%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET920+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 : n017.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 08:57:48 AM UTC 2026
% Result : Theorem 9.96s 15.24s
% Output : Proof 9.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 20 unt; 0 def)
% Number of atoms : 202 ( 95 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 247 ( 91 ~; 83 |; 67 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 117 ( 5 sgn 85 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(t63_zfmisc_1,conjecture,
! [A,B,C] :
( set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B)
=> in(A,C) ),
file('theBenchmark.p',t63_zfmisc_1) ).
fof(f_4_1,plain,
! [A,B,C] :
( ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( D = B
| D = A ) )
| ( D != B
& D != A
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( D != B
& D != A ) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(f_4_2,plain,
! [U_10,U_9,U_8] :
( ( U_8 = unordered_pair(U_10,U_9)
| ? [U_7] :
( ( ~ in(U_7,U_8)
& ( U_7 = U_9
| U_7 = U_10 ) )
| ( U_7 != U_9
& U_7 != U_10
& in(U_7,U_8) ) ) )
& ( ! [U_6] :
( ( in(U_6,U_8)
| ( U_6 != U_9
& U_6 != U_10 ) )
& ( U_6 = U_9
| U_6 = U_10
| ~ in(U_6,U_8) ) )
| U_8 != unordered_pair(U_10,U_9) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_20,U_18,U_16] :
( U_16 = unordered_pair(U_20,U_18)
| ? [U_14] :
( ~ in(U_14,U_16)
& ( U_14 = U_18
| U_14 = U_20 ) )
| ? [U_13] :
( U_13 != U_18
& U_13 != U_20
& in(U_13,U_16) ) )
& ! [U_19,U_17,U_15] :
( ( ! [U_12] :
( in(U_12,U_15)
| ( U_12 != U_17
& U_12 != U_19 ) )
& ! [U_11] :
( U_11 = U_17
| U_11 = U_19
| ~ in(U_11,U_15) ) )
| U_15 != unordered_pair(U_19,U_17) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_20,U_18,U_16] :
( U_16 = unordered_pair(U_20,U_18)
| ? [U_14] :
( ~ in(U_14,U_16)
& ( U_14 = U_18
| U_14 = U_20 ) )
| ( sK1(U_20,U_18,U_16) != U_18
& sK1(U_20,U_18,U_16) != U_20
& in(sK1(U_20,U_18,U_16),U_16) ) )
& ! [U_19,U_17,U_15] :
( ( ! [U_12] :
( in(U_12,U_15)
| ( U_12 != U_17
& U_12 != U_19 ) )
& ! [U_11] :
( U_11 = U_17
| U_11 = U_19
| ~ in(U_11,U_15) ) )
| U_15 != unordered_pair(U_19,U_17) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_13,sK1(U_20,U_18,U_16))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_20,U_18,U_16] :
( U_16 = unordered_pair(U_20,U_18)
| ( ~ in(sK2(U_20,U_18,U_16),U_16)
& ( sK2(U_20,U_18,U_16) = U_18
| sK2(U_20,U_18,U_16) = U_20 ) )
| ( sK1(U_20,U_18,U_16) != U_18
& sK1(U_20,U_18,U_16) != U_20
& in(sK1(U_20,U_18,U_16),U_16) ) )
& ! [U_19,U_17,U_15] :
( ( ! [U_12] :
( in(U_12,U_15)
| ( U_12 != U_17
& U_12 != U_19 ) )
& ! [U_11] :
( U_11 = U_17
| U_11 = U_19
| ~ in(U_11,U_15) ) )
| U_15 != unordered_pair(U_19,U_17) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_14,sK2(U_20,U_18,U_16))],[f_4_4]) ).
cnf(f_4_7,plain,
( U_12 != U_19
| in(U_12,U_15)
| U_15 != unordered_pair(U_19,U_17) ),
inference(clausify,[status(thm)],[f_4_5]) ).
