%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET893+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n002.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 08:57:45 AM UTC 2026
% Result : Theorem 30.33s 30.66s
% Output : Proof 30.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 96 ( 34 unt; 0 def)
% Number of atoms : 303 ( 120 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 347 ( 140 ~; 125 |; 77 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 181 ( 16 sgn 93 !; 49 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(l55_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',l55_zfmisc_1) ).
fof(t34_zfmisc_1,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D)))
<=> ( B = D
& A = C ) ),
file('theBenchmark.p',t34_zfmisc_1) ).
fof(f_3_1,plain,
! [A,B] :
( ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
& C = A )
| ( C != A
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| C != A )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_3_2,plain,
! [U_7,U_6] :
( ( U_6 = singleton(U_7)
| ? [U_5] :
( ( ~ in(U_5,U_6)
& U_5 = U_7 )
| ( U_5 != U_7
& in(U_5,U_6) ) ) )
& ( ! [U_4] :
( ( in(U_4,U_6)
| U_4 != U_7 )
& ( U_4 = U_7
| ~ in(U_4,U_6) ) )
| U_6 != singleton(U_7) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& U_11 = U_15 )
| ? [U_10] :
( U_10 != U_15
& in(U_10,U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(U_14) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& U_11 = U_15 )
| ( sK1(U_15,U_13) != U_15
& in(sK1(U_15,U_13),U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_15,U_13))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ( ~ in(sK2(U_15,U_13),U_13)
& sK2(U_15,U_13) = U_15 )
| ( sK1(U_15,U_13) != U_15
& in(sK1(U_15,U_13),U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_11,sK2(U_15,U_13))],[f_3_4]) ).
fof(f_3_6,plain,
( ! [U_13,U_15] :
( ~ in(sK2(U_15,U_13),U_13)
| ~ sP2(U_13,U_15) )
& ! [U_13,U_15] :
( sK2(U_15,U_13) = U_15
| ~ sP2(U_13,U_15) )
& ! [U_13,U_15] :
( sK1(U_15,U_13) != U_15
| ~ sP1(U_13,U_15) )
& ! [U_13,U_15] :
( in(sK1(U_15,U_13),U_13)
| ~ sP1(U_13,U_15) )
& ! [U_8,U_9,U_14,U_12] :
( in(U_9,U_12)
| U_9 != U_14
| ~ sP0(U_8,U_9,U_14,U_12) )
& ! [U_8,U_9,U_14,U_12] :
( U_8 = U_14
| ~ in(U_8,U_12)
| ~ sP0(U_8,U_9,U_14,U_12) )
& ! [U_13,U_15] :
( U_13 = singleton(U_15)
| sP2(U_13,U_15)
| sP1(U_13,U_15) )
& ! [U_8,U_9,U_14,U_12] :
( sP0(U_8,U_9,U_14,U_12)
| U_12 != singleton(U_14) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2])],[f_3_5]) ).
cnf(f_3_7,plain,
( sP0(U_8,U_9,U_14,U_12)
| U_12 != singleton(U_14) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_9,plain,
( U_8 = U_14
| ~ in(U_8,U_12)
| ~ sP0(U_8,U_9,U_14,U_12) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_10,plain,
( in(U_9,U_12)
| U_9 != U_14
| ~ sP0(U_8,U_9,U_14,U_12) ),
inference(clausify,[status(thm)],[f_3_6]) ).
fof(f_6_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(B,D)
| ~ in(A,C) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[l55_zfmisc_1]) ).
fof(f_6_2,plain,
! [U_23,U_22,U_21,U_20] :
( ( in(ordered_pair(U_23,U_22),cartesian_product2(U_21,U_20))
| ~ in(U_22,U_20)
| ~ in(U_23,U_21) )
& ( ( in(U_22,U_20)
& in(U_23,U_21) )
| ~ in(ordered_pair(U_23,U_22),cartesian_product2(U_21,U_20)) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_31,U_29,U_27,U_25] :
( in(ordered_pair(U_31,U_29),cartesian_product2(U_27,U_25))
| ~ in(U_29,U_25)
| ~ in(U_31,U_27) )
& ! [U_30,U_28,U_26,U_24] :
( ( in(U_28,U_24)
& in(U_30,U_26) )
| ~ in(ordered_pair(U_30,U_28),cartesian_product2(U_26,U_24)) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_28,U_24,U_30,U_26] :
( in(U_28,U_24)
| ~ sP3(U_28,U_24,U_30,U_26) )
& ! [U_28,U_24,U_30,U_26] :
( in(U_30,U_26)
| ~ sP3(U_28,U_24,U_30,U_26) )
& ! [U_29,U_27,U_31,U_25] :
( in(ordered_pair(U_31,U_29),cartesian_product2(U_27,U_25))
| ~ in(U_29,U_25)
| ~ in(U_31,U_27) )
& ! [U_28,U_24,U_30,U_26] :
( sP3(U_28,U_24,U_30,U_26)
| ~ in(ordered_pair(U_30,U_28),cartesian_product2(U_26,U_24)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_6_3]) ).
