%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET887+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n006.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 08:57:44 AM UTC 2026
% Result : Theorem 65.78s 66.12s
% Output : Proof 65.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 92 ( 34 unt; 0 def)
% Number of atoms : 312 ( 205 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 375 ( 155 ~; 128 |; 87 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-5 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 232 ( 9 sgn 174 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(l46_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('theBenchmark.p',l46_zfmisc_1) ).
fof(t10_zfmisc_1,axiom,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('theBenchmark.p',t10_zfmisc_1) ).
fof(t28_zfmisc_1,conjecture,
! [A,B,C,D] :
~ ( A != D
& A != C
& subset(unordered_pair(A,B),unordered_pair(C,D)) ),
file('theBenchmark.p',t28_zfmisc_1) ).
fof(t8_zfmisc_1,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(f_2_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_2_2,plain,
! [U_3,U_2] : unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_2] : unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_3_2,plain,
! [U_6] :
( ( U_6 = empty_set
| ? [U_5] : in(U_5,U_6) )
& ( ! [U_4] : ~ in(U_4,U_6)
| U_6 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_8] :
( U_8 = empty_set
| ? [U_5] : in(U_5,U_8) )
& ! [U_7] :
( ! [U_4] : ~ in(U_4,U_7)
| U_7 != empty_set ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_8] :
( U_8 = empty_set
| in(sK1(U_8),U_8) )
& ! [U_7] :
( ! [U_4] : ~ in(U_4,U_7)
| U_7 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1(U_8))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_8] :
( U_8 = empty_set
| in(sK1(U_8),U_8) )
& ! [U_4,U_7] :
( ~ in(U_4,U_7)
| U_7 != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_3_4]) ).
cnf(f_3_6,plain,
( ~ in(U_4,U_7)
| U_7 != empty_set ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_4_1,plain,
! [A,B,C] :
( ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( D = B
| D = A ) )
| ( D != B
& D != A
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( D != B
& D != A ) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(f_4_2,plain,
! [U_13,U_12,U_11] :
( ( U_11 = unordered_pair(U_13,U_12)
| ? [U_10] :
( ( ~ in(U_10,U_11)
& ( U_10 = U_12
| U_10 = U_13 ) )
| ( U_10 != U_12
& U_10 != U_13
& in(U_10,U_11) ) ) )
& ( ! [U_9] :
( ( in(U_9,U_11)
| ( U_9 != U_12
& U_9 != U_13 ) )
& ( U_9 = U_12
| U_9 = U_13
| ~ in(U_9,U_11) ) )
| U_11 != unordered_pair(U_13,U_12) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_23,U_21,U_19] :
( U_19 = unordered_pair(U_23,U_21)
| ? [U_17] :
( ~ in(U_17,U_19)
& ( U_17 = U_21
| U_17 = U_23 ) )
| ? [U_16] :
( U_16 != U_21
& U_16 != U_23
& in(U_16,U_19) ) )
& ! [U_22,U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| ( U_15 != U_20
& U_15 != U_22 ) )
& ! [U_14] :
( U_14 = U_20
| U_14 = U_22
| ~ in(U_14,U_18) ) )
| U_18 != unordered_pair(U_22,U_20) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_23,U_21,U_19] :
( U_19 = unordered_pair(U_23,U_21)
| ? [U_17] :
( ~ in(U_17,U_19)
& ( U_17 = U_21
| U_17 = U_23 ) )
| ( sK2(U_23,U_21,U_19) != U_21
& sK2(U_23,U_21,U_19) != U_23
& in(sK2(U_23,U_21,U_19),U_19) ) )
& ! [U_22,U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| ( U_15 != U_20
& U_15 != U_22 ) )
& ! [U_14] :
( U_14 = U_20
| U_14 = U_22
| ~ in(U_14,U_18) ) )
| U_18 != unordered_pair(U_22,U_20) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_16,sK2(U_23,U_21,U_19))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_23,U_21,U_19] :
( U_19 = unordered_pair(U_23,U_21)
| ( ~ in(sK3(U_23,U_21,U_19),U_19)
& ( sK3(U_23,U_21,U_19) = U_21
| sK3(U_23,U_21,U_19) = U_23 ) )
| ( sK2(U_23,U_21,U_19) != U_21
& sK2(U_23,U_21,U_19) != U_23
& in(sK2(U_23,U_21,U_19),U_19) ) )
& ! [U_22,U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| ( U_15 != U_20
& U_15 != U_22 ) )
& ! [U_14] :
( U_14 = U_20
| U_14 = U_22
| ~ in(U_14,U_18) ) )
| U_18 != unordered_pair(U_22,U_20) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_17,sK3(U_23,U_21,U_19))],[f_4_4]) ).