fof(f_5_1,plain,
! [A,B,C] :
( ( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(D,B)
& in(D,A) )
| ( ( ~ in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(D,B)
| ~ in(D,A) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(f_5_2,plain,
! [U_25,U_24,U_23] :
( ( U_23 = set_intersection2(U_25,U_24)
| ? [U_22] :
( ( ~ in(U_22,U_23)
& in(U_22,U_24)
& in(U_22,U_25) )
| ( ( ~ in(U_22,U_24)
| ~ in(U_22,U_25) )
& in(U_22,U_23) ) ) )
& ( ! [U_21] :
( ( in(U_21,U_23)
| ~ in(U_21,U_24)
| ~ in(U_21,U_25) )
& ( ( in(U_21,U_24)
& in(U_21,U_25) )
| ~ in(U_21,U_23) ) )
| U_23 != set_intersection2(U_25,U_24) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_35,U_33,U_31] :
( U_31 = set_intersection2(U_35,U_33)
| ? [U_29] :
( ~ in(U_29,U_31)
& in(U_29,U_33)
& in(U_29,U_35) )
| ? [U_28] :
( ( ~ in(U_28,U_33)
| ~ in(U_28,U_35) )
& in(U_28,U_31) ) )
& ! [U_34,U_32,U_30] :
( ( ! [U_27] :
( in(U_27,U_30)
| ~ in(U_27,U_32)
| ~ in(U_27,U_34) )
& ! [U_26] :
( ( in(U_26,U_32)
& in(U_26,U_34) )
| ~ in(U_26,U_30) ) )
| U_30 != set_intersection2(U_34,U_32) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_35,U_33,U_31] :
( U_31 = set_intersection2(U_35,U_33)
| ? [U_29] :
( ~ in(U_29,U_31)
& in(U_29,U_33)
& in(U_29,U_35) )
| ( ( ~ in(sK3(U_35,U_33,U_31),U_33)
| ~ in(sK3(U_35,U_33,U_31),U_35) )
& in(sK3(U_35,U_33,U_31),U_31) ) )
& ! [U_34,U_32,U_30] :
( ( ! [U_27] :
( in(U_27,U_30)
| ~ in(U_27,U_32)
| ~ in(U_27,U_34) )
& ! [U_26] :
( ( in(U_26,U_32)
& in(U_26,U_34) )
| ~ in(U_26,U_30) ) )
| U_30 != set_intersection2(U_34,U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_28,sK3(U_35,U_33,U_31))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_35,U_33,U_31] :
( U_31 = set_intersection2(U_35,U_33)
| ( ~ in(sK4(U_35,U_33,U_31),U_31)
& in(sK4(U_35,U_33,U_31),U_33)
& in(sK4(U_35,U_33,U_31),U_35) )
| ( ( ~ in(sK3(U_35,U_33,U_31),U_33)
| ~ in(sK3(U_35,U_33,U_31),U_35) )
& in(sK3(U_35,U_33,U_31),U_31) ) )
& ! [U_34,U_32,U_30] :
( ( ! [U_27] :
( in(U_27,U_30)
| ~ in(U_27,U_32)
| ~ in(U_27,U_34) )
& ! [U_26] :
( ( in(U_26,U_32)
& in(U_26,U_34) )
| ~ in(U_26,U_30) ) )
| U_30 != set_intersection2(U_34,U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_29,sK4(U_35,U_33,U_31))],[f_5_4]) ).
cnf(f_5_7,plain,
( in(U_26,U_32)
| ~ in(U_26,U_30)
| U_30 != set_intersection2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_5_5]) ).
