%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET587+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n024.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 03:32:17 PM UTC 2025
% Result : Theorem 12.71s 1.93s
% Output : CNFRefutation 12.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 6 unt; 0 def)
% Number of atoms : 89 ( 16 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 88 ( 40 ~; 37 |; 1 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 4 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_difference_empty_set,plain,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_empty_set) ).
fof(prove_difference_empty_set_negated,plain,
~ ! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
inference(negate_conjecture,[status(cth)],[prove_difference_empty_set]) ).
cnf(21,plain,
( difference(sK5,sK6) = empty_set
| subset(sK5,sK6) ),
inference(cnf,[status(esa)],[prove_difference_empty_set_negated]) ).
cnf(l0,plain,
( difference(sK5,sK6) = empty_set
| subset(sK5,sK6) ),
inference(instantiation,[status(thm)],[21]) ).
fof(subset_defn,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
cnf(6,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l4,plain,
( ~ member(sK1(difference(sK5,sK6),empty_set),sK5)
| ~ subset(sK5,sK6)
| member(sK1(difference(sK5,sK6),empty_set),sK6) ),
inference(instantiation,[status(thm)],[6]) ).
fof(difference_defn,plain,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
cnf(2,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l16,plain,
( ~ member(sK1(difference(sK5,sK6),empty_set),difference(sK5,sK6))
| member(sK1(difference(sK5,sK6),empty_set),sK5) ),
inference(instantiation,[status(thm)],[2]) ).
fof(member_equal,plain,
! [B,C] :
( ! [D] :
( member(D,B)
<=> member(D,C) )
=> B = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_equal) ).
cnf(0,plain,
( X0 = X1
| member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) ),
inference(cnf,[status(esa)],[member_equal]) ).
cnf(l23,plain,
( difference(sK5,sK6) = empty_set
| member(sK1(difference(sK5,sK6),empty_set),difference(sK5,sK6))
| member(sK1(difference(sK5,sK6),empty_set),empty_set) ),
inference(instantiation,[status(thm)],[0]) ).
fof(empty_set_defn,plain,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
cnf(5,plain,
~ member(X0,empty_set),
inference(cnf,[status(esa)],[empty_set_defn]) ).
cnf(l24,plain,
~ member(sK1(difference(sK5,sK6),empty_set),empty_set),
inference(instantiation,[status(thm)],[5]) ).
cnf(3,plain,
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l14,plain,
( ~ member(sK1(difference(sK5,sK6),empty_set),sK6)
| ~ member(sK1(difference(sK5,sK6),empty_set),difference(sK5,sK6)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(22,plain,
( difference(sK5,sK6) != empty_set
| ~ subset(sK5,sK6) ),
inference(cnf,[status(esa)],[prove_difference_empty_set_negated]) ).
cnf(l27,plain,
( difference(sK5,sK6) != empty_set
| ~ subset(sK5,sK6) ),
inference(instantiation,[status(thm)],[22]) ).
fof(equal_member_defn,plain,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
cnf(12,plain,
( X0 != X1
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l1,plain,
( difference(sK5,sK6) != empty_set
| ~ member(sK2(sK5,sK6),difference(sK5,sK6))
| member(sK2(sK5,sK6),empty_set) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l33,plain,
( difference(sK5,sK6) = empty_set
| member(sK1(difference(sK5,sK6),empty_set),difference(sK5,sK6))
| member(sK1(difference(sK5,sK6),empty_set),empty_set) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l34,plain,
( difference(sK5,sK6) != empty_set
| ~ subset(sK5,sK6) ),
inference(instantiation,[status(thm)],[22]) ).
cnf(l106,plain,
~ member(sK1(difference(sK5,sK6),empty_set),empty_set),
inference(instantiation,[status(thm)],[5]) ).
fof(empty_defn,plain,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
cnf(19,plain,
( ~ member(X0,X1)
| ~ empty(X1) ),
inference(cnf,[status(esa)],[empty_defn]) ).
cnf(l2,plain,
( ~ member(sK2(sK5,sK6),empty_set)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[19]) ).
cnf(20,plain,
( member(sK4(X0),X0)
| empty(X0) ),
inference(cnf,[status(esa)],[empty_defn]) ).
cnf(l78,plain,
( member(sK4(empty_set),empty_set)
| empty(empty_set) ),
inference(instantiation,[status(thm)],[20]) ).
cnf(l79,plain,
~ member(sK4(empty_set),empty_set),
inference(instantiation,[status(thm)],[5]) ).
cnf(4,plain,
( ~ member(X0,X1)
| member(X0,X2)
| member(X0,difference(X1,X2)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l3,plain,
( ~ member(sK2(sK5,sK6),sK5)
| member(sK2(sK5,sK6),sK6)
| member(sK2(sK5,sK6),difference(sK5,sK6)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(7,plain,
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l5,plain,
( member(sK2(sK5,sK6),sK5)
| subset(sK5,sK6) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l35,plain,
( difference(sK5,sK6) != empty_set
| ~ subset(sK5,sK6) ),
inference(instantiation,[status(thm)],[22]) ).
cnf(8,plain,
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l43,plain,
( ~ member(sK2(sK5,sK6),sK6)
| subset(sK5,sK6) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l46,plain,
( difference(sK5,sK6) != empty_set
| ~ subset(sK5,sK6) ),
inference(instantiation,[status(thm)],[22]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l4,l16,l23,l24,l14,l27,l1,l33,l34,l106,l2,l78,l79,l3,l5,l35,l43,l46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET587+3 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 21 22:03:34 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 5
% 0.13/0.34 % launching worker at depth: 4
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.35 % launching worker at depth: 10
% 0.19/0.45 % launching worker at depth: 11
% 12.71/1.93 % SZS status Theorem for theBenchmark
% 12.71/1.93 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------