%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET974+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 : n004.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 08:57:53 AM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.13s
% 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(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_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(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t104_zfmisc_1,axiom,
! [A,B,C,D,E] :
~ ( ! [F,G] :
~ ( in(G,set_intersection2(C,E))
& in(F,set_intersection2(B,D))
& A = ordered_pair(F,G) )
& in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
file('theBenchmark.p',t104_zfmisc_1) ).
fof(t127_zfmisc_1,conjecture,
! [A,B,C,D] :
( ( disjoint(C,D)
| disjoint(A,B) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t127_zfmisc_1) ).
fof(t4_xboole_0,axiom,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
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,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_3_2,plain,
! [U_5,U_4] : set_intersection2(U_5,U_4) = set_intersection2(U_4,U_5),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
set_intersection2(U_5,U_4) = set_intersection2(U_4,U_5),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_4_2,plain,
! [U_7,U_6] : ordered_pair(U_7,U_6) = unordered_pair(unordered_pair(U_7,U_6),singleton(U_7)),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
ordered_pair(U_7,U_6) = unordered_pair(unordered_pair(U_7,U_6),singleton(U_7)),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_5_2,plain,
! [U_9,U_8] : ~ empty(ordered_pair(U_9,U_8)),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
~ empty(ordered_pair(U_9,U_8)),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_6_2,plain,
! [U_11,U_10] : set_intersection2(U_11,U_11) = U_11,
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_11] : set_intersection2(U_11,U_11) = U_11,
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
set_intersection2(U_11,U_11) = U_11,
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_7_2,plain,
? [U_12] : empty(U_12),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_12,sK1)],[f_7_2]) ).
cnf(f_7_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_8_2,plain,
? [U_13] : ~ empty(U_13),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_13,sK2)],[f_8_2]) ).
cnf(f_8_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_9_2,plain,
! [U_15,U_14] :
( disjoint(U_14,U_15)
| ~ disjoint(U_15,U_14) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( disjoint(U_14,U_15)
| ~ disjoint(U_15,U_14) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A,B,C,D,E] :
( ? [F,G] :
( in(G,set_intersection2(C,E))
& in(F,set_intersection2(B,D))
& A = ordered_pair(F,G) )
| ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
inference(fof_nnf,[status(thm)],[t104_zfmisc_1]) ).
fof(f_10_2,plain,
! [U_22,U_21,U_20,U_19,U_18] :
( ? [U_17,U_16] :
( in(U_16,set_intersection2(U_20,U_18))
& in(U_17,set_intersection2(U_21,U_19))
& U_22 = ordered_pair(U_17,U_16) )
| ~ in(U_22,set_intersection2(cartesian_product2(U_21,U_20),cartesian_product2(U_19,U_18))) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_22,U_21,U_20,U_19,U_18] :
( ? [U_17] :
( ? [U_16] :
( in(U_16,set_intersection2(U_20,U_18))
& U_22 = ordered_pair(U_17,U_16) )
& in(U_17,set_intersection2(U_21,U_19)) )
| ~ in(U_22,set_intersection2(cartesian_product2(U_21,U_20),cartesian_product2(U_19,U_18))) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
! [U_22,U_21,U_20,U_19,U_18] :
( ( ? [U_16] :
( in(U_16,set_intersection2(U_20,U_18))
& U_22 = ordered_pair(sK3(U_22,U_21,U_20,U_19,U_18),U_16) )
& in(sK3(U_22,U_21,U_20,U_19,U_18),set_intersection2(U_21,U_19)) )
| ~ in(U_22,set_intersection2(cartesian_product2(U_21,U_20),cartesian_product2(U_19,U_18))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_17,sK3(U_22,U_21,U_20,U_19,U_18))],[f_10_3]) ).
fof(f_10_5,plain,
! [U_22,U_21,U_20,U_19,U_18] :
( ( in(sK4(U_22,U_21,U_20,U_19,U_18),set_intersection2(U_20,U_18))
& U_22 = ordered_pair(sK3(U_22,U_21,U_20,U_19,U_18),sK4(U_22,U_21,U_20,U_19,U_18))
& in(sK3(U_22,U_21,U_20,U_19,U_18),set_intersection2(U_21,U_19)) )
| ~ in(U_22,set_intersection2(cartesian_product2(U_21,U_20),cartesian_product2(U_19,U_18))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_16,sK4(U_22,U_21,U_20,U_19,U_18))],[f_10_4]) ).