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_37,U_36] : set_intersection2(U_37,U_37) = U_37,
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_37] : set_intersection2(U_37,U_37) = U_37,
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
set_intersection2(U_37,U_37) = U_37,
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_9_1,negated_conjecture,
~ ! [A,B,C] :
( set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B)
=> in(A,C) ),
inference(negate,[status(cth)],[t63_zfmisc_1]) ).
fof(f_9_2,negated_conjecture,
? [A,B,C] :
( ~ in(A,C)
& set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B) ),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_42,U_41,U_40] :
( ~ in(U_42,U_40)
& set_intersection2(unordered_pair(U_42,U_41),U_40) = unordered_pair(U_42,U_41) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
? [U_41,U_40] :
( ~ in(sK7,U_40)
& set_intersection2(unordered_pair(sK7,U_41),U_40) = unordered_pair(sK7,U_41) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_42,sK7)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
? [U_40] :
( ~ in(sK7,U_40)
& set_intersection2(unordered_pair(sK7,sK8),U_40) = unordered_pair(sK7,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_41,sK8)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( ~ in(sK7,sK9)
& set_intersection2(unordered_pair(sK7,sK8),sK9) = unordered_pair(sK7,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_40,sK9)],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( ~ in(sK7,sK9)
& set_intersection2(unordered_pair(sK7,sK8),sK9) = unordered_pair(sK7,sK8) ),
inference(definitional_conversion,[status(esa)],[f_9_6]) ).
cnf(f_9_8,negated_conjecture,
set_intersection2(unordered_pair(sK7,sK8),sK9) = unordered_pair(sK7,sK8),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_9,negated_conjecture,
~ in(sK7,sK9),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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(t1,plain,
~ in(sK7,sK9),
inference(start,[status(thm),parent(0:0)],[f_9_9]) ).
cnf(t2,plain,
( ~ in(sK7,set_intersection2(set_intersection2(unordered_pair(sK7,sK8),sK9),set_intersection2(unordered_pair(sK7,sK8),sK9)))
| set_intersection2(set_intersection2(unordered_pair(sK7,sK8),sK9),set_intersection2(unordered_pair(sK7,sK8),sK9)) != set_intersection2(unordered_pair(sK7,sK8),sK9)
| in(sK7,sK9) ),
inference(extension,[status(thm),parent(t1:1)],[f_5_7]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
set_intersection2(set_intersection2(unordered_pair(sK7,sK8),sK9),set_intersection2(unordered_pair(sK7,sK8),sK9)) = set_intersection2(unordered_pair(sK7,sK8),sK9),
inference(extension,[status(thm),parent(t2:2)],[f_6_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( sK7 != sK7
| set_intersection2(set_intersection2(unordered_pair(sK7,sK8),sK9),set_intersection2(unordered_pair(sK7,sK8),sK9)) != unordered_pair(sK7,sK8)
| in(sK7,set_intersection2(set_intersection2(unordered_pair(sK7,sK8),sK9),set_intersection2(unordered_pair(sK7,sK8),sK9))) ),
inference(extension,[status(thm),parent(t2:3)],[f_4_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( set_intersection2(unordered_pair(sK7,sK8),sK9) != unordered_pair(sK7,sK8)
| set_intersection2(set_intersection2(unordered_pair(sK7,sK8),sK9),set_intersection2(unordered_pair(sK7,sK8),sK9)) != set_intersection2(unordered_pair(sK7,sK8),sK9)
| set_intersection2(set_intersection2(unordered_pair(sK7,sK8),sK9),set_intersection2(unordered_pair(sK7,sK8),sK9)) = unordered_pair(sK7,sK8) ),
inference(extension,[status(thm),parent(t6:2)],[equality_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
set_intersection2(set_intersection2(unordered_pair(sK7,sK8),sK9),set_intersection2(unordered_pair(sK7,sK8),sK9)) = set_intersection2(unordered_pair(sK7,sK8),sK9),
inference(extension,[status(thm),parent(t8:2)],[f_6_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
set_intersection2(unordered_pair(sK7,sK8),sK9) = unordered_pair(sK7,sK8),
inference(extension,[status(thm),parent(t8:3)],[f_9_8]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
sK7 = sK7,
inference(extension,[status(thm),parent(t6:3)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET920+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
% 0.09/5.36 % Computer : n017.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 19 23:02:46 UTC 2026
% 0.09/5.37 % CPUTime :
% 9.96/15.24 % SZS status Theorem for theBenchmark
% 9.96/15.24 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------