%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU167+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 08:58:19 AM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 65 ( 25 ~; 15 |; 21 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 30 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t118_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
file('theBenchmark.p',t118_zfmisc_1) ).
fof(t119_zfmisc_1,conjecture,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t119_zfmisc_1) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(f_4_1,plain,
! [A,B,C] :
( ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) )
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t118_zfmisc_1]) ).
fof(f_4_2,plain,
! [U_6,U_5,U_4] :
( ( subset(cartesian_product2(U_4,U_6),cartesian_product2(U_4,U_5))
& subset(cartesian_product2(U_6,U_4),cartesian_product2(U_5,U_4)) )
| ~ subset(U_6,U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_6,U_5] :
( ( ! [U_8] : subset(cartesian_product2(U_8,U_6),cartesian_product2(U_8,U_5))
& ! [U_7] : subset(cartesian_product2(U_6,U_7),cartesian_product2(U_5,U_7)) )
| ~ subset(U_6,U_5) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( subset(cartesian_product2(U_6,U_7),cartesian_product2(U_5,U_7))
| ~ subset(U_6,U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( subset(cartesian_product2(U_8,U_6),cartesian_product2(U_8,U_5))
| ~ subset(U_6,U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,negated_conjecture,
~ ! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(negate,[status(cth)],[t119_zfmisc_1]) ).
fof(f_5_2,negated_conjecture,
? [A,B,C,D] :
( ~ subset(cartesian_product2(A,C),cartesian_product2(B,D))
& subset(C,D)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[f_5_1]) ).
fof(f_5_3,negated_conjecture,
? [U_12,U_11,U_10,U_9] :
( ~ subset(cartesian_product2(U_12,U_10),cartesian_product2(U_11,U_9))
& subset(U_10,U_9)
& subset(U_12,U_11) ),
inference(variable_rename,[status(thm)],[f_5_2]) ).
fof(f_5_4,negated_conjecture,
? [U_11,U_10,U_9] :
( ~ subset(cartesian_product2(sK3,U_10),cartesian_product2(U_11,U_9))
& subset(U_10,U_9)
& subset(sK3,U_11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_12,sK3)],[f_5_3]) ).
fof(f_5_5,negated_conjecture,
? [U_10,U_9] :
( ~ subset(cartesian_product2(sK3,U_10),cartesian_product2(sK4,U_9))
& subset(U_10,U_9)
& subset(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_11,sK4)],[f_5_4]) ).
fof(f_5_6,negated_conjecture,
? [U_9] :
( ~ subset(cartesian_product2(sK3,sK5),cartesian_product2(sK4,U_9))
& subset(sK5,U_9)
& subset(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_10,sK5)],[f_5_5]) ).
fof(f_5_7,negated_conjecture,
( ~ subset(cartesian_product2(sK3,sK5),cartesian_product2(sK4,sK6))
& subset(sK5,sK6)
& subset(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_9,sK6)],[f_5_6]) ).
fof(f_5_8,negated_conjecture,
( ~ subset(cartesian_product2(sK3,sK5),cartesian_product2(sK4,sK6))
& subset(sK5,sK6)
& subset(sK3,sK4) ),
inference(definitional_conversion,[status(esa)],[f_5_7]) ).
cnf(f_5_9,negated_conjecture,
subset(sK3,sK4),
inference(clausify,[status(thm)],[f_5_8]) ).
cnf(f_5_10,negated_conjecture,
subset(sK5,sK6),
inference(clausify,[status(thm)],[f_5_8]) ).
cnf(f_5_11,negated_conjecture,
~ subset(cartesian_product2(sK3,sK5),cartesian_product2(sK4,sK6)),
inference(clausify,[status(thm)],[f_5_8]) ).
fof(f_6_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_6_2,plain,
! [U_15,U_14,U_13] :
( subset(U_15,U_13)
| ~ subset(U_14,U_13)
| ~ subset(U_15,U_14) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( subset(U_15,U_13)
| ~ subset(U_14,U_13)
| ~ subset(U_15,U_14) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(t1,plain,
~ subset(cartesian_product2(sK3,sK5),cartesian_product2(sK4,sK6)),
inference(start,[status(thm),parent(0:0)],[f_5_11]) ).
cnf(t2,plain,
( ~ subset(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK6))
| ~ subset(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6))
| subset(cartesian_product2(sK3,sK5),cartesian_product2(sK4,sK6)) ),
inference(extension,[status(thm),parent(t1:1)],[f_6_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ subset(sK5,sK6)
| subset(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)) ),
inference(extension,[status(thm),parent(t2:2)],[f_4_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
subset(sK5,sK6),
inference(extension,[status(thm),parent(t4:2)],[f_5_10]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ subset(sK3,sK4)
| subset(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK6)) ),
inference(extension,[status(thm),parent(t2:3)],[f_4_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
subset(sK3,sK4),
inference(extension,[status(thm),parent(t8:2)],[f_5_9]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU167+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 23:29:50 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------