sandbox on n004,
% 0.09/0.37 % Sat Sep 26 14:41:24 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.44
% 0.09/0.44 % From the command line: assign(max_seconds, 300).
% 33.14/4.66
% 33.14/4.66 % given #500 (I,wt=4): 1191 c_Int_OBit0(A) != c_Int_OMin # tptp_name(cls_rel__simps_I45_J_0) # clausal_fof(1). [assumption].
% 33.14/4.66
% 33.14/4.66 % given #1000 (I,wt=10): 1925 c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_fun(B,C)) = A | -class_Lattices_Olattice(C). [resolve(357,a,358,a)].
% 33.14/4.66
% 33.14/4.66 % given #1500 (I,wt=124): 2568 hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,C,tc_nat)),C))),B). [back_rewrite(1028),rewrite([1311(10),1311(30)])].
% 33.14/4.66
% 33.14/4.66 % SZS status Unsatisfiable for theBenchmark
% 33.14/4.66
% 33.14/4.66 % Proof 1 at 3.65 (+ 0.36) seconds.
% 33.14/4.66 % Length of proof is 9.
% 33.14/4.66 % Level of proof is 3.
% 33.14/4.66 % Maximum clause weight is 26.000.
% 33.14/4.66 % Given clauses 1589.
% 33.14/4.66
% 33.14/4.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------