cnf(f_6_5,plain,
( sP3(U_28,U_24,U_30,U_26)
| ~ in(ordered_pair(U_30,U_28),cartesian_product2(U_26,U_24)) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( in(ordered_pair(U_31,U_29),cartesian_product2(U_27,U_25))
| ~ in(U_29,U_25)
| ~ in(U_31,U_27) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_7,plain,
( in(U_30,U_26)
| ~ sP3(U_28,U_24,U_30,U_26) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_8,plain,
( in(U_28,U_24)
| ~ sP3(U_28,U_24,U_30,U_26) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_9_1,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D)))
<=> ( B = D
& A = C ) ),
inference(negate,[status(cth)],[t34_zfmisc_1]) ).
fof(f_9_2,negated_conjecture,
? [A,B,C,D] :
( ( ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D)))
& B = D
& A = C )
| ( ( B != D
| A != C )
& in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D))) ) ),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_37,U_36,U_35,U_34] :
( ( ~ in(ordered_pair(U_37,U_36),cartesian_product2(singleton(U_35),singleton(U_34)))
& U_36 = U_34
& U_37 = U_35 )
| ( ( U_36 != U_34
| U_37 != U_35 )
& in(ordered_pair(U_37,U_36),cartesian_product2(singleton(U_35),singleton(U_34))) ) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
( ? [U_45,U_43,U_41,U_39] :
( ~ in(ordered_pair(U_45,U_43),cartesian_product2(singleton(U_41),singleton(U_39)))
& U_43 = U_39
& U_45 = U_41 )
| ? [U_44,U_42,U_40,U_38] :
( ( U_42 != U_38
| U_44 != U_40 )
& in(ordered_pair(U_44,U_42),cartesian_product2(singleton(U_40),singleton(U_38))) ) ),
inference(miniscope,[status(thm)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
( ? [U_45,U_43,U_41,U_39] :
( ~ in(ordered_pair(U_45,U_43),cartesian_product2(singleton(U_41),singleton(U_39)))
& U_43 = U_39
& U_45 = U_41 )
| ? [U_42,U_40,U_38] :
( ( U_42 != U_38
| sK5 != U_40 )
& in(ordered_pair(sK5,U_42),cartesian_product2(singleton(U_40),singleton(U_38))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_44,sK5)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( ? [U_45,U_43,U_41,U_39] :
( ~ in(ordered_pair(U_45,U_43),cartesian_product2(singleton(U_41),singleton(U_39)))
& U_43 = U_39
& U_45 = U_41 )
| ? [U_40,U_38] :
( ( sK6 != U_38
| sK5 != U_40 )
& in(ordered_pair(sK5,sK6),cartesian_product2(singleton(U_40),singleton(U_38))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_42,sK6)],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( ? [U_45,U_43,U_41,U_39] :
( ~ in(ordered_pair(U_45,U_43),cartesian_product2(singleton(U_41),singleton(U_39)))
& U_43 = U_39
& U_45 = U_41 )
| ? [U_38] :
( ( sK6 != U_38
| sK5 != sK7 )
& in(ordered_pair(sK5,sK6),cartesian_product2(singleton(sK7),singleton(U_38))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_40,sK7)],[f_9_6]) ).
fof(f_9_8,negated_conjecture,
( ? [U_45,U_43,U_41,U_39] :
( ~ in(ordered_pair(U_45,U_43),cartesian_product2(singleton(U_41),singleton(U_39)))
& U_43 = U_39
& U_45 = U_41 )
| ( ( sK6 != sK8
| sK5 != sK7 )
& in(ordered_pair(sK5,sK6),cartesian_product2(singleton(sK7),singleton(sK8))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_38,sK8)],[f_9_7]) ).
fof(f_9_9,negated_conjecture,
( ? [U_43,U_41,U_39] :
( ~ in(ordered_pair(sK9,U_43),cartesian_product2(singleton(U_41),singleton(U_39)))
& U_43 = U_39
& sK9 = U_41 )
| ( ( sK6 != sK8
| sK5 != sK7 )
& in(ordered_pair(sK5,sK6),cartesian_product2(singleton(sK7),singleton(sK8))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_45,sK9)],[f_9_8]) ).
