%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET929+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 : n014.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 0.11s 0.43s
% Output : Proof 0.11s
% 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(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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t38_zfmisc_1,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t73_zfmisc_1,conjecture,
! [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(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] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_4_2,plain,
? [U_4] : empty(U_4),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_4,sK1)],[f_4_2]) ).
cnf(f_4_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_5_2,plain,
? [U_5] : ~ empty(U_5),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_5,sK2)],[f_5_2]) ).
cnf(f_5_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_6_2,plain,
! [U_7,U_6] : subset(U_7,U_7),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_7] : subset(U_7,U_7),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
subset(U_7,U_7),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A,B] :
( ( set_difference(A,B) = empty_set
| ~ subset(A,B) )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[t37_xboole_1]) ).
fof(f_7_2,plain,
! [U_9,U_8] :
( ( set_difference(U_9,U_8) = empty_set
| ~ subset(U_9,U_8) )
& ( subset(U_9,U_8)
| set_difference(U_9,U_8) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_13,U_11] :
( set_difference(U_13,U_11) = empty_set
| ~ subset(U_13,U_11) )
& ! [U_12,U_10] :
( subset(U_12,U_10)
| set_difference(U_12,U_10) != empty_set ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( subset(U_12,U_10)
| set_difference(U_12,U_10) != empty_set ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( set_difference(U_13,U_11) = empty_set
| ~ subset(U_13,U_11) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B,C] :
( ( subset(unordered_pair(A,B),C)
| ~ in(B,C)
| ~ in(A,C) )
& ( ( in(B,C)
& in(A,C) )
| ~ subset(unordered_pair(A,B),C) ) ),
inference(fof_nnf,[status(thm)],[t38_zfmisc_1]) ).
fof(f_8_2,plain,
! [U_16,U_15,U_14] :
( ( subset(unordered_pair(U_16,U_15),U_14)
| ~ in(U_15,U_14)
| ~ in(U_16,U_14) )
& ( ( in(U_15,U_14)
& in(U_16,U_14) )
| ~ subset(unordered_pair(U_16,U_15),U_14) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_22,U_20,U_18] :
( subset(unordered_pair(U_22,U_20),U_18)
| ~ in(U_20,U_18)
| ~ in(U_22,U_18) )
& ! [U_21,U_19,U_17] :
( ( in(U_19,U_17)
& in(U_21,U_17) )
| ~ subset(unordered_pair(U_21,U_19),U_17) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( in(U_21,U_17)
| ~ subset(unordered_pair(U_21,U_19),U_17) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( in(U_19,U_17)
| ~ subset(unordered_pair(U_21,U_19),U_17) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( subset(unordered_pair(U_22,U_20),U_18)
| ~ in(U_20,U_18)
| ~ in(U_22,U_18) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(B,C)
& in(A,C) ) ),
inference(negate,[status(cth)],[t73_zfmisc_1]) ).
fof(f_9_2,negated_conjecture,
? [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)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_25,U_24,U_23] :
( ( set_difference(unordered_pair(U_25,U_24),U_23) != empty_set
& in(U_24,U_23)
& in(U_25,U_23) )
| ( ( ~ in(U_24,U_23)
| ~ in(U_25,U_23) )
& set_difference(unordered_pair(U_25,U_24),U_23) = empty_set ) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
( ? [U_31,U_29,U_27] :
( set_difference(unordered_pair(U_31,U_29),U_27) != empty_set
& in(U_29,U_27)
& in(U_31,U_27) )
| ? [U_30,U_28,U_26] :
( ( ~ in(U_28,U_26)
| ~ in(U_30,U_26) )
& set_difference(unordered_pair(U_30,U_28),U_26) = empty_set ) ),
inference(miniscope,[status(thm)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
( ? [U_31,U_29,U_27] :
( set_difference(unordered_pair(U_31,U_29),U_27) != empty_set
& in(U_29,U_27)
& in(U_31,U_27) )
| ? [U_28,U_26] :
( ( ~ in(U_28,U_26)
| ~ in(sK3,U_26) )
& set_difference(unordered_pair(sK3,U_28),U_26) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_30,sK3)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( ? [U_31,U_29,U_27] :
( set_difference(unordered_pair(U_31,U_29),U_27) != empty_set
& in(U_29,U_27)
& in(U_31,U_27) )
| ? [U_26] :
( ( ~ in(sK4,U_26)
| ~ in(sK3,U_26) )
& set_difference(unordered_pair(sK3,sK4),U_26) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_28,sK4)],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( ? [U_31,U_29,U_27] :
( set_difference(unordered_pair(U_31,U_29),U_27) != empty_set
& in(U_29,U_27)
& in(U_31,U_27) )
| ( ( ~ in(sK4,sK5)
| ~ in(sK3,sK5) )
& set_difference(unordered_pair(sK3,sK4),sK5) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_26,sK5)],[f_9_6]) ).
fof(f_9_8,negated_conjecture,
( ? [U_29,U_27] :
( set_difference(unordered_pair(sK6,U_29),U_27) != empty_set
& in(U_29,U_27)
& in(sK6,U_27) )
| ( ( ~ in(sK4,sK5)
| ~ in(sK3,sK5) )
& set_difference(unordered_pair(sK3,sK4),sK5) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_31,sK6)],[f_9_7]) ).
fof(f_9_9,negated_conjecture,
( ? [U_27] :
( set_difference(unordered_pair(sK6,sK7),U_27) != empty_set
& in(sK7,U_27)
& in(sK6,U_27) )
| ( ( ~ in(sK4,sK5)
| ~ in(sK3,sK5) )
& set_difference(unordered_pair(sK3,sK4),sK5) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_29,sK7)],[f_9_8]) ).
fof(f_9_10,negated_conjecture,
( ( set_difference(unordered_pair(sK6,sK7),sK8) != empty_set
& in(sK7,sK8)
& in(sK6,sK8) )
| ( ( ~ in(sK4,sK5)
| ~ in(sK3,sK5) )
& set_difference(unordered_pair(sK3,sK4),sK5) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_27,sK8)],[f_9_9]) ).
fof(f_9_11,negated_conjecture,
( ( set_difference(unordered_pair(sK6,sK7),sK8) != empty_set
| ~ sP1 )
& ( in(sK7,sK8)
| ~ sP1 )
& ( in(sK6,sK8)
| ~ sP1 )
& ( ~ in(sK4,sK5)
| ~ in(sK3,sK5)
| ~ sP0 )
& ( set_difference(unordered_pair(sK3,sK4),sK5) = empty_set
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_9_10]) ).
cnf(f_9_12,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_9_11]) ).
cnf(f_9_13,negated_conjecture,
( set_difference(unordered_pair(sK3,sK4),sK5) = empty_set
| ~ sP0 ),
inference(clausify,[status(thm)],[f_9_11]) ).
cnf(f_9_14,negated_conjecture,
( ~ in(sK4,sK5)
| ~ in(sK3,sK5)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_9_11]) ).
cnf(f_9_15,negated_conjecture,
( in(sK6,sK8)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_9_11]) ).
cnf(f_9_16,negated_conjecture,
( in(sK7,sK8)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_9_11]) ).
cnf(f_9_17,negated_conjecture,
( set_difference(unordered_pair(sK6,sK7),sK8) != empty_set
| ~ sP1 ),
inference(clausify,[status(thm)],[f_9_11]) ).
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,
( 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_7,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_8,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| 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 : SET929+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 19 23:07:51 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.11/0.43 % SZS status Theorem for theBenchmark
% 0.11/0.43 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------