%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL747-1 : 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 : 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 07:59:37 AM UTC 2026
% Result : Unsatisfiable 7.69s 1.47s
% Output : CNFRefutation 7.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-4 aty)
% Number of variables : 92 ( 39 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_ATP__Linkup_OCOMBB__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_ATP__Linkup_OCOMBB__def_0) ).
cnf(c_272,plain,
hAPP(hAPP(hAPP(c_COMBB(A,B,C),D),E),F) = hAPP(D,hAPP(E,F)),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBB__def_0]) ).
fof(cls_ATP__Linkup_OCOMBC__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(c_COMBC(VAR_0,VAR_1,VAR_2,VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),VAR_4),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
cnf(c_273,plain,
hAPP(hAPP(c_COMBC(A,B,C,D),E),F) = hAPP(hAPP(A,F),E),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBC__def_0]) ).
fof(cls_ATP__Linkup_OCOMBS__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_ATP__Linkup_OCOMBS__def_0) ).
cnf(c_274,plain,
hAPP(hAPP(c_COMBS(A,B,C,D),E),F) = hAPP(hAPP(A,F),hAPP(E,F)),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBS__def_0]) ).
fof(cls_n__not__Suc__n_0,axiom,
! [VAR_0] : VAR_0 != c_Suc(VAR_0),
file('theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(c_429,plain,
A != c_Suc(A),
inference(clausify,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(c_430,plain,
c_Suc(A) != A,
inference(copy,[status(thm)],[c_429]) ).
fof(cls_Suc__eq__plus1__left_0,axiom,
! [VAR_0] : c_Suc(VAR_0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),VAR_0),
file('theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
cnf(c_635,plain,
c_Suc(A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),
inference(clausify,[status(thm)],[cls_Suc__eq__plus1__left_0]) ).
cnf(c_848,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) != A,
inference(paramod,[status(thm)],[c_635,c_430]) ).
cnf(c_6023,plain,
hAPP(hAPP(hAPP(c_COMBB(A,B,C),D),hAPP(c_COMBC(E,F,V6,V7),V8)),V9) = hAPP(D,hAPP(hAPP(E,V9),V8)),
inference(paramod,[status(thm)],[c_273,c_272]) ).
cnf(c_907,plain,
hAPP(A,hAPP(hAPP(c_COMBC(B,C,D,E),F),V6)) = hAPP(A,hAPP(hAPP(B,V6),F)),
inference(paramod,[status(thm)],[c_272,c_6023]) ).
cnf(c_909,plain,
hAPP(hAPP(c_COMBC(hAPP(c_COMBB(A,B,C),D),E,F,V6),V7),V8) = hAPP(D,hAPP(V8,V7)),
inference(paramod,[status(thm)],[c_273,c_272]) ).
cnf(c_5890,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_COMBC(A,B,C,D),E),F)) != hAPP(hAPP(A,F),E),
inference(paramod,[status(thm)],[c_907,c_848]) ).
cnf(c_6021,plain,
hAPP(hAPP(c_COMBS(c_COMBC(hAPP(c_COMBB(A,B,C),D),E,F,V6),V7,V8,V9),V10),V11) = hAPP(D,hAPP(hAPP(V10,V11),V11)),
inference(paramod,[status(thm)],[c_909,c_274]) ).
cnf(c_6024,plain,
hAPP(hAPP(A,F),E) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_COMBC(A,B,C,D),E),F)),
inference(copy,[status(thm)],[c_5890]) ).
cnf(c_6022,plain,
$false,
inference(resolve,[status(thm)],[c_6021,c_6024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL747-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 23:28:33 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 3988366 was started by sandbox on n019,
% 0.10/0.35 % Fri Sep 25 23:28:33 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 7.69/1.47
% 7.69/1.47 % given #500 (A,wt=100): 885 hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_COMBC(c_lessequals(tc_nat),E,F,V6),C),A)). [para(273(a,2),228(c,1))].
% 7.69/1.47
% 7.69/1.47 % SZS status Unsatisfiable for theBenchmark
% 7.69/1.47
% 7.69/1.47 % Proof 1 at 0.94 (+ 0.14) seconds.
% 7.69/1.47 % Length of proof is 12.
% 7.69/1.47 % Level of proof is 4.
% 7.69/1.47 % Maximum clause weight is 76.000.
% 7.69/1.47 % Given clauses 553.
% 7.69/1.47
% 7.69/1.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------