fof(f_9_10,negated_conjecture,
( ? [U_41,U_39] :
( ~ in(ordered_pair(sK9,sK10),cartesian_product2(singleton(U_41),singleton(U_39)))
& sK10 = U_39
& sK9 = U_41 )
| ( ( sK6 != sK8
| sK5 != sK7 )
& in(ordered_pair(sK5,sK6),cartesian_product2(singleton(sK7),singleton(sK8))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_43,sK10)],[f_9_9]) ).
fof(f_9_11,negated_conjecture,
( ? [U_39] :
( ~ in(ordered_pair(sK9,sK10),cartesian_product2(singleton(sK11),singleton(U_39)))
& sK10 = U_39
& sK9 = sK11 )
| ( ( sK6 != sK8
| sK5 != sK7 )
& in(ordered_pair(sK5,sK6),cartesian_product2(singleton(sK7),singleton(sK8))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_41,sK11)],[f_9_10]) ).
fof(f_9_12,negated_conjecture,
( ( ~ in(ordered_pair(sK9,sK10),cartesian_product2(singleton(sK11),singleton(sK12)))
& sK10 = sK12
& sK9 = sK11 )
| ( ( sK6 != sK8
| sK5 != sK7 )
& in(ordered_pair(sK5,sK6),cartesian_product2(singleton(sK7),singleton(sK8))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_39,sK12)],[f_9_11]) ).
fof(f_9_13,negated_conjecture,
( ( ~ in(ordered_pair(sK9,sK10),cartesian_product2(singleton(sK11),singleton(sK12)))
| ~ sP5 )
& ( sK10 = sK12
| ~ sP5 )
& ( sK9 = sK11
| ~ sP5 )
& ( sK6 != sK8
| sK5 != sK7
| ~ sP4 )
& ( in(ordered_pair(sK5,sK6),cartesian_product2(singleton(sK7),singleton(sK8)))
| ~ sP4 )
& ( sP5
| sP4 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4,sP5])],[f_9_12]) ).
cnf(f_9_14,negated_conjecture,
( sP5
| sP4 ),
inference(clausify,[status(thm)],[f_9_13]) ).
cnf(f_9_15,negated_conjecture,
( in(ordered_pair(sK5,sK6),cartesian_product2(singleton(sK7),singleton(sK8)))
| ~ sP4 ),
inference(clausify,[status(thm)],[f_9_13]) ).
cnf(f_9_16,negated_conjecture,
( sK6 != sK8
| sK5 != sK7
| ~ sP4 ),
inference(clausify,[status(thm)],[f_9_13]) ).
cnf(f_9_17,negated_conjecture,
( sK9 = sK11
| ~ sP5 ),
inference(clausify,[status(thm)],[f_9_13]) ).
cnf(f_9_18,negated_conjecture,
( sK10 = sK12
| ~ sP5 ),
inference(clausify,[status(thm)],[f_9_13]) ).
cnf(f_9_19,negated_conjecture,
( ~ in(ordered_pair(sK9,sK10),cartesian_product2(singleton(sK11),singleton(sK12)))
| ~ sP5 ),
inference(clausify,[status(thm)],[f_9_13]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_5,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
( sP5
| sP4 ),
inference(start,[status(thm),parent(0:0)],[f_9_14]) ).
cnf(t2,plain,
( sK5 != sK7
| sK6 != sK8
| ~ sP4 ),
inference(extension,[status(thm),parent(t1:1)],[f_9_16]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ in(sK6,singleton(sK8))
| ~ sP0(sK6,U_574,sK8,singleton(sK8))
| sK6 = sK8 ),
inference(extension,[status(thm),parent(t2:2)],[f_3_9]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( singleton(sK8) != singleton(sK8)
| sP0(sK6,U_574,sK8,singleton(sK8)) ),
inference(extension,[status(thm),parent(t4:2)],[f_3_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( sK8 != sK8
| singleton(sK8) = singleton(sK8) ),
inference(extension,[status(thm),parent(t6:2)],[equality_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
sK8 = sK8,
inference(extension,[status(thm),parent(t8:2)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ sP3(sK6,singleton(sK8),sK5,singleton(sK7))
| in(sK6,singleton(sK8)) ),
inference(extension,[status(thm),parent(t4:3)],[f_6_8]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
( ~ in(ordered_pair(sK5,sK6),cartesian_product2(singleton(sK7),singleton(sK8)))
| sP3(sK6,singleton(sK8),sK5,singleton(sK7)) ),
inference(extension,[status(thm),parent(t12:2)],[f_6_5]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ sP4
| in(ordered_pair(sK5,sK6),cartesian_product2(singleton(sK7),singleton(sK8))) ),
inference(extension,[status(thm),parent(t14:2)],[f_9_15]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
$false,
inference(reduction,[status(thm),parent(t16:2)],[t16:2,t1:1]) ).
