%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET696+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 : n015.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 91.93s 92.24s
% Output : Proof 91.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 20 unt; 0 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 173 ( 72 ~; 61 |; 33 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 7 sgn 66 !; 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(intersection,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,B)
& member(X,A) ) ),
file('SET006+0.ax',intersection) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set),
file('SET006+0.ax',empty_set) ).
fof(difference,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
file('SET006+0.ax',difference) ).
fof(thI28,conjecture,
! [A,E] :
( subset(A,E)
=> equal_set(intersection(difference(E,A),A),empty_set) ),
file('theBenchmark.p',thI28) ).
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_4_1,plain,
! [X,A,B] :
( ( member(X,intersection(A,B))
| ~ member(X,B)
| ~ member(X,A) )
& ( ( member(X,B)
& member(X,A) )
| ~ member(X,intersection(A,B)) ) ),
inference(fof_nnf,[status(thm)],[intersection]) ).
fof(f_4_2,plain,
! [U_22,U_21,U_20] :
( ( member(U_22,intersection(U_21,U_20))
| ~ member(U_22,U_20)
| ~ member(U_22,U_21) )
& ( ( member(U_22,U_20)
& member(U_22,U_21) )
| ~ member(U_22,intersection(U_21,U_20)) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_28,U_26,U_24] :
( member(U_28,intersection(U_26,U_24))
| ~ member(U_28,U_24)
| ~ member(U_28,U_26) )
& ! [U_27,U_25,U_23] :
( ( member(U_27,U_23)
& member(U_27,U_25) )
| ~ member(U_27,intersection(U_25,U_23)) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( member(U_27,U_25)
| ~ member(U_27,intersection(U_25,U_23)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( member(U_27,U_23)
| ~ member(U_27,intersection(U_25,U_23)) ),
inference(clausify,[status(thm)],[f_4_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_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]) ).
fof(f_12_1,negated_conjecture,
~ ! [A,E] :
( subset(A,E)
=> equal_set(intersection(difference(E,A),A),empty_set) ),
inference(negate,[status(cth)],[thI28]) ).
fof(f_12_2,negated_conjecture,
? [A,E] :
( ~ equal_set(intersection(difference(E,A),A),empty_set)
& subset(A,E) ),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_80,U_79] :
( ~ equal_set(intersection(difference(U_79,U_80),U_80),empty_set)
& subset(U_80,U_79) ),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
? [U_79] :
( ~ equal_set(intersection(difference(U_79,sK4),sK4),empty_set)
& 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(intersection(difference(sK5,sK4),sK4),empty_set)
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_79,sK5)],[f_12_4]) ).
cnf(f_12_7,negated_conjecture,
~ equal_set(intersection(difference(sK5,sK4),sK4),empty_set),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(t1,plain,
~ equal_set(intersection(difference(sK5,sK4),sK4),empty_set),
inference(start,[status(thm),parent(0:0)],[f_12_7]) ).
cnf(t2,plain,
( ~ subset(empty_set,intersection(difference(sK5,sK4),sK4))
| ~ subset(intersection(difference(sK5,sK4),sK4),empty_set)
| equal_set(intersection(difference(sK5,sK4),sK4),empty_set) ),
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(intersection(difference(sK5,sK4),sK4),empty_set),intersection(difference(sK5,sK4),sK4))
| subset(intersection(difference(sK5,sK4),sK4),empty_set) ),
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(intersection(difference(sK5,sK4),sK4),empty_set),sK4)
| ~ member(sK1(intersection(difference(sK5,sK4),sK4),empty_set),intersection(difference(sK5,sK4),sK4)) ),
inference(extension,[status(thm),parent(t4:2)],[f_4_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ member(sK1(intersection(difference(sK5,sK4),sK4),empty_set),difference(sK5,sK4))
| ~ member(sK1(intersection(difference(sK5,sK4),sK4),empty_set),sK4) ),
inference(extension,[status(thm),parent(t6:2)],[f_7_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ member(sK1(intersection(difference(sK5,sK4),sK4),empty_set),intersection(difference(sK5,sK4),sK4))
| member(sK1(intersection(difference(sK5,sK4),sK4),empty_set),difference(sK5,sK4)) ),
inference(extension,[status(thm),parent(t8:2)],[f_4_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,
( ~ member(sK1(empty_set,intersection(difference(sK5,sK4),sK4)),intersection(difference(sK5,sK4),sK4))
| subset(empty_set,intersection(difference(sK5,sK4),sK4)) ),
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(empty_set,intersection(difference(sK5,sK4),sK4)),difference(intersection(difference(sK5,sK4),sK4),U_740))
| member(sK1(empty_set,intersection(difference(sK5,sK4),sK4)),intersection(difference(sK5,sK4),sK4)) ),
inference(extension,[status(thm),parent(t13:2)],[f_7_4]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
( ~ member(sK1(empty_set,intersection(difference(sK5,sK4),sK4)),empty_set)
| ~ subset(empty_set,difference(intersection(difference(sK5,sK4),sK4),U_740))
| member(sK1(empty_set,intersection(difference(sK5,sK4),sK4)),difference(intersection(difference(sK5,sK4),sK4),U_740)) ),
inference(extension,[status(thm),parent(t15:2)],[f_1_5]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t15:2]) ).
cnf(t19,plain,
( member(sK1(empty_set,difference(intersection(difference(sK5,sK4),sK4),U_740)),empty_set)
| subset(empty_set,difference(intersection(difference(sK5,sK4),sK4),U_740)) ),
inference(extension,[status(thm),parent(t17:2)],[f_1_6]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t17:2]) ).
cnf(t21,plain,
~ member(sK1(empty_set,difference(intersection(difference(sK5,sK4),sK4),U_740)),empty_set),
inference(extension,[status(thm),parent(t19:2)],[f_6_3]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(t23,plain,
( subset(empty_set,intersection(difference(sK5,sK4),sK4))
| member(sK1(empty_set,intersection(difference(sK5,sK4),sK4)),empty_set) ),
inference(extension,[status(thm),parent(t17:3)],[f_1_6]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t17:3]) ).
cnf(t25,plain,
$false,
inference(reduction,[status(thm),parent(t23:2)],[t23:2,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET696+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
% 0.09/0.38 % Computer : n015.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sat Sep 19 22:51:52 UTC 2026
% 0.09/0.39 % CPUTime :
% 91.93/92.24 % SZS status Theorem for theBenchmark
% 91.93/92.24 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------