%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET012+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 08:55:53 AM UTC 2026
% Result : Theorem 88.45s 88.96s
% Output : Proof 88.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 59 ( 21 unt; 0 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 148 ( 60 ~; 56 |; 26 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 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 : 74 ( 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(difference,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
file('SET006+0.ax',difference) ).
fof(thI23,conjecture,
! [A,E] :
( subset(A,E)
=> equal_set(difference(E,difference(E,A)),A) ),
file('theBenchmark.p',thI23) ).
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_5,plain,
( member(U_0,U_4)
| ~ member(U_0,U_6)
| ~ subset(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_4]) ).
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_7_1,plain,
! [B,A,E] :
( ( member(B,difference(E,A))
| member(B,A)
| ~ member(B,E) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(fof_nnf,[status(thm)],[difference]) ).
fof(f_7_2,plain,
! [U_41,U_40,U_39] :
( ( member(U_41,difference(U_39,U_40))
| member(U_41,U_40)
| ~ member(U_41,U_39) )
& ( ( ~ member(U_41,U_40)
& member(U_41,U_39) )
| ~ member(U_41,difference(U_39,U_40)) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_47,U_45,U_43] :
( member(U_47,difference(U_43,U_45))
| member(U_47,U_45)
| ~ member(U_47,U_43) )
& ! [U_46,U_44,U_42] :
( ( ~ member(U_46,U_44)
& member(U_46,U_42) )
| ~ member(U_46,difference(U_42,U_44)) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( member(U_46,U_42)
| ~ member(U_46,difference(U_42,U_44)) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( ~ member(U_46,U_44)
| ~ member(U_46,difference(U_42,U_44)) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( member(U_47,difference(U_43,U_45))
| member(U_47,U_45)
| ~ member(U_47,U_43) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_12_1,negated_conjecture,
~ ! [A,E] :
( subset(A,E)
=> equal_set(difference(E,difference(E,A)),A) ),
inference(negate,[status(cth)],[thI23]) ).
fof(f_12_2,negated_conjecture,
? [A,E] :
( ~ equal_set(difference(E,difference(E,A)),A)
& subset(A,E) ),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_80,U_79] :
( ~ equal_set(difference(U_79,difference(U_79,U_80)),U_80)
& subset(U_80,U_79) ),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
? [U_79] :
( ~ equal_set(difference(U_79,difference(U_79,sK4)),sK4)
& subset(sK4,U_79) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_80,sK4)],[f_12_3]) ).
fof(f_12_5,negated_conjecture,
( ~ equal_set(difference(sK5,difference(sK5,sK4)),sK4)
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_79,sK5)],[f_12_4]) ).
cnf(f_12_6,negated_conjecture,
subset(sK4,sK5),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_7,negated_conjecture,
~ equal_set(difference(sK5,difference(sK5,sK4)),sK4),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(t1,plain,
~ equal_set(difference(sK5,difference(sK5,sK4)),sK4),
inference(start,[status(thm),parent(0:0)],[f_12_7]) ).
cnf(t2,plain,
( ~ subset(sK4,difference(sK5,difference(sK5,sK4)))
| ~ subset(difference(sK5,difference(sK5,sK4)),sK4)
| equal_set(difference(sK5,difference(sK5,sK4)),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(difference(sK5,difference(sK5,sK4)),sK4),difference(sK5,difference(sK5,sK4)))
| subset(difference(sK5,difference(sK5,sK4)),sK4) ),
inference(extension,[status(thm),parent(t2:2)],[f_1_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ member(sK1(difference(sK5,difference(sK5,sK4)),sK4),difference(sK5,sK4))
| ~ member(sK1(difference(sK5,difference(sK5,sK4)),sK4),difference(sK5,difference(sK5,sK4))) ),
inference(extension,[status(thm),parent(t4:2)],[f_7_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( member(sK1(difference(sK5,difference(sK5,sK4)),sK4),sK4)
| ~ member(sK1(difference(sK5,difference(sK5,sK4)),sK4),sK5)
| member(sK1(difference(sK5,difference(sK5,sK4)),sK4),difference(sK5,sK4)) ),
inference(extension,[status(thm),parent(t6:2)],[f_7_6]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ member(sK1(difference(sK5,difference(sK5,sK4)),sK4),difference(sK5,difference(sK5,sK4)))
| member(sK1(difference(sK5,difference(sK5,sK4)),sK4),sK5) ),
inference(extension,[status(thm),parent(t8:2)],[f_7_4]) ).
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,t4:2]) ).
cnf(t13,plain,
( subset(difference(sK5,difference(sK5,sK4)),sK4)
| ~ member(sK1(difference(sK5,difference(sK5,sK4)),sK4),sK4) ),
inference(extension,[status(thm),parent(t8:3)],[f_1_7]) ).
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,t2:2]) ).
cnf(t16,plain,
( ~ member(sK1(sK4,difference(sK5,difference(sK5,sK4))),difference(sK5,difference(sK5,sK4)))
| subset(sK4,difference(sK5,difference(sK5,sK4))) ),
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(sK4,difference(sK5,difference(sK5,sK4))),difference(sK5,sK4))
| ~ member(sK1(sK4,difference(sK5,difference(sK5,sK4))),sK5)
| member(sK1(sK4,difference(sK5,difference(sK5,sK4))),difference(sK5,difference(sK5,sK4))) ),
inference(extension,[status(thm),parent(t16:2)],[f_7_6]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( ~ member(sK1(sK4,difference(sK5,difference(sK5,sK4))),sK4)
| ~ subset(sK4,sK5)
| member(sK1(sK4,difference(sK5,difference(sK5,sK4))),sK5) ),
inference(extension,[status(thm),parent(t18:2)],[f_1_5]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
subset(sK4,sK5),
inference(extension,[status(thm),parent(t20:2)],[f_12_6]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( subset(sK4,difference(sK5,difference(sK5,sK4)))
| member(sK1(sK4,difference(sK5,difference(sK5,sK4))),sK4) ),
inference(extension,[status(thm),parent(t20:3)],[f_1_6]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
$false,
inference(reduction,[status(thm),parent(t24:2)],[t24:2,t2:3]) ).
cnf(t27,plain,
( ~ member(sK1(sK4,difference(sK5,difference(sK5,sK4))),sK4)
| ~ member(sK1(sK4,difference(sK5,difference(sK5,sK4))),difference(sK5,sK4)) ),
inference(extension,[status(thm),parent(t18:3)],[f_7_5]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t18:3]) ).
cnf(t29,plain,
( subset(sK4,difference(sK5,difference(sK5,sK4)))
| member(sK1(sK4,difference(sK5,difference(sK5,sK4))),sK4) ),
inference(extension,[status(thm),parent(t27:2)],[f_1_6]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t27:2]) ).
cnf(t31,plain,
$false,
inference(reduction,[status(thm),parent(t29:2)],[t29:2,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET012+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n019.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Sat Sep 19 21:26:22 UTC 2026
% 0.08/0.56 % CPUTime :
% 88.45/88.96 % SZS status Theorem for theBenchmark
% 88.45/88.96 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------