fof(f_4_6,plain,
( ! [U_23,U_19,U_21] :
( ~ in(sK3(U_23,U_21,U_19),U_19)
| ~ sP3(U_23,U_19,U_21) )
& ! [U_23,U_19,U_21] :
( sK3(U_23,U_21,U_19) = U_21
| sK3(U_23,U_21,U_19) = U_23
| ~ sP3(U_23,U_19,U_21) )
& ! [U_23,U_19,U_21] :
( sK2(U_23,U_21,U_19) != U_21
| ~ sP2(U_23,U_19,U_21) )
& ! [U_23,U_19,U_21] :
( sK2(U_23,U_21,U_19) != U_23
| ~ sP2(U_23,U_19,U_21) )
& ! [U_23,U_19,U_21] :
( in(sK2(U_23,U_21,U_19),U_19)
| ~ sP2(U_23,U_19,U_21) )
& ! [U_15,U_20,U_22] :
( U_15 != U_20
| ~ sP0(U_15,U_20,U_22) )
& ! [U_15,U_20,U_22] :
( U_15 != U_22
| ~ sP0(U_15,U_20,U_22) )
& ! [U_14,U_15,U_20,U_18,U_22] :
( in(U_15,U_18)
| sP0(U_15,U_20,U_22)
| ~ sP1(U_14,U_15,U_20,U_18,U_22) )
& ! [U_14,U_15,U_20,U_18,U_22] :
( U_14 = U_20
| U_14 = U_22
| ~ in(U_14,U_18)
| ~ sP1(U_14,U_15,U_20,U_18,U_22) )
& ! [U_23,U_19,U_21] :
( U_19 = unordered_pair(U_23,U_21)
| sP3(U_23,U_19,U_21)
| sP2(U_23,U_19,U_21) )
& ! [U_14,U_15,U_20,U_18,U_22] :
( sP1(U_14,U_15,U_20,U_18,U_22)
| U_18 != unordered_pair(U_22,U_20) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3])],[f_4_5]) ).
cnf(f_4_7,plain,
( sP1(U_14,U_15,U_20,U_18,U_22)
| U_18 != unordered_pair(U_22,U_20) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_10,plain,
( in(U_15,U_18)
| sP0(U_15,U_20,U_22)
| ~ sP1(U_14,U_15,U_20,U_18,U_22) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_12,plain,
( U_15 != U_20
| ~ sP0(U_15,U_20,U_22) ),
inference(clausify,[status(thm)],[f_4_6]) ).
fof(f_6_1,plain,
! [A,B,C] :
( ( subset(A,unordered_pair(B,C))
| ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) )
& ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set
| ~ subset(A,unordered_pair(B,C)) ) ),
inference(fof_nnf,[status(thm)],[l46_zfmisc_1]) ).
fof(f_6_2,plain,
! [U_26,U_25,U_24] :
( ( subset(U_26,unordered_pair(U_25,U_24))
| ( U_26 != unordered_pair(U_25,U_24)
& U_26 != singleton(U_24)
& U_26 != singleton(U_25)
& U_26 != empty_set ) )
& ( U_26 = unordered_pair(U_25,U_24)
| U_26 = singleton(U_24)
| U_26 = singleton(U_25)
| U_26 = empty_set
| ~ subset(U_26,unordered_pair(U_25,U_24)) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_32,U_30,U_28] :
( subset(U_32,unordered_pair(U_30,U_28))
| ( U_32 != unordered_pair(U_30,U_28)
& U_32 != singleton(U_28)
& U_32 != singleton(U_30)
& U_32 != empty_set ) )
& ! [U_31,U_29,U_27] :
( U_31 = unordered_pair(U_29,U_27)
| U_31 = singleton(U_27)
| U_31 = singleton(U_29)
| U_31 = empty_set
| ~ subset(U_31,unordered_pair(U_29,U_27)) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_28,U_30,U_32] :
( U_32 != unordered_pair(U_30,U_28)
| ~ sP4(U_28,U_30,U_32) )
& ! [U_28,U_30,U_32] :
( U_32 != singleton(U_28)
| ~ sP4(U_28,U_30,U_32) )
& ! [U_28,U_30,U_32] :
( U_32 != singleton(U_30)
| ~ sP4(U_28,U_30,U_32) )
& ! [U_28,U_30,U_32] :
( U_32 != empty_set
| ~ sP4(U_28,U_30,U_32) )
& ! [U_28,U_30,U_32] :
( subset(U_32,unordered_pair(U_30,U_28))
| sP4(U_28,U_30,U_32) )
& ! [U_29,U_31,U_27] :
( U_31 = unordered_pair(U_29,U_27)
| U_31 = singleton(U_27)
| U_31 = singleton(U_29)
| U_31 = empty_set
| ~ subset(U_31,unordered_pair(U_29,U_27)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_6_3]) ).
