%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET575+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n020.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 08:56:59 AM UTC 2026
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 73 ( 31 ~; 23 |; 16 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 27 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(prove_th15,conjecture,
! [B,C] :
( intersect(B,C)
=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',prove_th15) ).
fof(f_1_1,plain,
! [B,C] :
( ( intersect(B,C)
| ! [D] :
( ~ member(D,C)
| ~ member(D,B) ) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(fof_nnf,[status(thm)],[intersect_defn]) ).
fof(f_1_2,plain,
! [U_3,U_2] :
( ( intersect(U_3,U_2)
| ! [U_1] :
( ~ member(U_1,U_2)
| ~ member(U_1,U_3) ) )
& ( ? [U_0] :
( member(U_0,U_2)
& member(U_0,U_3) )
| ~ intersect(U_3,U_2) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_7,U_5] :
( intersect(U_7,U_5)
| ! [U_1] :
( ~ member(U_1,U_5)
| ~ member(U_1,U_7) ) )
& ! [U_6,U_4] :
( ? [U_0] :
( member(U_0,U_4)
& member(U_0,U_6) )
| ~ intersect(U_6,U_4) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_7,U_5] :
( intersect(U_7,U_5)
| ! [U_1] :
( ~ member(U_1,U_5)
| ~ member(U_1,U_7) ) )
& ! [U_6,U_4] :
( ( member(sK1(U_6,U_4),U_4)
& member(sK1(U_6,U_4),U_6) )
| ~ intersect(U_6,U_4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_6,U_4))],[f_1_3]) ).
cnf(f_1_5,plain,
( member(sK1(U_6,U_4),U_6)
| ~ intersect(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_6,plain,
( member(sK1(U_6,U_4),U_4)
| ~ intersect(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_3_1,negated_conjecture,
~ ! [B,C] :
( intersect(B,C)
=> ? [D] :
( member(D,C)
& member(D,B) ) ),
inference(negate,[status(cth)],[prove_th15]) ).
fof(f_3_2,negated_conjecture,
? [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
& intersect(B,C) ),
inference(fof_nnf,[status(thm)],[f_3_1]) ).
fof(f_3_3,negated_conjecture,
? [U_12,U_11] :
( ! [U_10] :
( ~ member(U_10,U_11)
| ~ member(U_10,U_12) )
& intersect(U_12,U_11) ),
inference(variable_rename,[status(thm)],[f_3_2]) ).
fof(f_3_4,negated_conjecture,
? [U_11] :
( ! [U_10] :
( ~ member(U_10,U_11)
| ~ member(U_10,sK2) )
& intersect(sK2,U_11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_12,sK2)],[f_3_3]) ).
fof(f_3_5,negated_conjecture,
( ! [U_10] :
( ~ member(U_10,sK3)
| ~ member(U_10,sK2) )
& intersect(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_11,sK3)],[f_3_4]) ).
fof(f_3_6,negated_conjecture,
( ! [U_10] :
( ~ member(U_10,sK3)
| ~ member(U_10,sK2) )
& intersect(sK2,sK3) ),
inference(definitional_conversion,[status(esa)],[f_3_5]) ).
cnf(f_3_7,negated_conjecture,
intersect(sK2,sK3),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_8,negated_conjecture,
( ~ member(U_10,sK3)
| ~ member(U_10,sK2) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(t1,plain,
( ~ member(sK1(sK2,sK3),sK3)
| ~ member(sK1(sK2,sK3),sK2) ),
inference(start,[status(thm),parent(0:0)],[f_3_8]) ).
cnf(t2,plain,
( ~ intersect(sK2,sK3)
| member(sK1(sK2,sK3),sK2) ),
inference(extension,[status(thm),parent(t1:1)],[f_1_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
intersect(sK2,sK3),
inference(extension,[status(thm),parent(t2:2)],[f_3_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ intersect(sK2,sK3)
| member(sK1(sK2,sK3),sK3) ),
inference(extension,[status(thm),parent(t1:2)],[f_1_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t1:2]) ).
cnf(t8,plain,
intersect(sK2,sK3),
inference(extension,[status(thm),parent(t6:2)],[f_3_7]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET575+3 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.07/0.35 % Computer : n020.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 19 22:41:31 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.11/0.37 % SZS status Theorem for theBenchmark
% 0.11/0.37 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------