cnf(t19,plain,
( ~ in(sK5,singleton(sK7))
| ~ sP0(sK5,U_593,sK7,singleton(sK7))
| sK5 = sK7 ),
inference(extension,[status(thm),parent(t2:3)],[f_3_9]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t2:3]) ).
cnf(t21,plain,
( singleton(sK7) != singleton(sK7)
| sP0(sK5,U_593,sK7,singleton(sK7)) ),
inference(extension,[status(thm),parent(t19:2)],[f_3_7]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(t23,plain,
( sK7 != sK7
| singleton(sK7) = singleton(sK7) ),
inference(extension,[status(thm),parent(t21:2)],[equality_5]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t21:2]) ).
cnf(t25,plain,
sK7 = sK7,
inference(extension,[status(thm),parent(t23:2)],[equality_1]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t23:2]) ).
cnf(t27,plain,
( ~ sP3(sK6,singleton(sK8),sK5,singleton(sK7))
| in(sK5,singleton(sK7)) ),
inference(extension,[status(thm),parent(t19:3)],[f_6_7]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t19:3]) ).
cnf(t29,plain,
( ~ in(ordered_pair(sK5,sK6),cartesian_product2(singleton(sK7),singleton(sK8)))
| sP3(sK6,singleton(sK8),sK5,singleton(sK7)) ),
inference(extension,[status(thm),parent(t27:2)],[f_6_5]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t27:2]) ).
cnf(t31,plain,
( ~ sP4
| in(ordered_pair(sK5,sK6),cartesian_product2(singleton(sK7),singleton(sK8))) ),
inference(extension,[status(thm),parent(t29:2)],[f_9_15]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t29:2]) ).
cnf(t33,plain,
$false,
inference(reduction,[status(thm),parent(t31:2)],[t31:2,t1:1]) ).
cnf(t34,plain,
( ~ in(ordered_pair(sK9,sK10),cartesian_product2(singleton(sK11),singleton(sK12)))
| ~ sP5 ),
inference(extension,[status(thm),parent(t1:2)],[f_9_19]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t1:2]) ).
cnf(t36,plain,
( ~ in(sK10,singleton(sK12))
| ~ in(sK9,singleton(sK11))
| in(ordered_pair(sK9,sK10),cartesian_product2(singleton(sK11),singleton(sK12))) ),
inference(extension,[status(thm),parent(t34:2)],[f_6_6]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
( sK9 != sK11
| ~ sP0(U_615,sK9,sK11,singleton(sK11))
| in(sK9,singleton(sK11)) ),
inference(extension,[status(thm),parent(t36:2)],[f_3_10]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( singleton(sK11) != singleton(sK11)
| sP0(U_615,sK9,sK11,singleton(sK11)) ),
inference(extension,[status(thm),parent(t38:2)],[f_3_7]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
singleton(sK11) = singleton(sK11),
inference(extension,[status(thm),parent(t40:2)],[equality_1]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( ~ sP5
| sK9 = sK11 ),
inference(extension,[status(thm),parent(t38:3)],[f_9_17]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t38:3]) ).
cnf(t46,plain,
$false,
inference(reduction,[status(thm),parent(t44:2)],[t44:2,t1:2]) ).
cnf(t47,plain,
( sK10 != sK12
| ~ sP0(U_624,sK10,sK12,singleton(sK12))
| in(sK10,singleton(sK12)) ),
inference(extension,[status(thm),parent(t36:3)],[f_3_10]) ).
cnf(t48,plain,
$false,
inference(connection,[status(thm),parent(t47:1)],[t47:1,t36:3]) ).
cnf(t49,plain,
( singleton(sK12) != singleton(sK12)
| sP0(U_624,sK10,sK12,singleton(sK12)) ),
inference(extension,[status(thm),parent(t47:2)],[f_3_7]) ).
cnf(t50,plain,
$false,
inference(connection,[status(thm),parent(t49:1)],[t49:1,t47:2]) ).
cnf(t51,plain,
singleton(sK12) = singleton(sK12),
inference(extension,[status(thm),parent(t49:2)],[equality_1]) ).
cnf(t52,plain,
$false,
inference(connection,[status(thm),parent(t51:1)],[t51:1,t49:2]) ).
cnf(t53,plain,
( ~ sP5
| sK10 = sK12 ),
inference(extension,[status(thm),parent(t47:3)],[f_9_18]) ).
cnf(t54,plain,
$false,
inference(connection,[status(thm),parent(t53:1)],[t53:1,t47:3]) ).
cnf(t55,plain,
$false,
inference(reduction,[status(thm),parent(t53:2)],[t53:2,t1:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET893+1 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 19 23:09:16 UTC 2026
% 0.07/0.36 % CPUTime :
% 30.33/30.66 % SZS status Theorem for theBenchmark
% 30.33/30.66 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------