%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET949+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 : n015.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 08:57:51 AM UTC 2026
% Result : Theorem 0.14s 0.67s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 10 unt; 0 def)
% Number of atoms : 205 ( 77 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 273 ( 101 ~; 87 |; 83 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 182 ( 2 sgn 128 !; 45 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('theBenchmark.p',d2_zfmisc_1) ).
fof(t102_zfmisc_1,conjecture,
! [A,B,C] :
~ ( ! [D,E] : ordered_pair(D,E) != A
& in(A,cartesian_product2(B,C)) ),
file('theBenchmark.p',t102_zfmisc_1) ).
fof(f_3_1,plain,
! [A,B,C] :
( ( C = cartesian_product2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) )
| ( ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) ) )
& ( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_zfmisc_1]) ).
fof(f_3_2,plain,
! [U_16,U_15,U_14] :
( ( U_14 = cartesian_product2(U_16,U_15)
| ? [U_13] :
( ( ~ in(U_13,U_14)
& ? [U_12,U_11] :
( U_13 = ordered_pair(U_12,U_11)
& in(U_11,U_15)
& in(U_12,U_16) ) )
| ( ! [U_10,U_9] :
( U_13 != ordered_pair(U_10,U_9)
| ~ in(U_9,U_15)
| ~ in(U_10,U_16) )
& in(U_13,U_14) ) ) )
& ( ! [U_8] :
( ( in(U_8,U_14)
| ! [U_7,U_6] :
( U_8 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_15)
| ~ in(U_7,U_16) ) )
& ( ? [U_5,U_4] :
( U_8 = ordered_pair(U_5,U_4)
& in(U_4,U_15)
& in(U_5,U_16) )
| ~ in(U_8,U_14) ) )
| U_14 != cartesian_product2(U_16,U_15) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ? [U_20] :
( ~ in(U_20,U_22)
& ? [U_12] :
( ? [U_11] :
( U_20 = ordered_pair(U_12,U_11)
& in(U_11,U_24) )
& in(U_12,U_26) ) )
| ? [U_19] :
( ! [U_10] :
( ! [U_9] :
( U_19 != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(U_19,U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ? [U_5] :
( ? [U_4] :
( U_17 = ordered_pair(U_5,U_4)
& in(U_4,U_23) )
& in(U_5,U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ? [U_20] :
( ~ in(U_20,U_22)
& ? [U_12] :
( ? [U_11] :
( U_20 = ordered_pair(U_12,U_11)
& in(U_11,U_24) )
& in(U_12,U_26) ) )
| ? [U_19] :
( ! [U_10] :
( ! [U_9] :
( U_19 != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(U_19,U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ( ? [U_4] :
( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),U_4)
& in(U_4,U_23) )
& in(sK1(U_25,U_23,U_21,U_17),U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1(U_25,U_23,U_21,U_17))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ? [U_20] :
( ~ in(U_20,U_22)
& ? [U_12] :
( ? [U_11] :
( U_20 = ordered_pair(U_12,U_11)
& in(U_11,U_24) )
& in(U_12,U_26) ) )
| ? [U_19] :
( ! [U_10] :
( ! [U_9] :
( U_19 != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(U_19,U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),sK2(U_25,U_23,U_21,U_17))
& in(sK2(U_25,U_23,U_21,U_17),U_23)
& in(sK1(U_25,U_23,U_21,U_17),U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_4,sK2(U_25,U_23,U_21,U_17))],[f_3_4]) ).
fof(f_3_6,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ? [U_20] :
( ~ in(U_20,U_22)
& ? [U_12] :
( ? [U_11] :
( U_20 = ordered_pair(U_12,U_11)
& in(U_11,U_24) )
& in(U_12,U_26) ) )
| ( ! [U_10] :
( ! [U_9] :
( sK3(U_26,U_24,U_22) != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(sK3(U_26,U_24,U_22),U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),sK2(U_25,U_23,U_21,U_17))
& in(sK2(U_25,U_23,U_21,U_17),U_23)
& in(sK1(U_25,U_23,U_21,U_17),U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3(U_26,U_24,U_22))],[f_3_5]) ).
