%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET909+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 08:57:46 AM UTC 2026
% Result : Theorem 1.05s 6.31s
% Output : Proof 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 32 unt; 0 def)
% Number of atoms : 214 ( 107 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 253 ( 94 ~; 90 |; 64 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 146 ( 6 sgn 109 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
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(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(t50_zfmisc_1,conjecture,
! [A,B,C] : set_union2(unordered_pair(A,B),C) != empty_set,
file('theBenchmark.p',t50_zfmisc_1) ).
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_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_3_2,plain,
! [U_5,U_4] : set_union2(U_5,U_4) = set_union2(U_4,U_5),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
set_union2(U_5,U_4) = set_union2(U_4,U_5),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_4_2,plain,
! [U_8] :
( ( U_8 = empty_set
| ? [U_7] : in(U_7,U_8) )
& ( ! [U_6] : ~ in(U_6,U_8)
| U_8 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_10] :
( U_10 = empty_set
| ? [U_7] : in(U_7,U_10) )
& ! [U_9] :
( ! [U_6] : ~ in(U_6,U_9)
| U_9 != empty_set ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_10] :
( U_10 = empty_set
| in(sK1(U_10),U_10) )
& ! [U_9] :
( ! [U_6] : ~ in(U_6,U_9)
| U_9 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_7,sK1(U_10))],[f_4_3]) ).
cnf(f_4_5,plain,
( ~ in(U_6,U_9)
| U_9 != empty_set ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_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_5_2,plain,
! [U_15,U_14,U_13] :
( ( U_13 = unordered_pair(U_15,U_14)
| ? [U_12] :
( ( ~ in(U_12,U_13)
& ( U_12 = U_14
| U_12 = U_15 ) )
| ( U_12 != U_14
& U_12 != U_15
& in(U_12,U_13) ) ) )
& ( ! [U_11] :
( ( in(U_11,U_13)
| ( U_11 != U_14
& U_11 != U_15 ) )
& ( U_11 = U_14
| U_11 = U_15
| ~ in(U_11,U_13) ) )
| U_13 != unordered_pair(U_15,U_14) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_25,U_23,U_21] :
( U_21 = unordered_pair(U_25,U_23)
| ? [U_19] :
( ~ in(U_19,U_21)
& ( U_19 = U_23
| U_19 = U_25 ) )
| ? [U_18] :
( U_18 != U_23
& U_18 != U_25
& in(U_18,U_21) ) )
& ! [U_24,U_22,U_20] :
( ( ! [U_17] :
( in(U_17,U_20)
| ( U_17 != U_22
& U_17 != U_24 ) )
& ! [U_16] :
( U_16 = U_22
| U_16 = U_24
| ~ in(U_16,U_20) ) )
| U_20 != unordered_pair(U_24,U_22) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_25,U_23,U_21] :
( U_21 = unordered_pair(U_25,U_23)
| ? [U_19] :
( ~ in(U_19,U_21)
& ( U_19 = U_23
| U_19 = U_25 ) )
| ( sK2(U_25,U_23,U_21) != U_23
& sK2(U_25,U_23,U_21) != U_25
& in(sK2(U_25,U_23,U_21),U_21) ) )
& ! [U_24,U_22,U_20] :
( ( ! [U_17] :
( in(U_17,U_20)
| ( U_17 != U_22
& U_17 != U_24 ) )
& ! [U_16] :
( U_16 = U_22
| U_16 = U_24
| ~ in(U_16,U_20) ) )
| U_20 != unordered_pair(U_24,U_22) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_18,sK2(U_25,U_23,U_21))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_25,U_23,U_21] :
( U_21 = unordered_pair(U_25,U_23)
| ( ~ in(sK3(U_25,U_23,U_21),U_21)
& ( sK3(U_25,U_23,U_21) = U_23
| sK3(U_25,U_23,U_21) = U_25 ) )
| ( sK2(U_25,U_23,U_21) != U_23
& sK2(U_25,U_23,U_21) != U_25
& in(sK2(U_25,U_23,U_21),U_21) ) )
& ! [U_24,U_22,U_20] :
( ( ! [U_17] :
( in(U_17,U_20)
| ( U_17 != U_22
& U_17 != U_24 ) )
& ! [U_16] :
( U_16 = U_22
| U_16 = U_24
| ~ in(U_16,U_20) ) )
| U_20 != unordered_pair(U_24,U_22) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3(U_25,U_23,U_21))],[f_5_4]) ).
