%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET930+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 : n015.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 0.57s 6.06s
% Output : Proof 0.57s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
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(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(t72_zfmisc_1,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(B,C)
& ~ in(A,C) ) ),
file('theBenchmark.p',t72_zfmisc_1) ).
fof(t73_zfmisc_1,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t73_zfmisc_1) ).
fof(t74_zfmisc_1,conjecture,
! [A,B,C] :
~ ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != empty_set ),
file('theBenchmark.p',t74_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
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,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_3_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_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_4_2,plain,
! [U_6,U_5,U_4] :
( ( set_difference(unordered_pair(U_6,U_5),U_4) = singleton(U_6)
| ( U_6 != U_5
& ~ in(U_5,U_4) )
| in(U_6,U_4) )
& ( ( ( U_6 = U_5
| in(U_5,U_4) )
& ~ in(U_6,U_4) )
| set_difference(unordered_pair(U_6,U_5),U_4) != singleton(U_6) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_12,U_10,U_8] :
( set_difference(unordered_pair(U_12,U_10),U_8) = singleton(U_12)
| ( U_12 != U_10
& ~ in(U_10,U_8) )
| in(U_12,U_8) )
& ! [U_11,U_9,U_7] :
( ( ( U_11 = U_9
| in(U_9,U_7) )
& ~ in(U_11,U_7) )
| set_difference(unordered_pair(U_11,U_9),U_7) != singleton(U_11) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( ~ in(U_11,U_7)
| set_difference(unordered_pair(U_11,U_9),U_7) != singleton(U_11) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( U_11 = U_9
| in(U_9,U_7)
| set_difference(unordered_pair(U_11,U_9),U_7) != singleton(U_11) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( ~ in(U_10,U_8)
| in(U_12,U_8)
| set_difference(unordered_pair(U_12,U_10),U_8) = singleton(U_12) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_7,plain,
( U_12 != U_10
| in(U_12,U_8)
| set_difference(unordered_pair(U_12,U_10),U_8) = singleton(U_12) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_5_2,plain,
? [U_13] : empty(U_13),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_13,sK1)],[f_5_2]) ).
cnf(f_5_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_6_2,plain,
? [U_14] : ~ empty(U_14),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_14,sK2)],[f_6_2]) ).
cnf(f_6_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
| in(B,C)
| in(A,C) )
& ( ( ~ in(B,C)
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[t72_zfmisc_1]) ).
fof(f_7_2,plain,
! [U_17,U_16,U_15] :
( ( set_difference(unordered_pair(U_17,U_16),U_15) = unordered_pair(U_17,U_16)
| in(U_16,U_15)
| in(U_17,U_15) )
& ( ( ~ in(U_16,U_15)
& ~ in(U_17,U_15) )
| set_difference(unordered_pair(U_17,U_16),U_15) != unordered_pair(U_17,U_16) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_23,U_21,U_19] :
( set_difference(unordered_pair(U_23,U_21),U_19) = unordered_pair(U_23,U_21)
| in(U_21,U_19)
| in(U_23,U_19) )
& ! [U_22,U_20,U_18] :
( ( ~ in(U_20,U_18)
& ~ in(U_22,U_18) )
| set_difference(unordered_pair(U_22,U_20),U_18) != unordered_pair(U_22,U_20) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( ~ in(U_22,U_18)
| set_difference(unordered_pair(U_22,U_20),U_18) != unordered_pair(U_22,U_20) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( ~ in(U_20,U_18)
| set_difference(unordered_pair(U_22,U_20),U_18) != unordered_pair(U_22,U_20) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( set_difference(unordered_pair(U_23,U_21),U_19) = unordered_pair(U_23,U_21)
| in(U_21,U_19)
| in(U_23,U_19) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = empty_set
| ~ in(B,C)
| ~ in(A,C) )
& ( ( in(B,C)
& in(A,C) )
| set_difference(unordered_pair(A,B),C) != empty_set ) ),
inference(fof_nnf,[status(thm)],[t73_zfmisc_1]) ).
