%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU149+3 : 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 : n012.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 08:58:13 AM UTC 2026
% Result : Theorem 4.13s 9.42s
% Output : Proof 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 14 unt; 0 def)
% Number of atoms : 179 ( 126 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 218 ( 82 ~; 73 |; 57 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 103 ( 1 sgn 69 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
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(t8_zfmisc_1,conjecture,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_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]) ).
cnf(f_3_6,plain,
( U_8 = U_14
| ~ in(U_8,U_12)
| U_12 != singleton(U_14) ),
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_20,U_19,U_18] :
( ( U_18 = unordered_pair(U_20,U_19)
| ? [U_17] :
( ( ~ in(U_17,U_18)
& ( U_17 = U_19
| U_17 = U_20 ) )
| ( U_17 != U_19
& U_17 != U_20
& in(U_17,U_18) ) ) )
& ( ! [U_16] :
( ( in(U_16,U_18)
| ( U_16 != U_19
& U_16 != U_20 ) )
& ( U_16 = U_19
| U_16 = U_20
| ~ in(U_16,U_18) ) )
| U_18 != unordered_pair(U_20,U_19) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_30,U_28,U_26] :
( U_26 = unordered_pair(U_30,U_28)
| ? [U_24] :
( ~ in(U_24,U_26)
& ( U_24 = U_28
| U_24 = U_30 ) )
| ? [U_23] :
( U_23 != U_28
& U_23 != U_30
& in(U_23,U_26) ) )
& ! [U_29,U_27,U_25] :
( ( ! [U_22] :
( in(U_22,U_25)
| ( U_22 != U_27
& U_22 != U_29 ) )
& ! [U_21] :
( U_21 = U_27
| U_21 = U_29
| ~ in(U_21,U_25) ) )
| U_25 != unordered_pair(U_29,U_27) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_30,U_28,U_26] :
( U_26 = unordered_pair(U_30,U_28)
| ? [U_24] :
( ~ in(U_24,U_26)
& ( U_24 = U_28
| U_24 = U_30 ) )
| ( sK3(U_30,U_28,U_26) != U_28
& sK3(U_30,U_28,U_26) != U_30
& in(sK3(U_30,U_28,U_26),U_26) ) )
& ! [U_29,U_27,U_25] :
( ( ! [U_22] :
( in(U_22,U_25)
| ( U_22 != U_27
& U_22 != U_29 ) )
& ! [U_21] :
( U_21 = U_27
| U_21 = U_29
| ~ in(U_21,U_25) ) )
| U_25 != unordered_pair(U_29,U_27) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_23,sK3(U_30,U_28,U_26))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_30,U_28,U_26] :
( U_26 = unordered_pair(U_30,U_28)
| ( ~ in(sK4(U_30,U_28,U_26),U_26)
& ( sK4(U_30,U_28,U_26) = U_28
| sK4(U_30,U_28,U_26) = U_30 ) )
| ( sK3(U_30,U_28,U_26) != U_28
& sK3(U_30,U_28,U_26) != U_30
& in(sK3(U_30,U_28,U_26),U_26) ) )
& ! [U_29,U_27,U_25] :
( ( ! [U_22] :
( in(U_22,U_25)
| ( U_22 != U_27
& U_22 != U_29 ) )
& ! [U_21] :
( U_21 = U_27
| U_21 = U_29
| ~ in(U_21,U_25) ) )
| U_25 != unordered_pair(U_29,U_27) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_24,sK4(U_30,U_28,U_26))],[f_4_4]) ).
cnf(f_4_7,plain,
( U_22 != U_29
| in(U_22,U_25)
| U_25 != unordered_pair(U_29,U_27) ),
inference(clausify,[status(thm)],[f_4_5]) ).
fof(f_7_1,negated_conjecture,
~ ! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
inference(negate,[status(cth)],[t8_zfmisc_1]) ).
fof(f_7_2,negated_conjecture,
? [A,B,C] :
( A != B
& singleton(A) = unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_35,U_34,U_33] :
( U_35 != U_34
& singleton(U_35) = unordered_pair(U_34,U_33) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
? [U_35,U_34] :
( ? [U_33] : singleton(U_35) = unordered_pair(U_34,U_33)
& U_35 != U_34 ),
inference(miniscope,[status(thm)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
? [U_34] :
( ? [U_33] : singleton(sK7) = unordered_pair(U_34,U_33)
& sK7 != U_34 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_35,sK7)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
( ? [U_33] : singleton(sK7) = unordered_pair(sK8,U_33)
& sK7 != sK8 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_34,sK8)],[f_7_5]) ).
fof(f_7_7,negated_conjecture,
( singleton(sK7) = unordered_pair(sK8,sK9)
& sK7 != sK8 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_33,sK9)],[f_7_6]) ).
fof(f_7_8,negated_conjecture,
( singleton(sK7) = unordered_pair(sK8,sK9)
& sK7 != sK8 ),
inference(definitional_conversion,[status(esa)],[f_7_7]) ).
cnf(f_7_9,negated_conjecture,
sK7 != sK8,
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_10,negated_conjecture,
singleton(sK7) = unordered_pair(sK8,sK9),
inference(clausify,[status(thm)],[f_7_8]) ).
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(equality_5,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
sK7 != sK8,
inference(start,[status(thm),parent(0:0)],[f_7_9]) ).
cnf(t2,plain,
( sK8 != sK7
| sK7 = sK8 ),
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(sK8,singleton(sK7))
| singleton(sK7) != singleton(sK7)
| sK8 = sK7 ),
inference(extension,[status(thm),parent(t2:2)],[f_3_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( sK7 != sK7
| singleton(sK7) = singleton(sK7) ),
inference(extension,[status(thm),parent(t4:2)],[equality_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
sK7 = sK7,
inference(extension,[status(thm),parent(t6:2)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( sK8 != sK8
| singleton(sK7) != unordered_pair(sK8,sK9)
| in(sK8,singleton(sK7)) ),
inference(extension,[status(thm),parent(t4:3)],[f_4_7]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
singleton(sK7) = unordered_pair(sK8,sK9),
inference(extension,[status(thm),parent(t10:2)],[f_7_10]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
sK8 = sK8,
inference(extension,[status(thm),parent(t10:3)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU149+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/5.32 % Computer : n012.cluster.edu
% 0.03/5.32 % Model : x86_64 x86_64
% 0.03/5.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.32 % Memory : 8046.5625MB
% 0.03/5.32 % OS : Linux 6.8.0-71-generic
% 0.03/5.32 % CPULimit : 300
% 0.03/5.32 % WCLimit : 300
% 0.03/5.32 % DateTime : Sat Sep 19 23:23:01 UTC 2026
% 0.03/5.32 % CPUTime :
% 4.13/9.42 % SZS status Theorem for theBenchmark
% 4.13/9.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------