%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV584-1 : 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 09:08:46 AM UTC 2026
% Result : Unsatisfiable 29.20s 9.26s
% Output : CNFRefutation 29.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-4 aty)
% Number of variables : 46 ( 17 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Collect__def_0,axiom,
! [VAR_0,VAR_1] : hAPP(c_Collect(VAR_0),VAR_1) = VAR_1,
file('theBenchmark.p',cls_Collect__def_0) ).
cnf(c_1934,plain,
hAPP(c_Collect(A),B) = B,
inference(clausify,[status(thm)],[cls_Collect__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_1949,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(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_1974,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_COMBS__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(c_COMBS(VAR_0,VAR_1,VAR_2,VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_COMBS__def_0) ).
cnf(c_1976,plain,
hAPP(hAPP(c_COMBS(A,B,C,D),E),F) = hAPP(hAPP(A,F),hAPP(E,F)),
inference(clausify,[status(thm)],[cls_COMBS__def_0]) ).
cnf(c_3584,plain,
hAPP(hAPP(hAPP(c_COMBB(A,B,C),c_Suc),D),E) != hAPP(D,E),
inference(paramod,[status(thm)],[c_1974,c_1949]) ).
cnf(c_3705,plain,
hAPP(hAPP(c_COMBS(A,B,C,D),c_Collect(E)),F) = hAPP(hAPP(A,F),F),
inference(paramod,[status(thm)],[c_1934,c_1976]) ).
cnf(c_3707,plain,
hAPP(D,E) != hAPP(hAPP(hAPP(c_COMBB(A,B,C),c_Suc),D),E),
inference(copy,[status(thm)],[c_3584]) ).
cnf(c_3706,plain,
$false,
inference(resolve,[status(thm)],[c_3705,c_3707]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV584-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n019.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 14:33:26 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 1563194 was started by sandbox2 on n019,
% 0.10/5.38 % Sat Sep 26 14:33:26 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.44
% 0.15/5.44 % From the command line: assign(max_seconds, 300).
% 29.20/9.26
% 29.20/9.26 % given #500 (I,wt=23): 1119 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A) # tptp_name(cls_nat__add__commute_0) # clausal_fof(1). [assumption].
% 29.20/9.26
% 29.20/9.26 % SZS status Unsatisfiable for theBenchmark
% 29.20/9.26
% 29.20/9.26 % Proof 1 at 3.37 (+ 0.27) seconds.
% 29.20/9.26 % Length of proof is 7.
% 29.20/9.26 % Level of proof is 2.
% 29.20/9.26 % Maximum clause weight is 32.000.
% 29.20/9.26 % Given clauses 993.
% 29.20/9.26
% 29.20/9.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------