%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET927+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 : n019.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 08:57:49 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(t70_zfmisc_1,conjecture,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
file('theBenchmark.p',t70_zfmisc_1) ).
fof(l39_zfmisc_1,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
file('theBenchmark.p',l39_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_1_2,plain,
! [U_1,U_0] : unordered_pair(U_1,U_0) = unordered_pair(U_0,U_1),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
unordered_pair(U_1,U_0) = unordered_pair(U_0,U_1),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ in(U_2,U_3)
| ~ in(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ in(U_2,U_3)
| ~ in(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_3_2,plain,
? [U_4] : empty(U_4),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_4,sK1)],[f_3_2]) ).
cnf(f_3_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_4_2,plain,
? [U_5] : ~ empty(U_5),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_5,sK2)],[f_4_2]) ).
cnf(f_4_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
inference(negate,[status(cth)],[t70_zfmisc_1]) ).
fof(f_5_2,negated_conjecture,
? [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) != singleton(A)
& ( A = B
| in(B,C) )
& ~ in(A,C) )
| ( ( ( A != B
& ~ in(B,C) )
| in(A,C) )
& set_difference(unordered_pair(A,B),C) = singleton(A) ) ),
inference(fof_nnf,[status(thm)],[f_5_1]) ).
fof(f_5_3,negated_conjecture,
? [U_8,U_7,U_6] :
( ( set_difference(unordered_pair(U_8,U_7),U_6) != singleton(U_8)
& ( U_8 = U_7
| in(U_7,U_6) )
& ~ in(U_8,U_6) )
| ( ( ( U_8 != U_7
& ~ in(U_7,U_6) )
| in(U_8,U_6) )
& set_difference(unordered_pair(U_8,U_7),U_6) = singleton(U_8) ) ),
inference(variable_rename,[status(thm)],[f_5_2]) ).
fof(f_5_4,negated_conjecture,
( ? [U_14,U_12,U_10] :
( set_difference(unordered_pair(U_14,U_12),U_10) != singleton(U_14)
& ( U_14 = U_12
| in(U_12,U_10) )
& ~ in(U_14,U_10) )
| ? [U_13,U_11,U_9] :
( ( ( U_13 != U_11
& ~ in(U_11,U_9) )
| in(U_13,U_9) )
& set_difference(unordered_pair(U_13,U_11),U_9) = singleton(U_13) ) ),
inference(miniscope,[status(thm)],[f_5_3]) ).
fof(f_5_5,negated_conjecture,
( ? [U_14,U_12,U_10] :
( set_difference(unordered_pair(U_14,U_12),U_10) != singleton(U_14)
& ( U_14 = U_12
| in(U_12,U_10) )
& ~ in(U_14,U_10) )
| ? [U_11,U_9] :
( ( ( sK3 != U_11
& ~ in(U_11,U_9) )
| in(sK3,U_9) )
& set_difference(unordered_pair(sK3,U_11),U_9) = singleton(sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_13,sK3)],[f_5_4]) ).
fof(f_5_6,negated_conjecture,
( ? [U_14,U_12,U_10] :
( set_difference(unordered_pair(U_14,U_12),U_10) != singleton(U_14)
& ( U_14 = U_12
| in(U_12,U_10) )
& ~ in(U_14,U_10) )
| ? [U_9] :
( ( ( sK3 != sK4
& ~ in(sK4,U_9) )
| in(sK3,U_9) )
& set_difference(unordered_pair(sK3,sK4),U_9) = singleton(sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_11,sK4)],[f_5_5]) ).
fof(f_5_7,negated_conjecture,
( ? [U_14,U_12,U_10] :
( set_difference(unordered_pair(U_14,U_12),U_10) != singleton(U_14)
& ( U_14 = U_12
| in(U_12,U_10) )
& ~ in(U_14,U_10) )
| ( ( ( sK3 != sK4
& ~ in(sK4,sK5) )
| in(sK3,sK5) )
& set_difference(unordered_pair(sK3,sK4),sK5) = singleton(sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_9,sK5)],[f_5_6]) ).
fof(f_5_8,negated_conjecture,
( ? [U_12,U_10] :
( set_difference(unordered_pair(sK6,U_12),U_10) != singleton(sK6)
& ( sK6 = U_12
| in(U_12,U_10) )
& ~ in(sK6,U_10) )
| ( ( ( sK3 != sK4
& ~ in(sK4,sK5) )
| in(sK3,sK5) )
& set_difference(unordered_pair(sK3,sK4),sK5) = singleton(sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_14,sK6)],[f_5_7]) ).
