%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET918+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 : n009.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 08:57:48 AM UTC 2026
% Result : Theorem 82.44s 82.79s
% Output : Proof 82.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 27 unt; 0 def)
% Number of atoms : 276 ( 142 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 339 ( 124 ~; 112 |; 97 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 162 ( 1 sgn 117 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
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(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(t59_zfmisc_1,conjecture,
! [A,B,C] :
~ ( A != B
& in(B,C)
& set_intersection2(unordered_pair(A,B),C) = singleton(A) ),
file('theBenchmark.p',t59_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]) ).
cnf(f_2_3,plain,
unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_3_2,plain,
! [U_5,U_4] : set_intersection2(U_5,U_4) = set_intersection2(U_4,U_5),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
set_intersection2(U_5,U_4) = set_intersection2(U_4,U_5),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_9,U_8] :
( ( U_8 = singleton(U_9)
| ? [U_7] :
( ( ~ in(U_7,U_8)
& U_7 = U_9 )
| ( U_7 != U_9
& in(U_7,U_8) ) ) )
& ( ! [U_6] :
( ( in(U_6,U_8)
| U_6 != U_9 )
& ( U_6 = U_9
| ~ in(U_6,U_8) ) )
| U_8 != singleton(U_9) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_17,U_15] :
( U_15 = singleton(U_17)
| ? [U_13] :
( ~ in(U_13,U_15)
& U_13 = U_17 )
| ? [U_12] :
( U_12 != U_17
& in(U_12,U_15) ) )
& ! [U_16,U_14] :
( ( ! [U_11] :
( in(U_11,U_14)
| U_11 != U_16 )
& ! [U_10] :
( U_10 = U_16
| ~ in(U_10,U_14) ) )
| U_14 != singleton(U_16) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_17,U_15] :
( U_15 = singleton(U_17)
| ? [U_13] :
( ~ in(U_13,U_15)
& U_13 = U_17 )
| ( sK1(U_17,U_15) != U_17
& in(sK1(U_17,U_15),U_15) ) )
& ! [U_16,U_14] :
( ( ! [U_11] :
( in(U_11,U_14)
| U_11 != U_16 )
& ! [U_10] :
( U_10 = U_16
| ~ in(U_10,U_14) ) )
| U_14 != singleton(U_16) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_12,sK1(U_17,U_15))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_17,U_15] :
( U_15 = singleton(U_17)
| ( ~ in(sK2(U_17,U_15),U_15)
& sK2(U_17,U_15) = U_17 )
| ( sK1(U_17,U_15) != U_17
& in(sK1(U_17,U_15),U_15) ) )
& ! [U_16,U_14] :
( ( ! [U_11] :
( in(U_11,U_14)
| U_11 != U_16 )
& ! [U_10] :
( U_10 = U_16
| ~ in(U_10,U_14) ) )
| U_14 != singleton(U_16) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_13,sK2(U_17,U_15))],[f_4_4]) ).
cnf(f_4_6,plain,
( U_10 = U_16
| ~ in(U_10,U_14)
| U_14 != singleton(U_16) ),
inference(clausify,[status(thm)],[f_4_5]) ).
fof(f_5_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_5_2,plain,
! [U_22,U_21,U_20] :
( ( U_20 = unordered_pair(U_22,U_21)
| ? [U_19] :
( ( ~ in(U_19,U_20)
& ( U_19 = U_21
| U_19 = U_22 ) )
| ( U_19 != U_21
& U_19 != U_22
& in(U_19,U_20) ) ) )
& ( ! [U_18] :
( ( in(U_18,U_20)
| ( U_18 != U_21
& U_18 != U_22 ) )
& ( U_18 = U_21
| U_18 = U_22
| ~ in(U_18,U_20) ) )
| U_20 != unordered_pair(U_22,U_21) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_32,U_30,U_28] :
( U_28 = unordered_pair(U_32,U_30)
| ? [U_26] :
( ~ in(U_26,U_28)
& ( U_26 = U_30
| U_26 = U_32 ) )
| ? [U_25] :
( U_25 != U_30
& U_25 != U_32
& in(U_25,U_28) ) )
& ! [U_31,U_29,U_27] :
( ( ! [U_24] :
( in(U_24,U_27)
| ( U_24 != U_29
& U_24 != U_31 ) )
& ! [U_23] :
( U_23 = U_29
| U_23 = U_31
| ~ in(U_23,U_27) ) )
| U_27 != unordered_pair(U_31,U_29) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_32,U_30,U_28] :
( U_28 = unordered_pair(U_32,U_30)
| ? [U_26] :
( ~ in(U_26,U_28)
& ( U_26 = U_30
| U_26 = U_32 ) )
| ( sK3(U_32,U_30,U_28) != U_30
& sK3(U_32,U_30,U_28) != U_32
& in(sK3(U_32,U_30,U_28),U_28) ) )
& ! [U_31,U_29,U_27] :
( ( ! [U_24] :
( in(U_24,U_27)
| ( U_24 != U_29
& U_24 != U_31 ) )
& ! [U_23] :
( U_23 = U_29
| U_23 = U_31
| ~ in(U_23,U_27) ) )
| U_27 != unordered_pair(U_31,U_29) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_25,sK3(U_32,U_30,U_28))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_32,U_30,U_28] :
( U_28 = unordered_pair(U_32,U_30)
| ( ~ in(sK4(U_32,U_30,U_28),U_28)
& ( sK4(U_32,U_30,U_28) = U_30
| sK4(U_32,U_30,U_28) = U_32 ) )
| ( sK3(U_32,U_30,U_28) != U_30
& sK3(U_32,U_30,U_28) != U_32
& in(sK3(U_32,U_30,U_28),U_28) ) )
& ! [U_31,U_29,U_27] :
( ( ! [U_24] :
( in(U_24,U_27)
| ( U_24 != U_29
& U_24 != U_31 ) )
& ! [U_23] :
( U_23 = U_29
| U_23 = U_31
| ~ in(U_23,U_27) ) )
| U_27 != unordered_pair(U_31,U_29) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_26,sK4(U_32,U_30,U_28))],[f_5_4]) ).