cnf(f_5_8,plain,
( U_17 != U_22
| in(U_17,U_20)
| U_20 != unordered_pair(U_24,U_22) ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_1,plain,
! [A,B,C] :
( ( C = set_union2(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_union2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_xboole_0]) ).
fof(f_6_2,plain,
! [U_30,U_29,U_28] :
( ( U_28 = set_union2(U_30,U_29)
| ? [U_27] :
( ( ~ in(U_27,U_28)
& ( in(U_27,U_29)
| in(U_27,U_30) ) )
| ( ~ in(U_27,U_29)
& ~ in(U_27,U_30)
& in(U_27,U_28) ) ) )
& ( ! [U_26] :
( ( in(U_26,U_28)
| ( ~ in(U_26,U_29)
& ~ in(U_26,U_30) ) )
& ( in(U_26,U_29)
| in(U_26,U_30)
| ~ in(U_26,U_28) ) )
| U_28 != set_union2(U_30,U_29) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_40,U_38,U_36] :
( U_36 = set_union2(U_40,U_38)
| ? [U_34] :
( ~ in(U_34,U_36)
& ( in(U_34,U_38)
| in(U_34,U_40) ) )
| ? [U_33] :
( ~ in(U_33,U_38)
& ~ in(U_33,U_40)
& in(U_33,U_36) ) )
& ! [U_39,U_37,U_35] :
( ( ! [U_32] :
( in(U_32,U_35)
| ( ~ in(U_32,U_37)
& ~ in(U_32,U_39) ) )
& ! [U_31] :
( in(U_31,U_37)
| in(U_31,U_39)
| ~ in(U_31,U_35) ) )
| U_35 != set_union2(U_39,U_37) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_40,U_38,U_36] :
( U_36 = set_union2(U_40,U_38)
| ? [U_34] :
( ~ in(U_34,U_36)
& ( in(U_34,U_38)
| in(U_34,U_40) ) )
| ( ~ in(sK4(U_40,U_38,U_36),U_38)
& ~ in(sK4(U_40,U_38,U_36),U_40)
& in(sK4(U_40,U_38,U_36),U_36) ) )
& ! [U_39,U_37,U_35] :
( ( ! [U_32] :
( in(U_32,U_35)
| ( ~ in(U_32,U_37)
& ~ in(U_32,U_39) ) )
& ! [U_31] :
( in(U_31,U_37)
| in(U_31,U_39)
| ~ in(U_31,U_35) ) )
| U_35 != set_union2(U_39,U_37) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_33,sK4(U_40,U_38,U_36))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_40,U_38,U_36] :
( U_36 = set_union2(U_40,U_38)
| ( ~ in(sK5(U_40,U_38,U_36),U_36)
& ( in(sK5(U_40,U_38,U_36),U_38)
| in(sK5(U_40,U_38,U_36),U_40) ) )
| ( ~ in(sK4(U_40,U_38,U_36),U_38)
& ~ in(sK4(U_40,U_38,U_36),U_40)
& in(sK4(U_40,U_38,U_36),U_36) ) )
& ! [U_39,U_37,U_35] :
( ( ! [U_32] :
( in(U_32,U_35)
| ( ~ in(U_32,U_37)
& ~ in(U_32,U_39) ) )
& ! [U_31] :
( in(U_31,U_37)
| in(U_31,U_39)
| ~ in(U_31,U_35) ) )
| U_35 != set_union2(U_39,U_37) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_34,sK5(U_40,U_38,U_36))],[f_6_4]) ).
