%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV820-1 : 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 : n014.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 09:09:10 AM UTC 2026
% Result : Unsatisfiable 9.80s 2.07s
% Output : CNFRefutation 9.80s
% 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_176,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_177,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_344,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_665,plain,
hAPP(c_Collect(A),B) = B,
inference(clausify,[status(thm)],[cls_Collect__def_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_688,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_689,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]) ).
cnf(c_782,plain,
hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_bool),c_in(A)),B) = B,
inference(paramod,[status(thm)],[c_665,c_344]) ).
cnf(c_1882,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_177,c_688]) ).
cnf(c_1899,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_177,c_689]) ).
cnf(c_2306,plain,
hAPP(A,B) = hAPP(hAPP(c_in(C),B),A),
inference(paramod,[status(thm)],[c_782,c_176]) ).
cnf(c_2160,plain,
hAPP(hAPP(c_in(A),B),C) = hAPP(C,B),
inference(copy,[status(thm)],[c_2306]) ).
cnf(c_2193,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_2160,c_1899]) ).
cnf(c_2206,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_2160,c_1882]) ).
cnf(c_2302,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_2193]) ).
cnf(c_2307,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_2206]) ).
cnf(c_2305,plain,
$false,
inference(resolve,[status(thm)],[c_2302,c_2307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV820-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 15:01:16 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3454328 was started by sandbox on n014,
% 0.09/0.35 % Sat Sep 26 15:01:16 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 9.80/2.07
% 9.80/2.07 % SZS status Unsatisfiable for theBenchmark
% 9.80/2.07
% 9.80/2.07 % Proof 1 at 1.48 (+ 0.16) seconds.
% 9.80/2.07 % Length of proof is 14.
% 9.80/2.07 % Level of proof is 5.
% 9.80/2.07 % Maximum clause weight is 71.000.
% 9.80/2.07 % Given clauses 468.
% 9.80/2.07
% 9.80/2.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------