%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SWW473+7 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 05:04:27 PM UTC 2025
% Result : Theorem 48.47s 6.57s
% Output : CNFRefutation 48.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 32 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 8 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 28 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_6,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
fof(conj_6_negated,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(negate_conjecture,[status(cth)],[conj_6]) ).
cnf(1702,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(cnf,[status(esa)],[conj_6_negated]) ).
cnf(l0,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(instantiation,[status(thm)],[1702]) ).
fof(fact_103_insert__subset,plain,
! [X_b,X_1,A_3,B_1] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_1))
<=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1))
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_insert__subset) ).
cnf(208,plain,
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)),X2)) ),
inference(cnf,[status(esa)],[fact_103_insert__subset]) ).
cnf(l1,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
inference(instantiation,[status(thm)],[208]) ).
fof(fact_95_rev__image__eqI,plain,
! [X_c,X_b,B_3,F,X_1,A_3] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
=> ( ti(X_c,B_3) = hAPP(X_b,X_c,F,X_1)
=> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B_3),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_rev__image__eqI) ).
cnf(197,plain,
( ti(X0,X1) != hAPP(X2,X0,X3,X4)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X2,bool),fun(X0,bool),hAPP(fun(X2,X0),fun(fun(X2,bool),fun(X0,bool)),image(X2,X0),X3),X5))) ),
inference(cnf,[status(esa)],[fact_95_rev__image__eqI]) ).
cnf(l10,plain,
( ti(x_a,hAPP(pname,x_a,mgt_call,pn)) != hAPP(pname,x_a,mgt_call,pn)
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
inference(instantiation,[status(thm)],[197]) ).
fof(tsy_c_hAPP_res,plain,
! [X_c,X_a,B_1_1,B_2_1] : ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
cnf(59,plain,
ti(X0,hAPP(X1,X0,X2,X3)) = hAPP(X1,X0,X2,X3),
inference(cnf,[status(esa)],[tsy_c_hAPP_res]) ).
cnf(l12,plain,
ti(x_a,hAPP(pname,x_a,mgt_call,pn)) = hAPP(pname,x_a,mgt_call,pn),
inference(instantiation,[status(thm)],[59]) ).
fof(conj_4,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
cnf(1700,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(cnf,[status(esa)],[conj_4]) ).
cnf(l14,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(instantiation,[status(thm)],[1700]) ).
fof(conj_1,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
cnf(1697,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(cnf,[status(esa)],[conj_1]) ).
cnf(l2,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(instantiation,[status(thm)],[1697]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l10,l12,l14,l2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW473+7 : TPTP v9.0.0. Released v5.3.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Jul 22 14:04:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.46 % launching worker at depth: 6
% 0.19/0.46 % launching worker at depth: 1
% 0.19/0.46 % launching worker at depth: 4
% 0.19/0.46 % launching worker at depth: 2
% 0.19/0.46 % launching worker at depth: 5
% 0.19/0.46 % launching worker at depth: 3
% 0.19/0.46 % launching worker at depth: 7
% 0.19/0.46 % launching worker at depth: 8
% 0.19/0.47 % launching worker at depth: 9
% 3.95/0.97 % launching worker at depth: 10
% 48.47/6.57 % SZS status Theorem for theBenchmark
% 48.47/6.57 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------