%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET954+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 : Thu Sep 24 08:57:51 AM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 61 ( 27 ~; 17 |; 14 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 4 sgn 28 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l55_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',l55_zfmisc_1) ).
fof(t107_zfmisc_1,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
=> in(ordered_pair(B,A),cartesian_product2(D,C)) ),
file('theBenchmark.p',t107_zfmisc_1) ).
fof(f_5_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(B,D)
| ~ in(A,C) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[l55_zfmisc_1]) ).
fof(f_5_2,plain,
! [U_11,U_10,U_9,U_8] :
( ( in(ordered_pair(U_11,U_10),cartesian_product2(U_9,U_8))
| ~ in(U_10,U_8)
| ~ in(U_11,U_9) )
& ( ( in(U_10,U_8)
& in(U_11,U_9) )
| ~ in(ordered_pair(U_11,U_10),cartesian_product2(U_9,U_8)) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_19,U_17,U_15,U_13] :
( in(ordered_pair(U_19,U_17),cartesian_product2(U_15,U_13))
| ~ in(U_17,U_13)
| ~ in(U_19,U_15) )
& ! [U_18,U_16,U_14,U_12] :
( ( in(U_16,U_12)
& in(U_18,U_14) )
| ~ in(ordered_pair(U_18,U_16),cartesian_product2(U_14,U_12)) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( in(U_18,U_14)
| ~ in(ordered_pair(U_18,U_16),cartesian_product2(U_14,U_12)) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( in(U_16,U_12)
| ~ in(ordered_pair(U_18,U_16),cartesian_product2(U_14,U_12)) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( in(ordered_pair(U_19,U_17),cartesian_product2(U_15,U_13))
| ~ in(U_17,U_13)
| ~ in(U_19,U_15) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_8_1,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
=> in(ordered_pair(B,A),cartesian_product2(D,C)) ),
inference(negate,[status(cth)],[t107_zfmisc_1]) ).
fof(f_8_2,negated_conjecture,
? [A,B,C,D] :
( ~ in(ordered_pair(B,A),cartesian_product2(D,C))
& in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(fof_nnf,[status(thm)],[f_8_1]) ).
fof(f_8_3,negated_conjecture,
? [U_25,U_24,U_23,U_22] :
( ~ in(ordered_pair(U_24,U_25),cartesian_product2(U_22,U_23))
& in(ordered_pair(U_25,U_24),cartesian_product2(U_23,U_22)) ),
inference(variable_rename,[status(thm)],[f_8_2]) ).
fof(f_8_4,negated_conjecture,
? [U_24,U_23,U_22] :
( ~ in(ordered_pair(U_24,sK3),cartesian_product2(U_22,U_23))
& in(ordered_pair(sK3,U_24),cartesian_product2(U_23,U_22)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_25,sK3)],[f_8_3]) ).
fof(f_8_5,negated_conjecture,
? [U_23,U_22] :
( ~ in(ordered_pair(sK4,sK3),cartesian_product2(U_22,U_23))
& in(ordered_pair(sK3,sK4),cartesian_product2(U_23,U_22)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_24,sK4)],[f_8_4]) ).
fof(f_8_6,negated_conjecture,
? [U_22] :
( ~ in(ordered_pair(sK4,sK3),cartesian_product2(U_22,sK5))
& in(ordered_pair(sK3,sK4),cartesian_product2(sK5,U_22)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_23,sK5)],[f_8_5]) ).
fof(f_8_7,negated_conjecture,
( ~ in(ordered_pair(sK4,sK3),cartesian_product2(sK6,sK5))
& in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_22,sK6)],[f_8_6]) ).
fof(f_8_8,negated_conjecture,
( ~ in(ordered_pair(sK4,sK3),cartesian_product2(sK6,sK5))
& in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6)) ),
inference(definitional_conversion,[status(esa)],[f_8_7]) ).
cnf(f_8_9,negated_conjecture,
in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6)),
inference(clausify,[status(thm)],[f_8_8]) ).
cnf(f_8_10,negated_conjecture,
~ in(ordered_pair(sK4,sK3),cartesian_product2(sK6,sK5)),
inference(clausify,[status(thm)],[f_8_8]) ).
cnf(t1,plain,
~ in(ordered_pair(sK4,sK3),cartesian_product2(sK6,sK5)),
inference(start,[status(thm),parent(0:0)],[f_8_10]) ).
cnf(t2,plain,
( ~ in(sK3,sK5)
| ~ in(sK4,sK6)
| in(ordered_pair(sK4,sK3),cartesian_product2(sK6,sK5)) ),
inference(extension,[status(thm),parent(t1:1)],[f_5_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6))
| in(sK4,sK6) ),
inference(extension,[status(thm),parent(t2:2)],[f_5_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6)),
inference(extension,[status(thm),parent(t4:2)],[f_8_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6))
| in(sK3,sK5) ),
inference(extension,[status(thm),parent(t2:3)],[f_5_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6)),
inference(extension,[status(thm),parent(t8:2)],[f_8_9]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET954+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 23:11:20 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.39 % SZS status Theorem for theBenchmark
% 0.12/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------