cnf(f_5_7,plain,
( U_24 != U_31
| in(U_24,U_27)
| U_27 != unordered_pair(U_31,U_29) ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_1,plain,
! [A,B,C] :
( ( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(D,B)
& in(D,A) )
| ( ( ~ in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(D,B)
| ~ in(D,A) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(f_6_2,plain,
! [U_37,U_36,U_35] :
( ( U_35 = set_intersection2(U_37,U_36)
| ? [U_34] :
( ( ~ in(U_34,U_35)
& in(U_34,U_36)
& in(U_34,U_37) )
| ( ( ~ in(U_34,U_36)
| ~ in(U_34,U_37) )
& in(U_34,U_35) ) ) )
& ( ! [U_33] :
( ( in(U_33,U_35)
| ~ in(U_33,U_36)
| ~ in(U_33,U_37) )
& ( ( in(U_33,U_36)
& in(U_33,U_37) )
| ~ in(U_33,U_35) ) )
| U_35 != set_intersection2(U_37,U_36) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_47,U_45,U_43] :
( U_43 = set_intersection2(U_47,U_45)
| ? [U_41] :
( ~ in(U_41,U_43)
& in(U_41,U_45)
& in(U_41,U_47) )
| ? [U_40] :
( ( ~ in(U_40,U_45)
| ~ in(U_40,U_47) )
& in(U_40,U_43) ) )
& ! [U_46,U_44,U_42] :
( ( ! [U_39] :
( in(U_39,U_42)
| ~ in(U_39,U_44)
| ~ in(U_39,U_46) )
& ! [U_38] :
( ( in(U_38,U_44)
& in(U_38,U_46) )
| ~ in(U_38,U_42) ) )
| U_42 != set_intersection2(U_46,U_44) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_47,U_45,U_43] :
( U_43 = set_intersection2(U_47,U_45)
| ? [U_41] :
( ~ in(U_41,U_43)
& in(U_41,U_45)
& in(U_41,U_47) )
| ( ( ~ in(sK5(U_47,U_45,U_43),U_45)
| ~ in(sK5(U_47,U_45,U_43),U_47) )
& in(sK5(U_47,U_45,U_43),U_43) ) )
& ! [U_46,U_44,U_42] :
( ( ! [U_39] :
( in(U_39,U_42)
| ~ in(U_39,U_44)
| ~ in(U_39,U_46) )
& ! [U_38] :
( ( in(U_38,U_44)
& in(U_38,U_46) )
| ~ in(U_38,U_42) ) )
| U_42 != set_intersection2(U_46,U_44) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_40,sK5(U_47,U_45,U_43))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_47,U_45,U_43] :
( U_43 = set_intersection2(U_47,U_45)
| ( ~ in(sK6(U_47,U_45,U_43),U_43)
& in(sK6(U_47,U_45,U_43),U_45)
& in(sK6(U_47,U_45,U_43),U_47) )
| ( ( ~ in(sK5(U_47,U_45,U_43),U_45)
| ~ in(sK5(U_47,U_45,U_43),U_47) )
& in(sK5(U_47,U_45,U_43),U_43) ) )
& ! [U_46,U_44,U_42] :
( ( ! [U_39] :
( in(U_39,U_42)
| ~ in(U_39,U_44)
| ~ in(U_39,U_46) )
& ! [U_38] :
( ( in(U_38,U_44)
& in(U_38,U_46) )
| ~ in(U_38,U_42) ) )
| U_42 != set_intersection2(U_46,U_44) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_41,sK6(U_47,U_45,U_43))],[f_6_4]) ).
