%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET573+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 : n006.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 0.15s 5.40s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 84 ( 30 ~; 24 |; 26 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 34 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(disjoint_defn,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('theBenchmark.p',disjoint_defn) ).
fof(prove_th12,conjecture,
! [B,C,D] :
( ( disjoint(C,D)
& member(B,C) )
=> ~ member(B,D) ),
file('theBenchmark.p',prove_th12) ).
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_7,plain,
( intersect(U_7,U_5)
| ~ member(U_1,U_5)
| ~ member(U_1,U_7) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
! [B,C] :
( ( disjoint(B,C)
| intersect(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(fof_nnf,[status(thm)],[disjoint_defn]) ).
fof(f_2_2,plain,
! [U_9,U_8] :
( ( disjoint(U_9,U_8)
| intersect(U_9,U_8) )
& ( ~ intersect(U_9,U_8)
| ~ disjoint(U_9,U_8) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_13,U_11] :
( disjoint(U_13,U_11)
| intersect(U_13,U_11) )
& ! [U_12,U_10] :
( ~ intersect(U_12,U_10)
| ~ disjoint(U_12,U_10) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ intersect(U_12,U_10)
| ~ disjoint(U_12,U_10) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_4_1,negated_conjecture,
~ ! [B,C,D] :
( ( disjoint(C,D)
& member(B,C) )
=> ~ member(B,D) ),
inference(negate,[status(cth)],[prove_th12]) ).
fof(f_4_2,negated_conjecture,
? [B,C,D] :
( member(B,D)
& disjoint(C,D)
& member(B,C) ),
inference(fof_nnf,[status(thm)],[f_4_1]) ).
fof(f_4_3,negated_conjecture,
? [U_18,U_17,U_16] :
( member(U_18,U_16)
& disjoint(U_17,U_16)
& member(U_18,U_17) ),
inference(variable_rename,[status(thm)],[f_4_2]) ).
fof(f_4_4,negated_conjecture,
? [U_17,U_16] :
( member(sK2,U_16)
& disjoint(U_17,U_16)
& member(sK2,U_17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_18,sK2)],[f_4_3]) ).
fof(f_4_5,negated_conjecture,
? [U_16] :
( member(sK2,U_16)
& disjoint(sK3,U_16)
& member(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_17,sK3)],[f_4_4]) ).
fof(f_4_6,negated_conjecture,
( member(sK2,sK4)
& disjoint(sK3,sK4)
& member(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_16,sK4)],[f_4_5]) ).
fof(f_4_7,negated_conjecture,
( member(sK2,sK4)
& disjoint(sK3,sK4)
& member(sK2,sK3) ),
inference(definitional_conversion,[status(esa)],[f_4_6]) ).
cnf(f_4_8,negated_conjecture,
member(sK2,sK3),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_9,negated_conjecture,
disjoint(sK3,sK4),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_10,negated_conjecture,
member(sK2,sK4),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(t1,plain,
( ~ intersect(sK3,sK4)
| ~ disjoint(sK3,sK4) ),
inference(start,[status(thm),parent(0:0)],[f_2_4]) ).
cnf(t2,plain,
disjoint(sK3,sK4),
inference(extension,[status(thm),parent(t1:1)],[f_4_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ member(sK2,sK4)
| ~ member(sK2,sK3)
| intersect(sK3,sK4) ),
inference(extension,[status(thm),parent(t1:2)],[f_1_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
member(sK2,sK3),
inference(extension,[status(thm),parent(t4:2)],[f_4_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
member(sK2,sK4),
inference(extension,[status(thm),parent(t4:3)],[f_4_10]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET573+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.38 % Computer : n006.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Sat Sep 19 22:40:18 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.15/5.40 % SZS status Theorem for theBenchmark
% 0.15/5.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------