%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV880-1 : 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 09:09:16 AM UTC 2026
% Result : Unsatisfiable 27.69s 9.06s
% Output : CNFRefutation 27.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 16 unt; 0 def)
% Number of atoms : 36 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 41 ( 5 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_insert__subset_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_in(VAR_0,VAR_3,VAR_2)
| ~ c_lessequals(VAR_1,VAR_3,tc_fun(VAR_2,tc_bool))
| c_lessequals(c_Set_Oinsert(VAR_0,VAR_1,VAR_2),VAR_3,tc_fun(VAR_2,tc_bool)) ),
file('theBenchmark.p',cls_insert__subset_2) ).
cnf(c_392,plain,
( ~ c_in(A,D,C)
| ~ c_lessequals(B,D,tc_fun(C,tc_bool))
| c_lessequals(c_Set_Oinsert(A,B,C),D,tc_fun(C,tc_bool)) ),
inference(clausify,[status(thm)],[cls_insert__subset_2]) ).
fof(cls_empty__subsetI_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(VAR_0,tc_bool)),VAR_1,tc_fun(VAR_0,tc_bool)),
file('theBenchmark.p',cls_empty__subsetI_0) ).
cnf(c_417,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,tc_fun(A,tc_bool)),
inference(clausify,[status(thm)],[cls_empty__subsetI_0]) ).
fof(cls_mem__def_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(VAR_1,VAR_0))
| c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_mem__def_1) ).
cnf(c_426,plain,
( ~ hBOOL(hAPP(B,A))
| c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_mem__def_1]) ).
fof(cls_mem__def_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_in(VAR_1,VAR_0,VAR_2)
| hBOOL(hAPP(VAR_0,VAR_1)) ),
file('theBenchmark.p',cls_mem__def_0) ).
cnf(c_427,plain,
( ~ c_in(B,A,C)
| hBOOL(hAPP(A,B)) ),
inference(clausify,[status(thm)],[cls_mem__def_0]) ).
fof(cls_rev__image__eqI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( c_in(hAPP(VAR_3,VAR_0),c_Set_Oimage(VAR_3,VAR_1,VAR_2,VAR_4),VAR_4)
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_rev__image__eqI_0) ).
cnf(c_438,plain,
( c_in(hAPP(D,A),c_Set_Oimage(D,B,C,E),E)
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_rev__image__eqI_0]) ).
fof(cls_conjecture_1,axiom,
v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_441,plain,
v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_442,plain,
c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) = v_G,
inference(copy,[status(thm)],[c_441]) ).
fof(cls_conjecture_2,axiom,
c_in(v_pn,v_U,tc_Com_Opname),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_443,plain,
c_in(v_pn,v_U,tc_Com_Opname),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_444,plain,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_445,plain,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),v_G,tc_fun(t_a,tc_bool)),
inference(paramod,[status(thm)],[c_442,c_444]) ).
cnf(c_2507,plain,
hBOOL(hAPP(v_U,v_pn)),
inference(resolve,[status(thm)],[c_443,c_427]) ).
cnf(c_3234,plain,
c_in(v_pn,v_U,A),
inference(resolve,[status(thm)],[c_2507,c_426]) ).
cnf(c_3248,plain,
c_in(hAPP(A,v_pn),c_Set_Oimage(A,v_U,B,C),C),
inference(resolve,[status(thm)],[c_3234,c_438]) ).
cnf(c_6376,plain,
c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
inference(paramod,[status(thm)],[c_442,c_3248]) ).
cnf(c_6408,plain,
( ~ c_in(A,C,B)
| c_lessequals(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,tc_fun(B,tc_bool)) ),
inference(resolve,[status(thm)],[c_392,c_417]) ).
cnf(c_6409,plain,
c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),v_G,tc_fun(t_a,tc_bool)),
inference(resolve,[status(thm)],[c_6408,c_6376]) ).
cnf(c_6407,plain,
$false,
inference(resolve,[status(thm)],[c_445,c_6409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV880-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n026.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 15:09:16 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 1315605 was started by sandbox on n026,
% 0.11/5.39 % Sat Sep 26 15:09:16 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/5.41
% 0.15/5.41 % From the command line: assign(max_seconds, 300).
% 27.69/9.06
% 27.69/9.06 % given #500 (W,wt=19): 2385 c_in(A,c_COMBK(B,C,D),E) | -hBOOL(B). [para(363(a,1),426(b,1))].
% 27.69/9.06
% 27.69/9.06 % SZS status Unsatisfiable for theBenchmark
% 27.69/9.06
% 27.69/9.06 % Proof 1 at 2.98 (+ 0.62) seconds.
% 27.69/9.06 % Length of proof is 15.
% 27.69/9.06 % Level of proof is 5.
% 27.69/9.06 % Maximum clause weight is 34.000.
% 27.69/9.06 % Given clauses 566.
% 27.69/9.06
% 27.69/9.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------