cnf(f_6_5,plain,
( U_31 = unordered_pair(U_29,U_27)
| U_31 = singleton(U_27)
| U_31 = singleton(U_29)
| U_31 = empty_set
| ~ subset(U_31,unordered_pair(U_29,U_27)) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_10_1,plain,
! [A,B,C,D] :
( A = D
| A = C
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(fof_nnf,[status(thm)],[t10_zfmisc_1]) ).
fof(f_10_2,plain,
! [U_40,U_39,U_38,U_37] :
( U_40 = U_37
| U_40 = U_38
| unordered_pair(U_40,U_39) != unordered_pair(U_38,U_37) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_40,U_39,U_38] :
( ! [U_37] :
( U_40 = U_37
| unordered_pair(U_40,U_39) != unordered_pair(U_38,U_37) )
| U_40 = U_38 ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
! [U_40,U_38,U_37,U_39] :
( U_40 = U_37
| unordered_pair(U_40,U_39) != unordered_pair(U_38,U_37)
| U_40 = U_38 ),
inference(definitional_conversion,[status(esa)],[f_10_3]) ).
cnf(f_10_5,plain,
( U_40 = U_37
| unordered_pair(U_40,U_39) != unordered_pair(U_38,U_37)
| U_40 = U_38 ),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,negated_conjecture,
~ ! [A,B,C,D] :
~ ( A != D
& A != C
& subset(unordered_pair(A,B),unordered_pair(C,D)) ),
inference(negate,[status(cth)],[t28_zfmisc_1]) ).
fof(f_11_2,negated_conjecture,
? [A,B,C,D] :
( A != D
& A != C
& subset(unordered_pair(A,B),unordered_pair(C,D)) ),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_44,U_43,U_42,U_41] :
( U_44 != U_41
& U_44 != U_42
& subset(unordered_pair(U_44,U_43),unordered_pair(U_42,U_41)) ),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
? [U_44,U_43,U_42] :
( ? [U_41] :
( U_44 != U_41
& subset(unordered_pair(U_44,U_43),unordered_pair(U_42,U_41)) )
& U_44 != U_42 ),
inference(miniscope,[status(thm)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
? [U_43,U_42] :
( ? [U_41] :
( sK6 != U_41
& subset(unordered_pair(sK6,U_43),unordered_pair(U_42,U_41)) )
& sK6 != U_42 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_44,sK6)],[f_11_4]) ).
fof(f_11_6,negated_conjecture,
? [U_42] :
( ? [U_41] :
( sK6 != U_41
& subset(unordered_pair(sK6,sK7),unordered_pair(U_42,U_41)) )
& sK6 != U_42 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_43,sK7)],[f_11_5]) ).
fof(f_11_7,negated_conjecture,
( ? [U_41] :
( sK6 != U_41
& subset(unordered_pair(sK6,sK7),unordered_pair(sK8,U_41)) )
& sK6 != sK8 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_42,sK8)],[f_11_6]) ).
fof(f_11_8,negated_conjecture,
( sK6 != sK9
& subset(unordered_pair(sK6,sK7),unordered_pair(sK8,sK9))
& sK6 != sK8 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_41,sK9)],[f_11_7]) ).
fof(f_11_9,negated_conjecture,
( sK6 != sK9
& subset(unordered_pair(sK6,sK7),unordered_pair(sK8,sK9))
& sK6 != sK8 ),
inference(definitional_conversion,[status(esa)],[f_11_8]) ).
cnf(f_11_10,negated_conjecture,
sK6 != sK8,
inference(clausify,[status(thm)],[f_11_9]) ).
cnf(f_11_11,negated_conjecture,
subset(unordered_pair(sK6,sK7),unordered_pair(sK8,sK9)),
inference(clausify,[status(thm)],[f_11_9]) ).
