%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET886+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 : 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 08:57:44 AM UTC 2026
% Result : Theorem 12.56s 17.81s
% Output : Proof 12.65s
% 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(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(t26_zfmisc_1,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> A = C ),
file('theBenchmark.p',t26_zfmisc_1) ).
fof(t27_zfmisc_1,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> unordered_pair(A,B) = singleton(C) ),
file('theBenchmark.p',t27_zfmisc_1) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
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] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_2_2,plain,
? [U_2] : empty(U_2),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1)],[f_2_2]) ).
cnf(f_2_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_3_2,plain,
? [U_3] : ~ empty(U_3),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_3,sK2)],[f_3_2]) ).
cnf(f_3_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_4_2,plain,
! [U_5,U_4] : subset(U_5,U_5),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5] : subset(U_5,U_5),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
subset(U_5,U_5),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A,B,C] :
( A = C
| ~ subset(unordered_pair(A,B),singleton(C)) ),
inference(fof_nnf,[status(thm)],[t26_zfmisc_1]) ).
fof(f_5_2,plain,
! [U_8,U_7,U_6] :
( U_8 = U_6
| ~ subset(unordered_pair(U_8,U_7),singleton(U_6)) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( U_8 = U_6
| ~ subset(unordered_pair(U_8,U_7),singleton(U_6)) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> unordered_pair(A,B) = singleton(C) ),
inference(negate,[status(cth)],[t27_zfmisc_1]) ).
fof(f_6_2,negated_conjecture,
? [A,B,C] :
( unordered_pair(A,B) != singleton(C)
& subset(unordered_pair(A,B),singleton(C)) ),
inference(fof_nnf,[status(thm)],[f_6_1]) ).
fof(f_6_3,negated_conjecture,
? [U_11,U_10,U_9] :
( unordered_pair(U_11,U_10) != singleton(U_9)
& subset(unordered_pair(U_11,U_10),singleton(U_9)) ),
inference(variable_rename,[status(thm)],[f_6_2]) ).
fof(f_6_4,negated_conjecture,
? [U_10,U_9] :
( unordered_pair(sK3,U_10) != singleton(U_9)
& subset(unordered_pair(sK3,U_10),singleton(U_9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_11,sK3)],[f_6_3]) ).
fof(f_6_5,negated_conjecture,
? [U_9] :
( unordered_pair(sK3,sK4) != singleton(U_9)
& subset(unordered_pair(sK3,sK4),singleton(U_9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_10,sK4)],[f_6_4]) ).
fof(f_6_6,negated_conjecture,
( unordered_pair(sK3,sK4) != singleton(sK5)
& subset(unordered_pair(sK3,sK4),singleton(sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_9,sK5)],[f_6_5]) ).
fof(f_6_7,negated_conjecture,
( unordered_pair(sK3,sK4) != singleton(sK5)
& subset(unordered_pair(sK3,sK4),singleton(sK5)) ),
inference(definitional_conversion,[status(esa)],[f_6_6]) ).
cnf(f_6_8,negated_conjecture,
subset(unordered_pair(sK3,sK4),singleton(sK5)),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_9,negated_conjecture,
unordered_pair(sK3,sK4) != singleton(sK5),
inference(clausify,[status(thm)],[f_6_7]) ).
fof(f_7_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_7_2,plain,
! [U_12] : unordered_pair(U_12,U_12) = singleton(U_12),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
unordered_pair(U_12,U_12) = singleton(U_12),
inference(clausify,[status(thm)],[f_7_2]) ).
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,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_7,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
% 0.00/0.03 % Problem : SET886+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
% 0.10/5.36 % Computer : n014.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sat Sep 19 23:06:41 UTC 2026
% 0.10/5.37 % CPUTime :
% 12.56/17.81 % SZS status Theorem for theBenchmark
% 12.56/17.81 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------