cnf(f_6_8,plain,
( ~ in(U_32,U_37)
| in(U_32,U_35)
| U_35 != set_union2(U_39,U_37) ),
inference(clausify,[status(thm)],[f_6_5]) ).
fof(f_10_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_10_2,plain,
! [U_46,U_45] : set_union2(U_46,U_46) = U_46,
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_46] : set_union2(U_46,U_46) = U_46,
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
set_union2(U_46,U_46) = U_46,
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_13_1,negated_conjecture,
~ ! [A,B,C] : set_union2(unordered_pair(A,B),C) != empty_set,
inference(negate,[status(cth)],[t50_zfmisc_1]) ).
fof(f_13_2,negated_conjecture,
? [A,B,C] : set_union2(unordered_pair(A,B),C) = empty_set,
inference(fof_nnf,[status(thm)],[f_13_1]) ).
fof(f_13_3,negated_conjecture,
? [U_51,U_50,U_49] : set_union2(unordered_pair(U_51,U_50),U_49) = empty_set,
inference(variable_rename,[status(thm)],[f_13_2]) ).
fof(f_13_4,negated_conjecture,
? [U_50,U_49] : set_union2(unordered_pair(sK8,U_50),U_49) = empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_51,sK8)],[f_13_3]) ).
fof(f_13_5,negated_conjecture,
? [U_49] : set_union2(unordered_pair(sK8,sK9),U_49) = empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_50,sK9)],[f_13_4]) ).
fof(f_13_6,negated_conjecture,
set_union2(unordered_pair(sK8,sK9),sK10) = empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_49,sK10)],[f_13_5]) ).
fof(f_13_7,negated_conjecture,
set_union2(unordered_pair(sK8,sK9),sK10) = empty_set,
inference(definitional_conversion,[status(esa)],[f_13_6]) ).
cnf(f_13_8,negated_conjecture,
set_union2(unordered_pair(sK8,sK9),sK10) = empty_set,
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(t1,plain,
( ~ in(set_union2(sK8,sK8),set_union2(unordered_pair(sK8,sK9),sK10))
| set_union2(unordered_pair(sK8,sK9),sK10) != empty_set ),
inference(start,[status(thm),parent(0:0)],[f_4_5]) ).
cnf(t2,plain,
set_union2(unordered_pair(sK8,sK9),sK10) = empty_set,
inference(extension,[status(thm),parent(t1:1)],[f_13_8]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ in(set_union2(sK8,sK8),unordered_pair(sK8,sK9))
| set_union2(unordered_pair(sK8,sK9),sK10) != set_union2(sK10,unordered_pair(sK8,sK9))
| in(set_union2(sK8,sK8),set_union2(unordered_pair(sK8,sK9),sK10)) ),
inference(extension,[status(thm),parent(t1:2)],[f_6_8]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
set_union2(unordered_pair(sK8,sK9),sK10) = set_union2(sK10,unordered_pair(sK8,sK9)),
inference(extension,[status(thm),parent(t4:2)],[f_3_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( set_union2(sK8,sK8) != sK8
| unordered_pair(sK8,sK9) != unordered_pair(sK9,sK8)
| in(set_union2(sK8,sK8),unordered_pair(sK8,sK9)) ),
inference(extension,[status(thm),parent(t4:3)],[f_5_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
unordered_pair(sK8,sK9) = unordered_pair(sK9,sK8),
inference(extension,[status(thm),parent(t8:2)],[f_2_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
set_union2(sK8,sK8) = sK8,
inference(extension,[status(thm),parent(t8:3)],[f_10_4]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET909+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
% 0.09/5.37 % Computer : n014.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 19 23:07:12 UTC 2026
% 0.09/5.37 % CPUTime :
% 1.05/6.31 % SZS status Theorem for theBenchmark
% 1.05/6.31 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------