%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET015+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 : n014.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 08:55:55 AM UTC 2026
% Result : Theorem 85.89s 86.19s
% Output : Proof 85.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 53 ( 23 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 131 ( 53 ~; 53 |; 21 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 71 ( 2 sgn 48 !; 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(union,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('SET006+0.ax',union) ).
fof(thI07,conjecture,
! [A,B] : equal_set(union(A,B),union(B,A)),
file('theBenchmark.p',thI07) ).
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]) ).
cnf(f_5_6,plain,
( ~ member(U_37,U_33)
| member(U_37,union(U_35,U_33)) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_12_1,negated_conjecture,
~ ! [A,B] : equal_set(union(A,B),union(B,A)),
inference(negate,[status(cth)],[thI07]) ).
fof(f_12_2,negated_conjecture,
? [A,B] : ~ equal_set(union(A,B),union(B,A)),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_80,U_79] : ~ equal_set(union(U_80,U_79),union(U_79,U_80)),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
? [U_79] : ~ equal_set(union(sK4,U_79),union(U_79,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_80,sK4)],[f_12_3]) ).
fof(f_12_5,negated_conjecture,
~ equal_set(union(sK4,sK5),union(sK5,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_79,sK5)],[f_12_4]) ).
cnf(f_12_6,negated_conjecture,
~ equal_set(union(sK4,sK5),union(sK5,sK4)),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(t1,plain,
~ equal_set(union(sK4,sK5),union(sK5,sK4)),
inference(start,[status(thm),parent(0:0)],[f_12_6]) ).
cnf(t2,plain,
( ~ subset(union(sK5,sK4),union(sK4,sK5))
| ~ subset(union(sK4,sK5),union(sK5,sK4))
| equal_set(union(sK4,sK5),union(sK5,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,sK5),union(sK5,sK4)),union(sK5,sK4))
| subset(union(sK4,sK5),union(sK5,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,sK5),union(sK5,sK4)),sK4)
| member(sK1(union(sK4,sK5),union(sK5,sK4)),union(sK5,sK4)) ),
inference(extension,[status(thm),parent(t4:2)],[f_5_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( member(sK1(union(sK4,sK5),union(sK5,sK4)),sK5)
| ~ member(sK1(union(sK4,sK5),union(sK5,sK4)),union(sK4,sK5))
| member(sK1(union(sK4,sK5),union(sK5,sK4)),sK4) ),
inference(extension,[status(thm),parent(t6:2)],[f_5_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( subset(union(sK4,sK5),union(sK5,sK4))
| member(sK1(union(sK4,sK5),union(sK5,sK4)),union(sK4,sK5)) ),
inference(extension,[status(thm),parent(t8:2)],[f_1_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
$false,
inference(reduction,[status(thm),parent(t10:2)],[t10:2,t2:2]) ).
cnf(t13,plain,
( member(sK1(union(sK4,sK5),union(sK5,sK4)),union(sK5,sK4))
| ~ member(sK1(union(sK4,sK5),union(sK5,sK4)),sK5) ),
inference(extension,[status(thm),parent(t8:3)],[f_5_5]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t8:3]) ).
cnf(t15,plain,
$false,
inference(reduction,[status(thm),parent(t13:2)],[t13:2,t4:2]) ).
cnf(t16,plain,
( ~ member(sK1(union(sK5,sK4),union(sK4,sK5)),union(sK4,sK5))
| subset(union(sK5,sK4),union(sK4,sK5)) ),
inference(extension,[status(thm),parent(t2:3)],[f_1_7]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:3]) ).
cnf(t18,plain,
( ~ member(sK1(union(sK5,sK4),union(sK4,sK5)),sK5)
| member(sK1(union(sK5,sK4),union(sK4,sK5)),union(sK4,sK5)) ),
inference(extension,[status(thm),parent(t16:2)],[f_5_6]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( member(sK1(union(sK5,sK4),union(sK4,sK5)),sK4)
| ~ member(sK1(union(sK5,sK4),union(sK4,sK5)),union(sK5,sK4))
| member(sK1(union(sK5,sK4),union(sK4,sK5)),sK5) ),
inference(extension,[status(thm),parent(t18:2)],[f_5_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( subset(union(sK5,sK4),union(sK4,sK5))
| member(sK1(union(sK5,sK4),union(sK4,sK5)),union(sK5,sK4)) ),
inference(extension,[status(thm),parent(t20:2)],[f_1_6]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
$false,
inference(reduction,[status(thm),parent(t22:2)],[t22:2,t2:3]) ).
cnf(t25,plain,
( member(sK1(union(sK5,sK4),union(sK4,sK5)),union(sK4,sK5))
| ~ member(sK1(union(sK5,sK4),union(sK4,sK5)),sK4) ),
inference(extension,[status(thm),parent(t20:3)],[f_5_5]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t20:3]) ).
cnf(t27,plain,
$false,
inference(reduction,[status(thm),parent(t25:2)],[t25:2,t16:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET015+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
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 19 21:26:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 85.89/86.19 % SZS status Theorem for theBenchmark
% 85.89/86.19 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------