fof(f_8_2,plain,
! [U_26,U_25,U_24] :
( ( set_difference(unordered_pair(U_26,U_25),U_24) = empty_set
| ~ in(U_25,U_24)
| ~ in(U_26,U_24) )
& ( ( in(U_25,U_24)
& in(U_26,U_24) )
| set_difference(unordered_pair(U_26,U_25),U_24) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_32,U_30,U_28] :
( set_difference(unordered_pair(U_32,U_30),U_28) = empty_set
| ~ in(U_30,U_28)
| ~ in(U_32,U_28) )
& ! [U_31,U_29,U_27] :
( ( in(U_29,U_27)
& in(U_31,U_27) )
| set_difference(unordered_pair(U_31,U_29),U_27) != empty_set ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( in(U_31,U_27)
| set_difference(unordered_pair(U_31,U_29),U_27) != empty_set ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( in(U_29,U_27)
| set_difference(unordered_pair(U_31,U_29),U_27) != empty_set ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( set_difference(unordered_pair(U_32,U_30),U_28) = empty_set
| ~ in(U_30,U_28)
| ~ in(U_32,U_28) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,negated_conjecture,
~ ! [A,B,C] :
~ ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != empty_set ),
inference(negate,[status(cth)],[t74_zfmisc_1]) ).
fof(f_9_2,negated_conjecture,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != empty_set ),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_35,U_34,U_33] :
( set_difference(unordered_pair(U_35,U_34),U_33) != unordered_pair(U_35,U_34)
& set_difference(unordered_pair(U_35,U_34),U_33) != singleton(U_34)
& set_difference(unordered_pair(U_35,U_34),U_33) != singleton(U_35)
& set_difference(unordered_pair(U_35,U_34),U_33) != empty_set ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
? [U_34,U_33] :
( set_difference(unordered_pair(sK3,U_34),U_33) != unordered_pair(sK3,U_34)
& set_difference(unordered_pair(sK3,U_34),U_33) != singleton(U_34)
& set_difference(unordered_pair(sK3,U_34),U_33) != singleton(sK3)
& set_difference(unordered_pair(sK3,U_34),U_33) != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_35,sK3)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
? [U_33] :
( set_difference(unordered_pair(sK3,sK4),U_33) != unordered_pair(sK3,sK4)
& set_difference(unordered_pair(sK3,sK4),U_33) != singleton(sK4)
& set_difference(unordered_pair(sK3,sK4),U_33) != singleton(sK3)
& set_difference(unordered_pair(sK3,sK4),U_33) != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_34,sK4)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( set_difference(unordered_pair(sK3,sK4),sK5) != unordered_pair(sK3,sK4)
& set_difference(unordered_pair(sK3,sK4),sK5) != singleton(sK4)
& set_difference(unordered_pair(sK3,sK4),sK5) != singleton(sK3)
& set_difference(unordered_pair(sK3,sK4),sK5) != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_33,sK5)],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( set_difference(unordered_pair(sK3,sK4),sK5) != unordered_pair(sK3,sK4)
& set_difference(unordered_pair(sK3,sK4),sK5) != singleton(sK4)
& set_difference(unordered_pair(sK3,sK4),sK5) != singleton(sK3)
& set_difference(unordered_pair(sK3,sK4),sK5) != empty_set ),
inference(definitional_conversion,[status(esa)],[f_9_6]) ).
cnf(f_9_8,negated_conjecture,
set_difference(unordered_pair(sK3,sK4),sK5) != empty_set,
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_9,negated_conjecture,
set_difference(unordered_pair(sK3,sK4),sK5) != singleton(sK3),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_10,negated_conjecture,
set_difference(unordered_pair(sK3,sK4),sK5) != singleton(sK4),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_11,negated_conjecture,
set_difference(unordered_pair(sK3,sK4),sK5) != unordered_pair(sK3,sK4),
inference(clausify,[status(thm)],[f_9_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(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
% 0.00/0.02 % Problem : SET930+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
% 0.09/5.58 % Computer : n015.cluster.edu
% 0.09/5.58 % Model : x86_64 x86_64
% 0.09/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.58 % Memory : 8046.5625MB
% 0.09/5.58 % OS : Linux 6.8.0-71-generic
% 0.09/5.58 % CPULimit : 300
% 0.09/5.58 % WCLimit : 300
% 0.09/5.58 % DateTime : Sat Sep 19 23:11:25 UTC 2026
% 0.09/5.58 % CPUTime :
% 0.57/6.06 % SZS status Theorem for theBenchmark
% 0.57/6.06 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------