%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU186+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n016.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 08:58:23 AM UTC 2026
% Result : Theorem 0.13s 5.91s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 27 unt; 0 def)
% Number of atoms : 136 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 139 ( 63 ~; 47 |; 22 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 97 ( 3 sgn 65 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_relat_1,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('theBenchmark.p',d1_relat_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t56_relat_1,conjecture,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('theBenchmark.p',t56_relat_1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(f_4_1,plain,
! [A] :
( ( relation(A)
| ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) )
& ( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(fof_nnf,[status(thm)],[d1_relat_1]) ).
fof(f_4_2,plain,
! [U_11] :
( ( relation(U_11)
| ? [U_10] :
( ! [U_9,U_8] : U_10 != ordered_pair(U_9,U_8)
& in(U_10,U_11) ) )
& ( ! [U_7] :
( ? [U_6,U_5] : U_7 = ordered_pair(U_6,U_5)
| ~ in(U_7,U_11) )
| ~ relation(U_11) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_13] :
( relation(U_13)
| ? [U_10] :
( ! [U_9,U_8] : U_10 != ordered_pair(U_9,U_8)
& in(U_10,U_13) ) )
& ! [U_12] :
( ! [U_7] :
( ? [U_6,U_5] : U_7 = ordered_pair(U_6,U_5)
| ~ in(U_7,U_12) )
| ~ relation(U_12) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_13] :
( relation(U_13)
| ? [U_10] :
( ! [U_9,U_8] : U_10 != ordered_pair(U_9,U_8)
& in(U_10,U_13) ) )
& ! [U_12] :
( ! [U_7] :
( ? [U_5] : U_7 = ordered_pair(sK1(U_12,U_7),U_5)
| ~ in(U_7,U_12) )
| ~ relation(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_6,sK1(U_12,U_7))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_13] :
( relation(U_13)
| ? [U_10] :
( ! [U_9,U_8] : U_10 != ordered_pair(U_9,U_8)
& in(U_10,U_13) ) )
& ! [U_12] :
( ! [U_7] :
( U_7 = ordered_pair(sK1(U_12,U_7),sK2(U_12,U_7))
| ~ in(U_7,U_12) )
| ~ relation(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_5,sK2(U_12,U_7))],[f_4_4]) ).
fof(f_4_6,plain,
( ! [U_13] :
( relation(U_13)
| ( ! [U_9,U_8] : sK3(U_13) != ordered_pair(U_9,U_8)
& in(sK3(U_13),U_13) ) )
& ! [U_12] :
( ! [U_7] :
( U_7 = ordered_pair(sK1(U_12,U_7),sK2(U_12,U_7))
| ~ in(U_7,U_12) )
| ~ relation(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_10,sK3(U_13))],[f_4_5]) ).
cnf(f_4_7,plain,
( U_7 = ordered_pair(sK1(U_12,U_7),sK2(U_12,U_7))
| ~ in(U_7,U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_4_6]) ).
fof(f_11_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_11_2,plain,
! [U_17] :
? [U_16] : element(U_16,U_17),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_17] : element(sK4(U_17),U_17),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_16,sK4(U_17))],[f_11_2]) ).
cnf(f_11_4,plain,
element(sK4(U_17),U_17),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_22_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_22_2,plain,
! [U_30,U_29] :
( in(U_30,U_29)
| empty(U_29)
| ~ element(U_30,U_29) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( in(U_30,U_29)
| empty(U_29)
| ~ element(U_30,U_29) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
inference(negate,[status(cth)],[t56_relat_1]) ).
fof(f_23_2,negated_conjecture,
? [A] :
( A != empty_set
& ! [B,C] : ~ in(ordered_pair(B,C),A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_23_1]) ).
fof(f_23_3,negated_conjecture,
? [U_33] :
( U_33 != empty_set
& ! [U_32,U_31] : ~ in(ordered_pair(U_32,U_31),U_33)
& relation(U_33) ),
inference(variable_rename,[status(thm)],[f_23_2]) ).