cnf(f_6_8,plain,
( in(U_39,U_42)
| ~ in(U_39,U_44)
| ~ in(U_39,U_46)
| U_42 != set_intersection2(U_46,U_44) ),
inference(clausify,[status(thm)],[f_6_5]) ).
fof(f_10_1,negated_conjecture,
~ ! [A,B,C] :
~ ( A != B
& in(B,C)
& set_intersection2(unordered_pair(A,B),C) = singleton(A) ),
inference(negate,[status(cth)],[t59_zfmisc_1]) ).
fof(f_10_2,negated_conjecture,
? [A,B,C] :
( A != B
& in(B,C)
& set_intersection2(unordered_pair(A,B),C) = singleton(A) ),
inference(fof_nnf,[status(thm)],[f_10_1]) ).
fof(f_10_3,negated_conjecture,
? [U_54,U_53,U_52] :
( U_54 != U_53
& in(U_53,U_52)
& set_intersection2(unordered_pair(U_54,U_53),U_52) = singleton(U_54) ),
inference(variable_rename,[status(thm)],[f_10_2]) ).
fof(f_10_4,negated_conjecture,
? [U_54,U_53] :
( ? [U_52] :
( in(U_53,U_52)
& set_intersection2(unordered_pair(U_54,U_53),U_52) = singleton(U_54) )
& U_54 != U_53 ),
inference(miniscope,[status(thm)],[f_10_3]) ).
fof(f_10_5,negated_conjecture,
? [U_53] :
( ? [U_52] :
( in(U_53,U_52)
& set_intersection2(unordered_pair(sK9,U_53),U_52) = singleton(sK9) )
& sK9 != U_53 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_54,sK9)],[f_10_4]) ).
fof(f_10_6,negated_conjecture,
( ? [U_52] :
( in(sK10,U_52)
& set_intersection2(unordered_pair(sK9,sK10),U_52) = singleton(sK9) )
& sK9 != sK10 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_53,sK10)],[f_10_5]) ).
fof(f_10_7,negated_conjecture,
( in(sK10,sK11)
& set_intersection2(unordered_pair(sK9,sK10),sK11) = singleton(sK9)
& sK9 != sK10 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_52,sK11)],[f_10_6]) ).
cnf(f_10_8,negated_conjecture,
sK9 != sK10,
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_9,negated_conjecture,
set_intersection2(unordered_pair(sK9,sK10),sK11) = singleton(sK9),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_10,negated_conjecture,
in(sK10,sK11),
inference(clausify,[status(thm)],[f_10_7]) ).
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,
sK9 != sK10,
inference(start,[status(thm),parent(0:0)],[f_10_8]) ).
cnf(t2,plain,
( sK10 != sK9
| sK9 = sK10 ),
inference(extension,[status(thm),parent(t1:1)],[equality_2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ in(sK10,set_intersection2(unordered_pair(sK9,sK10),sK11))
| set_intersection2(unordered_pair(sK9,sK10),sK11) != singleton(sK9)
| sK10 = sK9 ),
inference(extension,[status(thm),parent(t2:2)],[f_4_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
set_intersection2(unordered_pair(sK9,sK10),sK11) = singleton(sK9),
inference(extension,[status(thm),parent(t4:2)],[f_10_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ in(sK10,sK11)
| ~ in(sK10,unordered_pair(sK9,sK10))
| set_intersection2(unordered_pair(sK9,sK10),sK11) != set_intersection2(sK11,unordered_pair(sK9,sK10))
| in(sK10,set_intersection2(unordered_pair(sK9,sK10),sK11)) ),
inference(extension,[status(thm),parent(t4:3)],[f_6_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
set_intersection2(unordered_pair(sK9,sK10),sK11) = set_intersection2(sK11,unordered_pair(sK9,sK10)),
inference(extension,[status(thm),parent(t8:2)],[f_3_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( sK10 != sK10
| unordered_pair(sK9,sK10) != unordered_pair(sK10,sK9)
| in(sK10,unordered_pair(sK9,sK10)) ),
inference(extension,[status(thm),parent(t8:3)],[f_5_7]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
unordered_pair(sK9,sK10) = unordered_pair(sK10,sK9),
inference(extension,[status(thm),parent(t12:2)],[f_2_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
sK10 = sK10,
inference(extension,[status(thm),parent(t12:3)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
in(sK10,sK11),
inference(extension,[status(thm),parent(t8:4)],[f_10_10]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t8:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET918+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
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 23:07:27 UTC 2026
% 0.08/0.37 % CPUTime :
% 82.44/82.79 % SZS status Theorem for theBenchmark
% 82.44/82.79 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------