%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV695-1 : 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 : n001.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 09:08:58 AM UTC 2026
% Result : Unsatisfiable 79.06s 11.52s
% Output : CNFRefutation 79.06s
% 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 : 44 ( 15 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_658,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(hAPP(hAPP(c_COMBB(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(VAR_3,hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_COMBB__def_0) ).
cnf(c_660,plain,
hAPP(hAPP(hAPP(c_COMBB(A,B,C),D),E),F) = hAPP(D,hAPP(E,F)),
inference(clausify,[status(thm)],[cls_COMBB__def_0]) ).
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_712,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_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_959,plain,
A != hAPP(c_Suc,A),
inference(clausify,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(c_960,plain,
hAPP(c_Suc,A) != A,
inference(copy,[status(thm)],[c_959]) ).
cnf(c_2076,plain,
hAPP(c_COMBS(A,hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B,C,D),E) = hAPP(hAPP(A,E),E),
inference(paramod,[status(thm)],[c_712,c_658]) ).
cnf(c_2357,plain,
hAPP(hAPP(hAPP(c_COMBB(A,B,C),c_Suc),D),E) != hAPP(D,E),
inference(paramod,[status(thm)],[c_660,c_960]) ).
cnf(c_2359,plain,
hAPP(hAPP(A,E),E) = hAPP(c_COMBS(A,hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B,C,D),E),
inference(copy,[status(thm)],[c_2076]) ).
cnf(c_2358,plain,
$false,
inference(resolve,[status(thm)],[c_2357,c_2359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV695-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n001.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 14:53:15 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 2038305 was started by sandbox on n001,
% 0.15/0.43 % Sat Sep 26 14:53:15 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.25/0.52
% 0.25/0.52 % From the command line: assign(max_seconds, 300).
% 79.06/11.52
% 79.06/11.52 % SZS status Unsatisfiable for theBenchmark
% 79.06/11.52
% 79.06/11.52 % Proof 1 at 2.87 (+ 0.07) seconds.
% 79.06/11.52 % Length of proof is 8.
% 79.06/11.52 % Level of proof is 3.
% 79.06/11.52 % Maximum clause weight is 28.000.
% 79.06/11.52 % Given clauses 258.
% 79.06/11.52
% 79.06/11.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------