%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV664-1 : 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 : n019.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 176.32s 45.43s
% Output : CNFRefutation 176.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 47 ( 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_458,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_520,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_522,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_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_1828,plain,
hAPP(c_Suc,A) != A,
inference(clausify,[status(thm)],[cls_Suc__n__not__n_0]) ).
cnf(c_3005,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_458,c_520]) ).
cnf(c_5935,plain,
hAPP(c_COMBB(c_Suc,A,B,C,D),E) != hAPP(A,E),
inference(paramod,[status(thm)],[c_522,c_1828]) ).
cnf(c_15244,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_458,c_3005]) ).
cnf(c_15246,plain,
hAPP(A,E) != hAPP(c_COMBB(c_Suc,A,B,C,D),E),
inference(copy,[status(thm)],[c_5935]) ).
cnf(c_15245,plain,
$false,
inference(resolve,[status(thm)],[c_15244,c_15246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV664-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/21.44 % Computer : n019.cluster.edu
% 0.10/21.44 % Model : x86_64 x86_64
% 0.10/21.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/21.44 % Memory : 8046.5625MB
% 0.10/21.44 % OS : Linux 6.8.0-71-generic
% 0.10/21.45 % CPULimit : 300
% 0.10/21.45 % WCLimit : 300
% 0.10/21.45 % DateTime : Sat Sep 26 14:42:57 UTC 2026
% 0.10/21.45 % CPUTime :
% 0.10/21.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/21.45 % Process 1575226 was started by sandbox2 on n019,
% 0.10/21.45 % Sat Sep 26 14:42:57 2026
% 0.10/21.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/21.52
% 0.17/21.52 % From the command line: assign(max_seconds, 300).
% 176.32/45.43
% 176.32/45.43 % given #500 (I,wt=25): 1334 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(A),A) = c_HOL_Ozero__class_Ozero(A) # tptp_name(cls_mod__by__1_0) # clausal_fof(1). [assumption].
% 176.32/45.43
% 176.32/45.43 % given #1000 (I,wt=69): 2179 hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_nat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),A)),A). [resolve(323,a,310,a)].
% 176.32/45.43
% 176.32/45.43 % given #1500 (I,wt=70): 2957 hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(A,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_Divides_Odiv__class_Odiv(A,hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat))) = c_HOL_Oone__class_Oone(tc_nat) | c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [back_rewrite(1797),rewrite([2796(17)])].
% 176.32/45.43
% 176.32/45.43 % SZS status Unsatisfiable for theBenchmark
% 176.32/45.43
% 176.32/45.43 % Proof 1 at 6.44 (+ 0.79) seconds.
% 176.32/45.43 % Length of proof is 8.
% 176.32/45.43 % Level of proof is 3.
% 176.32/45.43 % Maximum clause weight is 45.000.
% 176.32/45.43 % Given clauses 1674.
% 176.32/45.43
% 176.32/45.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------