cnf(f_11_12,negated_conjecture,
sK6 != sK9,
inference(clausify,[status(thm)],[f_11_9]) ).
fof(f_12_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_12_2,plain,
! [U_47,U_46,U_45] :
( U_47 = U_46
| singleton(U_47) != unordered_pair(U_46,U_45) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_47,U_46] :
( ! [U_45] : singleton(U_47) != unordered_pair(U_46,U_45)
| U_47 = U_46 ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
! [U_46,U_45,U_47] :
( singleton(U_47) != unordered_pair(U_46,U_45)
| U_47 = U_46 ),
inference(definitional_conversion,[status(esa)],[f_12_3]) ).
cnf(f_12_5,plain,
( singleton(U_47) != unordered_pair(U_46,U_45)
| U_47 = U_46 ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(t1,plain,
subset(unordered_pair(sK6,sK7),unordered_pair(sK8,sK9)),
inference(start,[status(thm),parent(0:0)],[f_11_11]) ).
cnf(t2,plain,
( unordered_pair(sK6,sK7) = empty_set
| unordered_pair(sK6,sK7) = singleton(sK8)
| unordered_pair(sK6,sK7) = singleton(sK9)
| unordered_pair(sK6,sK7) = unordered_pair(sK8,sK9)
| ~ subset(unordered_pair(sK6,sK7),unordered_pair(sK8,sK9)) ),
inference(extension,[status(thm),parent(t1:1)],[f_6_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sK6 = sK9
| sK6 = sK8
| unordered_pair(sK6,sK7) != unordered_pair(sK8,sK9) ),
inference(extension,[status(thm),parent(t2:2)],[f_10_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
sK6 != sK8,
inference(extension,[status(thm),parent(t4:2)],[f_11_10]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
sK6 != sK9,
inference(extension,[status(thm),parent(t4:3)],[f_11_12]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( singleton(sK9) = unordered_pair(sK6,sK7)
| unordered_pair(sK6,sK7) != singleton(sK9) ),
inference(extension,[status(thm),parent(t2:3)],[equality_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( sK9 = sK6
| singleton(sK9) != unordered_pair(sK6,sK7) ),
inference(extension,[status(thm),parent(t10:2)],[f_12_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( sK6 = sK9
| sK9 != sK6 ),
inference(extension,[status(thm),parent(t12:2)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
sK6 != sK9,
inference(extension,[status(thm),parent(t14:2)],[f_11_12]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( singleton(sK8) = unordered_pair(sK6,sK7)
| unordered_pair(sK6,sK7) != singleton(sK8) ),
inference(extension,[status(thm),parent(t2:4)],[equality_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:4]) ).
cnf(t20,plain,
( sK8 = sK6
| singleton(sK8) != unordered_pair(sK6,sK7) ),
inference(extension,[status(thm),parent(t18:2)],[f_12_5]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( sK6 = sK8
| sK8 != sK6 ),
inference(extension,[status(thm),parent(t20:2)],[equality_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
sK6 != sK8,
inference(extension,[status(thm),parent(t22:2)],[f_11_10]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ~ in(sK6,unordered_pair(sK6,sK7))
| unordered_pair(sK6,sK7) != empty_set ),
inference(extension,[status(thm),parent(t2:5)],[f_3_6]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t2:5]) ).
cnf(t28,plain,
( sP0(sK6,sK6,sK7)
| ~ sP1(U_808,sK6,sK6,unordered_pair(sK6,sK7),sK7)
| in(sK6,unordered_pair(sK6,sK7)) ),
inference(extension,[status(thm),parent(t26:2)],[f_4_10]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( unordered_pair(sK6,sK7) != unordered_pair(sK7,sK6)
| sP1(U_808,sK6,sK6,unordered_pair(sK6,sK7),sK7) ),
inference(extension,[status(thm),parent(t28:2)],[f_4_7]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
unordered_pair(sK6,sK7) = unordered_pair(sK7,sK6),
inference(extension,[status(thm),parent(t30:2)],[f_2_4]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
( sK6 != sK6
| ~ sP0(sK6,sK6,sK7) ),
inference(extension,[status(thm),parent(t28:3)],[f_4_12]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t28:3]) ).
cnf(t36,plain,
sK6 = sK6,
inference(extension,[status(thm),parent(t34:2)],[equality_1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET887+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 23:06:32 UTC 2026
% 0.08/0.36 % CPUTime :
% 65.78/66.12 % SZS status Theorem for theBenchmark
% 65.78/66.12 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------