cnf(f_10_6,plain,
( in(sK3(U_22,U_21,U_20,U_19,U_18),set_intersection2(U_21,U_19))
| ~ in(U_22,set_intersection2(cartesian_product2(U_21,U_20),cartesian_product2(U_19,U_18))) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( U_22 = ordered_pair(sK3(U_22,U_21,U_20,U_19,U_18),sK4(U_22,U_21,U_20,U_19,U_18))
| ~ in(U_22,set_intersection2(cartesian_product2(U_21,U_20),cartesian_product2(U_19,U_18))) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( in(sK4(U_22,U_21,U_20,U_19,U_18),set_intersection2(U_20,U_18))
| ~ in(U_22,set_intersection2(cartesian_product2(U_21,U_20),cartesian_product2(U_19,U_18))) ),
inference(clausify,[status(thm)],[f_10_5]) ).
fof(f_11_1,negated_conjecture,
~ ! [A,B,C,D] :
( ( disjoint(C,D)
| disjoint(A,B) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(negate,[status(cth)],[t127_zfmisc_1]) ).
fof(f_11_2,negated_conjecture,
? [A,B,C,D] :
( ~ disjoint(cartesian_product2(A,C),cartesian_product2(B,D))
& ( disjoint(C,D)
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_26,U_25,U_24,U_23] :
( ~ disjoint(cartesian_product2(U_26,U_24),cartesian_product2(U_25,U_23))
& ( disjoint(U_24,U_23)
| disjoint(U_26,U_25) ) ),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
? [U_25,U_24,U_23] :
( ~ disjoint(cartesian_product2(sK5,U_24),cartesian_product2(U_25,U_23))
& ( disjoint(U_24,U_23)
| disjoint(sK5,U_25) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_26,sK5)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
? [U_24,U_23] :
( ~ disjoint(cartesian_product2(sK5,U_24),cartesian_product2(sK6,U_23))
& ( disjoint(U_24,U_23)
| disjoint(sK5,sK6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_25,sK6)],[f_11_4]) ).
fof(f_11_6,negated_conjecture,
? [U_23] :
( ~ disjoint(cartesian_product2(sK5,sK7),cartesian_product2(sK6,U_23))
& ( disjoint(sK7,U_23)
| disjoint(sK5,sK6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_24,sK7)],[f_11_5]) ).
fof(f_11_7,negated_conjecture,
( ~ disjoint(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK8))
& ( disjoint(sK7,sK8)
| disjoint(sK5,sK6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_23,sK8)],[f_11_6]) ).
fof(f_11_8,negated_conjecture,
( ~ disjoint(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK8))
& ( disjoint(sK7,sK8)
| disjoint(sK5,sK6) ) ),
inference(definitional_conversion,[status(esa)],[f_11_7]) ).
cnf(f_11_9,negated_conjecture,
( disjoint(sK7,sK8)
| disjoint(sK5,sK6) ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_10,negated_conjecture,
~ disjoint(cartesian_product2(sK5,sK7),cartesian_product2(sK6,sK8)),
inference(clausify,[status(thm)],[f_11_8]) ).
fof(f_12_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t4_xboole_0]) ).
fof(f_12_2,plain,
! [U_30,U_29] :
( ( ~ disjoint(U_30,U_29)
| ! [U_28] : ~ in(U_28,set_intersection2(U_30,U_29)) )
& ( ? [U_27] : in(U_27,set_intersection2(U_30,U_29))
| disjoint(U_30,U_29) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_34,U_32] :
( ~ disjoint(U_34,U_32)
| ! [U_28] : ~ in(U_28,set_intersection2(U_34,U_32)) )
& ! [U_33,U_31] :
( ? [U_27] : in(U_27,set_intersection2(U_33,U_31))
| disjoint(U_33,U_31) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_34,U_32] :
( ~ disjoint(U_34,U_32)
| ! [U_28] : ~ in(U_28,set_intersection2(U_34,U_32)) )
& ! [U_33,U_31] :
( in(sK9(U_33,U_31),set_intersection2(U_33,U_31))
| disjoint(U_33,U_31) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_27,sK9(U_33,U_31))],[f_12_3]) ).
cnf(f_12_5,plain,
( in(sK9(U_33,U_31),set_intersection2(U_33,U_31))
| disjoint(U_33,U_31) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_6,plain,
( ~ disjoint(U_34,U_32)
| ~ in(U_28,set_intersection2(U_34,U_32)) ),
inference(clausify,[status(thm)],[f_12_4]) ).
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_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(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,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_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_7,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,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_13,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(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 : SET974+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
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 23:09:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.41 % SZS status Theorem for theBenchmark
% 0.13/0.41 % SZS output start Proof for theBenchmark
% See solution above
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