%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU131+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n023.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 03:44:33 PM UTC 2025
% Result : Theorem 113.00s 14.57s
% Output : CNFRefutation 113.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 10 unt; 0 def)
% Number of atoms : 80 ( 30 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 78 ( 36 ~; 34 |; 1 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 3 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l32_xboole_1,plain,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(l32_xboole_1_negated,plain,
~ ! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
inference(negate_conjecture,[status(cth)],[l32_xboole_1]) ).
cnf(42,plain,
( set_difference(sK6,sK7) = empty_set
| subset(sK6,sK7) ),
inference(cnf,[status(esa)],[l32_xboole_1_negated]) ).
cnf(l0,plain,
( set_difference(sK6,sK7) = empty_set
| subset(sK6,sK7) ),
inference(instantiation,[status(thm)],[42]) ).
fof(d3_tarski,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
cnf(16,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf,[status(esa)],[d3_tarski]) ).
cnf(l2,plain,
( ~ in(sK1(set_difference(sK6,sK7)),sK6)
| ~ subset(sK6,sK7)
| in(sK1(set_difference(sK6,sK7)),sK7) ),
inference(instantiation,[status(thm)],[16]) ).
fof(d4_xboole_0,plain,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
cnf(28,plain,
( X0 != set_difference(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X0) ),
inference(cnf,[status(esa)],[d4_xboole_0]) ).
cnf(l33,plain,
( set_difference(sK6,sK7) != set_difference(sK6,sK7)
| ~ in(sK1(set_difference(sK6,sK7)),sK7)
| ~ in(sK1(set_difference(sK6,sK7)),set_difference(sK6,sK7)) ),
inference(instantiation,[status(thm)],[28]) ).
cnf(27,plain,
( X0 != set_difference(X1,X2)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf,[status(esa)],[d4_xboole_0]) ).
cnf(l6,plain,
( set_difference(sK6,sK7) != set_difference(sK6,sK7)
| ~ in(sK1(set_difference(sK6,sK7)),set_difference(sK6,sK7))
| in(sK1(set_difference(sK6,sK7)),sK6) ),
inference(instantiation,[status(thm)],[27]) ).
fof(d1_xboole_0,plain,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
cnf(7,plain,
( X0 = empty_set
| in(sK1(X0),X0) ),
inference(cnf,[status(esa)],[d1_xboole_0]) ).
cnf(l34,plain,
( set_difference(sK6,sK7) = empty_set
| in(sK1(set_difference(sK6,sK7)),set_difference(sK6,sK7)) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(29,plain,
( X0 != set_difference(X1,X2)
| ~ in(X3,X1)
| in(X3,X2)
| in(X3,X0) ),
inference(cnf,[status(esa)],[d4_xboole_0]) ).
cnf(l3,plain,
( set_difference(sK6,sK7) != set_difference(sK6,sK7)
| ~ in(sK3(sK6,sK7),sK6)
| in(sK3(sK6,sK7),sK7)
| in(sK3(sK6,sK7),set_difference(sK6,sK7)) ),
inference(instantiation,[status(thm)],[29]) ).
cnf(l18,plain,
( set_difference(sK6,sK7) = empty_set
| in(sK1(set_difference(sK6,sK7)),set_difference(sK6,sK7)) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(43,plain,
( set_difference(sK6,sK7) != empty_set
| ~ subset(sK6,sK7) ),
inference(cnf,[status(esa)],[l32_xboole_1_negated]) ).
cnf(l24,plain,
( set_difference(sK6,sK7) != empty_set
| ~ subset(sK6,sK7) ),
inference(instantiation,[status(thm)],[43]) ).
cnf(l99,plain,
( set_difference(empty_set,empty_set) != set_difference(empty_set,empty_set)
| ~ in(set_union2(empty_set,sK3(sK6,sK7)),empty_set)
| ~ in(set_union2(empty_set,sK3(sK6,sK7)),set_difference(empty_set,empty_set)) ),
inference(instantiation,[status(thm)],[28]) ).
cnf(l36,plain,
( set_difference(sK6,sK7) != empty_set
| ~ subset(sK6,sK7) ),
inference(instantiation,[status(thm)],[43]) ).
cnf(17,plain,
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[d3_tarski]) ).
cnf(l55,plain,
( in(sK3(sK6,sK7),sK6)
| subset(sK6,sK7) ),
inference(instantiation,[status(thm)],[17]) ).
fof(commutativity_k2_xboole_0,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
cnf(1,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(l145,plain,
set_union2(sK3(sK6,sK7),empty_set) = set_union2(empty_set,sK3(sK6,sK7)),
inference(instantiation,[status(thm)],[1]) ).
cnf(18,plain,
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[d3_tarski]) ).
cnf(l8,plain,
( ~ in(sK3(sK6,sK7),sK7)
| subset(sK6,sK7) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(l57,plain,
( set_difference(sK6,sK7) != empty_set
| ~ subset(sK6,sK7) ),
inference(instantiation,[status(thm)],[43]) ).
fof(t1_boole,plain,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
cnf(51,plain,
set_union2(X0,empty_set) = X0,
inference(cnf,[status(esa)],[t1_boole]) ).
cnf(l144,plain,
set_union2(sK3(sK6,sK7),empty_set) = sK3(sK6,sK7),
inference(instantiation,[status(thm)],[51]) ).
cnf(l9,plain,
( set_difference(sK6,sK7) != empty_set
| ~ subset(sK6,sK7) ),
inference(instantiation,[status(thm)],[43]) ).
fof(t4_boole,plain,
! [A] : set_difference(empty_set,A) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
cnf(64,plain,
set_difference(empty_set,X0) = empty_set,
inference(cnf,[status(esa)],[t4_boole]) ).
cnf(l93,plain,
set_difference(empty_set,empty_set) = empty_set,
inference(instantiation,[status(thm)],[64]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l2,l33,l6,l34,l3,l18,l24,l99,l36,l55,l145,l8,l57,l144,l9,l93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU131+2 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 21 23:33:34 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 8
% 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: 5
% 0.13/0.34 % launching worker at depth: 6
% 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: 9
% 0.13/0.37 % launching worker at depth: 10
% 3.31/0.80 % launching worker at depth: 11
% 113.00/14.57 % SZS status Theorem for theBenchmark
% 113.00/14.57 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------