fof(f_5_9,negated_conjecture,
( ? [U_10] :
( set_difference(unordered_pair(sK6,sK7),U_10) != singleton(sK6)
& ( sK6 = sK7
| in(sK7,U_10) )
& ~ in(sK6,U_10) )
| ( ( ( sK3 != sK4
& ~ in(sK4,sK5) )
| in(sK3,sK5) )
& set_difference(unordered_pair(sK3,sK4),sK5) = singleton(sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_12,sK7)],[f_5_8]) ).
fof(f_5_10,negated_conjecture,
( ( set_difference(unordered_pair(sK6,sK7),sK8) != singleton(sK6)
& ( sK6 = sK7
| in(sK7,sK8) )
& ~ in(sK6,sK8) )
| ( ( ( sK3 != sK4
& ~ in(sK4,sK5) )
| in(sK3,sK5) )
& set_difference(unordered_pair(sK3,sK4),sK5) = singleton(sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_10,sK8)],[f_5_9]) ).
fof(f_5_11,negated_conjecture,
( ( set_difference(unordered_pair(sK6,sK7),sK8) != singleton(sK6)
| ~ sP2 )
& ( sK6 = sK7
| in(sK7,sK8)
| ~ sP2 )
& ( ~ in(sK6,sK8)
| ~ sP2 )
& ( sK3 != sK4
| ~ sP0 )
& ( ~ in(sK4,sK5)
| ~ sP0 )
& ( sP0
| in(sK3,sK5)
| ~ sP1 )
& ( set_difference(unordered_pair(sK3,sK4),sK5) = singleton(sK3)
| ~ sP1 )
& ( sP2
| sP1 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2])],[f_5_10]) ).
cnf(f_5_12,negated_conjecture,
( sP2
| sP1 ),
inference(clausify,[status(thm)],[f_5_11]) ).
cnf(f_5_13,negated_conjecture,
( set_difference(unordered_pair(sK3,sK4),sK5) = singleton(sK3)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_5_11]) ).
cnf(f_5_14,negated_conjecture,
( sP0
| in(sK3,sK5)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_5_11]) ).
cnf(f_5_15,negated_conjecture,
( ~ in(sK4,sK5)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_5_11]) ).
cnf(f_5_16,negated_conjecture,
( sK3 != sK4
| ~ sP0 ),
inference(clausify,[status(thm)],[f_5_11]) ).
cnf(f_5_17,negated_conjecture,
( ~ in(sK6,sK8)
| ~ sP2 ),
inference(clausify,[status(thm)],[f_5_11]) ).
cnf(f_5_18,negated_conjecture,
( sK6 = sK7
| in(sK7,sK8)
| ~ sP2 ),
inference(clausify,[status(thm)],[f_5_11]) ).
cnf(f_5_19,negated_conjecture,
( set_difference(unordered_pair(sK6,sK7),sK8) != singleton(sK6)
| ~ sP2 ),
inference(clausify,[status(thm)],[f_5_11]) ).
fof(f_6_1,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = singleton(A)
| ( A != B
& ~ in(B,C) )
| in(A,C) )
& ( ( ( A = B
| in(B,C) )
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[l39_zfmisc_1]) ).
fof(f_6_2,plain,
! [U_17,U_16,U_15] :
( ( set_difference(unordered_pair(U_17,U_16),U_15) = singleton(U_17)
| ( U_17 != U_16
& ~ in(U_16,U_15) )
| in(U_17,U_15) )
& ( ( ( U_17 = U_16
| in(U_16,U_15) )
& ~ in(U_17,U_15) )
| set_difference(unordered_pair(U_17,U_16),U_15) != singleton(U_17) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_23,U_21,U_19] :
( set_difference(unordered_pair(U_23,U_21),U_19) = singleton(U_23)
| ( U_23 != U_21
& ~ in(U_21,U_19) )
| in(U_23,U_19) )
& ! [U_22,U_20,U_18] :
( ( ( U_22 = U_20
| in(U_20,U_18) )
& ~ in(U_22,U_18) )
| set_difference(unordered_pair(U_22,U_20),U_18) != singleton(U_22) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( ~ in(U_22,U_18)
| set_difference(unordered_pair(U_22,U_20),U_18) != singleton(U_22) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( U_22 = U_20
| in(U_20,U_18)
| set_difference(unordered_pair(U_22,U_20),U_18) != singleton(U_22) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( ~ in(U_21,U_19)
| in(U_23,U_19)
| set_difference(unordered_pair(U_23,U_21),U_19) = singleton(U_23) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
( U_23 != U_21
| in(U_23,U_19)
| set_difference(unordered_pair(U_23,U_21),U_19) = singleton(U_23) ),
inference(clausify,[status(thm)],[f_6_3]) ).
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_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( set_difference(Eq_x_0,Eq_x_1) = set_difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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(equality_8,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET927+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
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:08:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.41 % SZS status Theorem for theBenchmark
% 0.14/0.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------