%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT077-1 : 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 : n018.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 08:28:28 AM UTC 2026
% Result : Unsatisfiable 20.68s 3.45s
% Output : CNFRefutation 20.68s
% 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_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_353,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_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_354,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_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_694,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_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_699,plain,
hAPP(c_Collect(A),B) = B,
inference(clausify,[status(thm)],[cls_Collect__def_0]) ).
fof(cls_COMBC__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_COMBC__def_0) ).
cnf(c_705,plain,
hAPP(hAPP(hAPP(c_COMBC(A,B,C),D),E),F) = hAPP(hAPP(D,F),E),
inference(clausify,[status(thm)],[cls_COMBC__def_0]) ).
fof(cls_COMBS__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_COMBS__def_0) ).
cnf(c_706,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F) = hAPP(hAPP(D,F),hAPP(E,F)),
inference(clausify,[status(thm)],[cls_COMBS__def_0]) ).
cnf(c_865,plain,
hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_bool),c_in(A)),B) = B,
inference(paramod,[status(thm)],[c_699,c_694]) ).
cnf(c_3535,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_706,c_353]) ).
cnf(c_3536,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_706,c_354]) ).
cnf(c_5676,plain,
hAPP(A,B) = hAPP(hAPP(c_in(C),B),A),
inference(paramod,[status(thm)],[c_865,c_705]) ).
cnf(c_4967,plain,
hAPP(hAPP(c_in(A),B),C) = hAPP(C,B),
inference(copy,[status(thm)],[c_5676]) ).
cnf(c_5197,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_4967,c_3536]) ).
cnf(c_5198,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_4967,c_3535]) ).
cnf(c_5674,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_5197]) ).
cnf(c_5677,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_5198]) ).
cnf(c_5675,plain,
$false,
inference(resolve,[status(thm)],[c_5674,c_5677]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT077-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 06:27:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3942412 was started by sandbox on n018,
% 0.08/0.36 % Sat Sep 26 06:27:21 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 20.68/3.45
% 20.68/3.45 % given #500 (I,wt=183): 807 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(B,tc_nat),tc_fun(tc_fun(B,tc_bool),tc_nat),A),c_Finite__Set_Osetsum(B,tc_nat)),hAPP(c_COMBC(B,A,tc_nat),C))),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),hAPP(hAPP(c_COMBC(B,tc_fun(A,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_nat),tc_fun(tc_fun(A,tc_bool),tc_nat),B),c_Finite__Set_Osetsum(A,tc_nat)),C)),E)),D). [copy(806),flip(a)].
% 20.68/3.45
% 20.68/3.45 % SZS status Unsatisfiable for theBenchmark
% 20.68/3.45
% 20.68/3.45 % Proof 1 at 2.49 (+ 0.42) seconds.
% 20.68/3.45 % Length of proof is 14.
% 20.68/3.45 % Level of proof is 5.
% 20.68/3.45 % Maximum clause weight is 71.000.
% 20.68/3.45 % Given clauses 533.
% 20.68/3.45
% 20.68/3.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------