%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET162+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 : n003.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 08:56:29 AM UTC 2026
% Result : Theorem 76.15s 76.42s
% Output : Proof 76.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 22 unt; 0 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 124 ( 52 ~; 47 |; 21 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 2 sgn 49 !; 5 ?)
% 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(union,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('SET006+0.ax',union) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set),
file('SET006+0.ax',empty_set) ).
fof(thI18,conjecture,
! [A] : equal_set(union(A,empty_set),A),
file('theBenchmark.p',thI18) ).
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]) ).
cnf(f_1_7,plain,
( ~ member(sK1(U_7,U_5),U_5)
| 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_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_5_1,plain,
! [X,A,B] :
( ( member(X,union(A,B))
| ( ~ member(X,B)
& ~ member(X,A) ) )
& ( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(fof_nnf,[status(thm)],[union]) ).
fof(f_5_2,plain,
! [U_31,U_30,U_29] :
( ( member(U_31,union(U_30,U_29))
| ( ~ member(U_31,U_29)
& ~ member(U_31,U_30) ) )
& ( member(U_31,U_29)
| member(U_31,U_30)
| ~ member(U_31,union(U_30,U_29)) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_37,U_35,U_33] :
( member(U_37,union(U_35,U_33))
| ( ~ member(U_37,U_33)
& ~ member(U_37,U_35) ) )
& ! [U_36,U_34,U_32] :
( member(U_36,U_32)
| member(U_36,U_34)
| ~ member(U_36,union(U_34,U_32)) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( member(U_36,U_32)
| member(U_36,U_34)
| ~ member(U_36,union(U_34,U_32)) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( ~ member(U_37,U_35)
| member(U_37,union(U_35,U_33)) ),
inference(clausify,[status(thm)],[f_5_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] : equal_set(union(A,empty_set),A),
inference(negate,[status(cth)],[thI18]) ).
fof(f_12_2,negated_conjecture,
? [A] : ~ equal_set(union(A,empty_set),A),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_79] : ~ equal_set(union(U_79,empty_set),U_79),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
~ equal_set(union(sK4,empty_set),sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_79,sK4)],[f_12_3]) ).
cnf(f_12_5,negated_conjecture,
~ equal_set(union(sK4,empty_set),sK4),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(t1,plain,
~ equal_set(union(sK4,empty_set),sK4),
inference(start,[status(thm),parent(0:0)],[f_12_5]) ).
cnf(t2,plain,
( ~ subset(sK4,union(sK4,empty_set))
| ~ subset(union(sK4,empty_set),sK4)
| equal_set(union(sK4,empty_set),sK4) ),
inference(extension,[status(thm),parent(t1:1)],[f_2_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ member(sK1(union(sK4,empty_set),sK4),sK4)
| subset(union(sK4,empty_set),sK4) ),
inference(extension,[status(thm),parent(t2:2)],[f_1_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( member(sK1(union(sK4,empty_set),sK4),empty_set)
| ~ member(sK1(union(sK4,empty_set),sK4),union(sK4,empty_set))
| member(sK1(union(sK4,empty_set),sK4),sK4) ),
inference(extension,[status(thm),parent(t4:2)],[f_5_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( subset(union(sK4,empty_set),sK4)
| member(sK1(union(sK4,empty_set),sK4),union(sK4,empty_set)) ),
inference(extension,[status(thm),parent(t6:2)],[f_1_6]) ).
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(t11,plain,
~ member(sK1(union(sK4,empty_set),sK4),empty_set),
inference(extension,[status(thm),parent(t6:3)],[f_6_3]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t6:3]) ).
cnf(t13,plain,
( ~ member(sK1(sK4,union(sK4,empty_set)),union(sK4,empty_set))
| subset(sK4,union(sK4,empty_set)) ),
inference(extension,[status(thm),parent(t2:3)],[f_1_7]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t2:3]) ).
cnf(t15,plain,
( ~ member(sK1(sK4,union(sK4,empty_set)),sK4)
| member(sK1(sK4,union(sK4,empty_set)),union(sK4,empty_set)) ),
inference(extension,[status(thm),parent(t13:2)],[f_5_5]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
( subset(sK4,union(sK4,empty_set))
| member(sK1(sK4,union(sK4,empty_set)),sK4) ),
inference(extension,[status(thm),parent(t15:2)],[f_1_6]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t15:2]) ).
cnf(t19,plain,
$false,
inference(reduction,[status(thm),parent(t17:2)],[t17:2,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET162+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 21:54:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 76.15/76.42 % SZS status Theorem for theBenchmark
% 76.15/76.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------