%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL801-1 : 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 : n026.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 07:59:46 AM UTC 2026
% Result : Unsatisfiable 19.54s 3.18s
% Output : CNFRefutation 19.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 14 unt; 0 def)
% Number of atoms : 30 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 80 ( 21 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_ATP__Linkup_OCOMBC__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(hAPP(c_COMBC(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_3,VAR_5),VAR_4),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
cnf(c_74,plain,
hAPP(hAPP(hAPP(c_COMBC(A,B,C),D),E),F) = hAPP(hAPP(D,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(hAPP(c_COMBS(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_3,VAR_5),hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
cnf(c_75,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F) = hAPP(hAPP(D,F),hAPP(E,F)),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBS__def_0]) ).
fof(cls_Collect__mem__eq_0,axiom,
! [VAR_0,VAR_1] : hAPP(c_Collect(VAR_0),hAPP(hAPP(c_COMBC(VAR_0,tc_fun(VAR_0,tc_bool),tc_bool),c_in(VAR_0)),VAR_1)) = VAR_1,
file('theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(c_262,plain,
hAPP(c_Collect(A),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_bool),c_in(A)),B)) = B,
inference(clausify,[status(thm)],[cls_Collect__mem__eq_0]) ).
fof(cls_ComplD_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(hAPP(c_in(VAR_0),VAR_1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(VAR_0,tc_bool)),VAR_2)))
| ~ hBOOL(hAPP(hAPP(c_in(VAR_0),VAR_1),VAR_2)) ),
file('theBenchmark.p',cls_ComplD_0) ).
cnf(c_780,plain,
( ~ hBOOL(hAPP(hAPP(c_in(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),C)))
| ~ hBOOL(hAPP(hAPP(c_in(A),B),C)) ),
inference(clausify,[status(thm)],[cls_ComplD_0]) ).
fof(cls_ComplI_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( hBOOL(hAPP(hAPP(c_in(VAR_0),VAR_1),VAR_2))
| hBOOL(hAPP(hAPP(c_in(VAR_0),VAR_1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(VAR_0,tc_bool)),VAR_2))) ),
file('theBenchmark.p',cls_ComplI_0) ).
cnf(c_781,plain,
( hBOOL(hAPP(hAPP(c_in(A),B),C))
| hBOOL(hAPP(hAPP(c_in(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),C))) ),
inference(clausify,[status(thm)],[cls_ComplI_0]) ).
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_799,plain,
hAPP(c_Collect(A),B) = B,
inference(clausify,[status(thm)],[cls_Collect__def_0]) ).
cnf(c_959,plain,
hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_bool),c_in(A)),B) = B,
inference(paramod,[status(thm)],[c_799,c_262]) ).
cnf(c_3437,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(C,D,E),c_in(A)),c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool))),B))
| ~ hBOOL(hAPP(hAPP(c_in(A),B),B)) ),
inference(paramod,[status(thm)],[c_75,c_780]) ).
cnf(c_3487,plain,
( hBOOL(hAPP(hAPP(c_in(D),E),E))
| hBOOL(hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_in(D)),c_HOL_Ouminus__class_Ouminus(tc_fun(D,tc_bool))),E)) ),
inference(paramod,[status(thm)],[c_75,c_781]) ).
cnf(c_5050,plain,
hAPP(A,B) = hAPP(hAPP(c_in(C),B),A),
inference(paramod,[status(thm)],[c_959,c_74]) ).
cnf(c_4611,plain,
hAPP(hAPP(c_in(A),B),C) = hAPP(C,B),
inference(copy,[status(thm)],[c_5050]) ).
cnf(c_4777,plain,
( hBOOL(hAPP(E,E))
| hBOOL(hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_in(D)),c_HOL_Ouminus__class_Ouminus(tc_fun(D,tc_bool))),E)) ),
inference(paramod,[status(thm)],[c_4611,c_3487]) ).
cnf(c_4822,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(B,C,D),c_in(E)),c_HOL_Ouminus__class_Ouminus(tc_fun(E,tc_bool))),A))
| ~ hBOOL(hAPP(A,A)) ),
inference(paramod,[status(thm)],[c_4611,c_3437]) ).
cnf(c_5040,plain,
hBOOL(hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_in(D)),c_HOL_Ouminus__class_Ouminus(tc_fun(D,tc_bool))),hAPP(hAPP(c_COMBS(A,B,C),c_in(D)),c_HOL_Ouminus__class_Ouminus(tc_fun(D,tc_bool))))),
inference(factor,[status(thm)],[c_4777]) ).
cnf(c_5051,plain,
~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_in(D)),c_HOL_Ouminus__class_Ouminus(tc_fun(D,tc_bool))),hAPP(hAPP(c_COMBS(A,B,C),c_in(D)),c_HOL_Ouminus__class_Ouminus(tc_fun(D,tc_bool))))),
inference(factor,[status(thm)],[c_4822]) ).
cnf(c_5049,plain,
$false,
inference(resolve,[status(thm)],[c_5040,c_5051]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL801-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.55 % Computer : n026.cluster.edu
% 0.08/0.55 % Model : x86_64 x86_64
% 0.08/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.55 % Memory : 8046.5625MB
% 0.08/0.55 % OS : Linux 6.8.0-71-generic
% 0.02/0.56 % CPULimit : 300
% 0.02/0.56 % WCLimit : 300
% 0.02/0.56 % DateTime : Fri Sep 25 23:38:56 UTC 2026
% 0.02/0.56 % CPUTime :
% 0.02/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.56 % Process 3746711 was started by sandbox on n026,
% 0.02/0.56 % Fri Sep 25 23:38:56 2026
% 0.02/0.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.60
% 0.02/0.60 % From the command line: assign(max_seconds, 300).
% 19.54/3.18
% 19.54/3.18 % given #500 (I,wt=61): 827 c_Finite__Set_Ofinite(hAPP(A,B),C) | -hBOOL(hAPP(hAPP(c_in(D),B),E)) | -c_Finite__Set_Ofinite(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(D,tc_fun(C,tc_bool)),E),A),C) | -c_Finite__Set_Ofinite(E,D) # tptp_name(cls_finite__UN_0) # clausal_fof(1). [assumption].
% 19.54/3.18
% 19.54/3.18 % SZS status Unsatisfiable for theBenchmark
% 19.54/3.18
% 19.54/3.18 % Proof 1 at 2.21 (+ 0.32) seconds.
% 19.54/3.18 % Length of proof is 14.
% 19.54/3.18 % Level of proof is 5.
% 19.54/3.18 % Maximum clause weight is 71.000.
% 19.54/3.18 % Given clauses 582.
% 19.54/3.18
% 19.54/3.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------