fof(f_23_4,negated_conjecture,
( sK9 != empty_set
& ! [U_32,U_31] : ~ in(ordered_pair(U_32,U_31),sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_33,sK9)],[f_23_3]) ).
fof(f_23_5,negated_conjecture,
( sK9 != empty_set
& ! [U_31,U_32] : ~ in(ordered_pair(U_32,U_31),sK9)
& relation(sK9) ),
inference(definitional_conversion,[status(esa)],[f_23_4]) ).
cnf(f_23_6,negated_conjecture,
relation(sK9),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_7,negated_conjecture,
~ in(ordered_pair(U_32,U_31),sK9),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_8,negated_conjecture,
sK9 != empty_set,
inference(clausify,[status(thm)],[f_23_5]) ).
fof(f_24_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_24_2,plain,
! [U_34] :
( U_34 = empty_set
| ~ empty(U_34) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( U_34 = empty_set
| ~ empty(U_34) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_25_2,plain,
! [U_36,U_35] :
( ~ empty(U_35)
| ~ in(U_36,U_35) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( ~ empty(U_35)
| ~ in(U_36,U_35) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_11,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
( ~ empty(sK9)
| ~ in(sK4(sK9),sK9) ),
inference(start,[status(thm),parent(0:0)],[f_25_3]) ).
cnf(t2,plain,
( empty(sK9)
| ~ element(sK4(sK9),sK9)
| in(sK4(sK9),sK9) ),
inference(extension,[status(thm),parent(t1:1)],[f_22_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
element(sK4(sK9),sK9),
inference(extension,[status(thm),parent(t2:2)],[f_11_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( sK9 = empty_set
| ~ empty(sK9) ),
inference(extension,[status(thm),parent(t2:3)],[f_24_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
sK9 != empty_set,
inference(extension,[status(thm),parent(t6:2)],[f_23_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( in(sK4(sK9),sK9)
| ~ element(sK4(sK9),sK9)
| empty(sK9) ),
inference(extension,[status(thm),parent(t1:2)],[f_22_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:2]) ).
cnf(t12,plain,
element(sK4(sK9),sK9),
inference(extension,[status(thm),parent(t10:2)],[f_11_4]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( sK4(sK9) = ordered_pair(sK1(sK9,sK4(sK9)),sK2(sK9,sK4(sK9)))
| ~ relation(sK9)
| ~ in(sK4(sK9),sK9) ),
inference(extension,[status(thm),parent(t10:3)],[f_4_7]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
relation(sK9),
inference(extension,[status(thm),parent(t14:2)],[f_23_6]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( sK9 != sK9
| ~ in(sK4(sK9),sK9)
| in(ordered_pair(sK1(sK9,sK4(sK9)),sK2(sK9,sK4(sK9))),sK9)
| sK4(sK9) != ordered_pair(sK1(sK9,sK4(sK9)),sK2(sK9,sK4(sK9))) ),
inference(extension,[status(thm),parent(t14:3)],[equality_11]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
~ in(ordered_pair(sK1(sK9,sK4(sK9)),sK2(sK9,sK4(sK9))),sK9),
inference(extension,[status(thm),parent(t18:2)],[f_23_7]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
$false,
inference(reduction,[status(thm),parent(t18:3)],[t18:3,t10:3]) ).
cnf(t23,plain,
sK9 = sK9,
inference(extension,[status(thm),parent(t18:4)],[equality_1]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t18:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU186+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.09/5.57 % Computer : n016.cluster.edu
% 0.09/5.57 % Model : x86_64 x86_64
% 0.09/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57 % Memory : 8046.5625MB
% 0.09/5.57 % OS : Linux 6.8.0-71-generic
% 0.09/5.57 % CPULimit : 300
% 0.09/5.57 % WCLimit : 300
% 0.09/5.57 % DateTime : Sat Sep 19 23:32:13 UTC 2026
% 0.09/5.57 % CPUTime :
% 0.13/5.91 % SZS status Theorem for theBenchmark
% 0.13/5.91 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------