%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET691+4 : 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 : n010.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 08:57:18 AM UTC 2026
% Result : Theorem 7.05s 7.31s
% Output : Proof 7.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 17 unt; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 144 ( 61 ~; 49 |; 29 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 1 sgn 34 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('SET006+0.ax',subset) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('SET006+0.ax',equal_set) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set),
file('SET006+0.ax',empty_set) ).
fof(thI16,conjecture,
! [A] :
( subset(A,empty_set)
<=> equal_set(A,empty_set) ),
file('theBenchmark.p',thI16) ).
fof(f_1_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [X] :
( ~ member(X,B)
& member(X,A) ) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[subset]) ).
fof(f_1_2,plain,
! [U_3,U_2] :
( ( subset(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) )
| ~ subset(U_3,U_2) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_7,U_5] :
( subset(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) )
| ~ subset(U_6,U_4) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_7,U_5] :
( subset(U_7,U_5)
| ( ~ member(sK1(U_7,U_5),U_5)
& member(sK1(U_7,U_5),U_7) ) )
& ! [U_6,U_4] :
( ! [U_0] :
( member(U_0,U_4)
| ~ member(U_0,U_6) )
| ~ subset(U_6,U_4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1(U_7,U_5))],[f_1_3]) ).
cnf(f_1_6,plain,
( member(sK1(U_7,U_5),U_7)
| subset(U_7,U_5) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
! [A,B] :
( ( equal_set(A,B)
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(fof_nnf,[status(thm)],[equal_set]) ).
fof(f_2_2,plain,
! [U_9,U_8] :
( ( equal_set(U_9,U_8)
| ~ subset(U_8,U_9)
| ~ subset(U_9,U_8) )
& ( ( subset(U_8,U_9)
& subset(U_9,U_8) )
| ~ equal_set(U_9,U_8) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_13,U_11] :
( equal_set(U_13,U_11)
| ~ subset(U_11,U_13)
| ~ subset(U_13,U_11) )
& ! [U_12,U_10] :
( ( subset(U_10,U_12)
& subset(U_12,U_10) )
| ~ equal_set(U_12,U_10) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( subset(U_12,U_10)
| ~ equal_set(U_12,U_10) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( equal_set(U_13,U_11)
| ~ subset(U_11,U_13)
| ~ subset(U_13,U_11) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_6_1,plain,
! [X] : ~ member(X,empty_set),
inference(fof_nnf,[status(thm)],[empty_set]) ).
fof(f_6_2,plain,
! [U_38] : ~ member(U_38,empty_set),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
~ member(U_38,empty_set),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_12_1,negated_conjecture,
~ ! [A] :
( subset(A,empty_set)
<=> equal_set(A,empty_set) ),
inference(negate,[status(cth)],[thI16]) ).
fof(f_12_2,negated_conjecture,
? [A] :
( ( ~ subset(A,empty_set)
& equal_set(A,empty_set) )
| ( ~ equal_set(A,empty_set)
& subset(A,empty_set) ) ),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_79] :
( ( ~ subset(U_79,empty_set)
& equal_set(U_79,empty_set) )
| ( ~ equal_set(U_79,empty_set)
& subset(U_79,empty_set) ) ),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
( ? [U_81] :
( ~ subset(U_81,empty_set)
& equal_set(U_81,empty_set) )
| ? [U_80] :
( ~ equal_set(U_80,empty_set)
& subset(U_80,empty_set) ) ),
inference(miniscope,[status(thm)],[f_12_3]) ).
fof(f_12_5,negated_conjecture,
( ? [U_81] :
( ~ subset(U_81,empty_set)
& equal_set(U_81,empty_set) )
| ( ~ equal_set(sK4,empty_set)
& subset(sK4,empty_set) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_80,sK4)],[f_12_4]) ).
fof(f_12_6,negated_conjecture,
( ( ~ subset(sK5,empty_set)
& equal_set(sK5,empty_set) )
| ( ~ equal_set(sK4,empty_set)
& subset(sK4,empty_set) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_81,sK5)],[f_12_5]) ).
fof(f_12_7,negated_conjecture,
( ( ~ subset(sK5,empty_set)
| ~ sP1 )
& ( equal_set(sK5,empty_set)
| ~ sP1 )
& ( ~ equal_set(sK4,empty_set)
| ~ sP0 )
& ( subset(sK4,empty_set)
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_12_6]) ).
cnf(f_12_8,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_9,negated_conjecture,
( subset(sK4,empty_set)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_10,negated_conjecture,
( ~ equal_set(sK4,empty_set)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_11,negated_conjecture,
( equal_set(sK5,empty_set)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_12,negated_conjecture,
( ~ subset(sK5,empty_set)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(t1,plain,
( ~ equal_set(sK4,empty_set)
| ~ sP0 ),
inference(start,[status(thm),parent(0:0)],[f_12_10]) ).
cnf(t2,plain,
( sP1
| sP0 ),
inference(extension,[status(thm),parent(t1:1)],[f_12_8]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ subset(sK5,empty_set)
| ~ sP1 ),
inference(extension,[status(thm),parent(t2:2)],[f_12_12]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ equal_set(sK5,empty_set)
| subset(sK5,empty_set) ),
inference(extension,[status(thm),parent(t4:2)],[f_2_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ sP1
| equal_set(sK5,empty_set) ),
inference(extension,[status(thm),parent(t6:2)],[f_12_11]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
$false,
inference(reduction,[status(thm),parent(t8:2)],[t8:2,t2:2]) ).
cnf(l1,lemma,
sP0,
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t11,plain,
( ~ subset(empty_set,sK4)
| ~ subset(sK4,empty_set)
| equal_set(sK4,empty_set) ),
inference(extension,[status(thm),parent(t1:2)],[f_2_6]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t1:2]) ).
cnf(t13,plain,
( ~ sP0
| subset(sK4,empty_set) ),
inference(extension,[status(thm),parent(t11:2)],[f_12_9]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t11:2]) ).
cnf(t15,plain,
sP0,
inference(lemma_extension,[status(thm),parent(t13:2)],[l1:1]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
( member(sK1(empty_set,sK4),empty_set)
| subset(empty_set,sK4) ),
inference(extension,[status(thm),parent(t11:3)],[f_1_6]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t11:3]) ).
cnf(t19,plain,
~ member(sK1(empty_set,sK4),empty_set),
inference(extension,[status(thm),parent(t17:2)],[f_6_3]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t17:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET691+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 19 22:47:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 7.05/7.31 % SZS status Theorem for theBenchmark
% 7.05/7.31 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------