fof(f_3_7,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ( ~ in(sK4(U_26,U_24,U_22),U_22)
& ? [U_12] :
( ? [U_11] :
( sK4(U_26,U_24,U_22) = ordered_pair(U_12,U_11)
& in(U_11,U_24) )
& in(U_12,U_26) ) )
| ( ! [U_10] :
( ! [U_9] :
( sK3(U_26,U_24,U_22) != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(sK3(U_26,U_24,U_22),U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),sK2(U_25,U_23,U_21,U_17))
& in(sK2(U_25,U_23,U_21,U_17),U_23)
& in(sK1(U_25,U_23,U_21,U_17),U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_20,sK4(U_26,U_24,U_22))],[f_3_6]) ).
fof(f_3_8,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ( ~ in(sK4(U_26,U_24,U_22),U_22)
& ? [U_11] :
( sK4(U_26,U_24,U_22) = ordered_pair(sK5(U_26,U_24,U_22),U_11)
& in(U_11,U_24) )
& in(sK5(U_26,U_24,U_22),U_26) )
| ( ! [U_10] :
( ! [U_9] :
( sK3(U_26,U_24,U_22) != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(sK3(U_26,U_24,U_22),U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),sK2(U_25,U_23,U_21,U_17))
& in(sK2(U_25,U_23,U_21,U_17),U_23)
& in(sK1(U_25,U_23,U_21,U_17),U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_12,sK5(U_26,U_24,U_22))],[f_3_7]) ).
fof(f_3_9,plain,
( ! [U_26,U_24,U_22] :
( U_22 = cartesian_product2(U_26,U_24)
| ( ~ in(sK4(U_26,U_24,U_22),U_22)
& sK4(U_26,U_24,U_22) = ordered_pair(sK5(U_26,U_24,U_22),sK6(U_26,U_24,U_22))
& in(sK6(U_26,U_24,U_22),U_24)
& in(sK5(U_26,U_24,U_22),U_26) )
| ( ! [U_10] :
( ! [U_9] :
( sK3(U_26,U_24,U_22) != ordered_pair(U_10,U_9)
| ~ in(U_9,U_24) )
| ~ in(U_10,U_26) )
& in(sK3(U_26,U_24,U_22),U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| ! [U_7] :
( ! [U_6] :
( U_18 != ordered_pair(U_7,U_6)
| ~ in(U_6,U_23) )
| ~ in(U_7,U_25) ) )
& ! [U_17] :
( ( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),sK2(U_25,U_23,U_21,U_17))
& in(sK2(U_25,U_23,U_21,U_17),U_23)
& in(sK1(U_25,U_23,U_21,U_17),U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != cartesian_product2(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_11,sK6(U_26,U_24,U_22))],[f_3_8]) ).
cnf(f_3_12,plain,
( U_17 = ordered_pair(sK1(U_25,U_23,U_21,U_17),sK2(U_25,U_23,U_21,U_17))
| ~ in(U_17,U_21)
| U_21 != cartesian_product2(U_25,U_23) ),
inference(clausify,[status(thm)],[f_3_9]) ).
fof(f_8_1,negated_conjecture,
~ ! [A,B,C] :
~ ( ! [D,E] : ordered_pair(D,E) != A
& in(A,cartesian_product2(B,C)) ),
inference(negate,[status(cth)],[t102_zfmisc_1]) ).
fof(f_8_2,negated_conjecture,
? [A,B,C] :
( ! [D,E] : ordered_pair(D,E) != A
& in(A,cartesian_product2(B,C)) ),
inference(fof_nnf,[status(thm)],[f_8_1]) ).
fof(f_8_3,negated_conjecture,
? [U_37,U_36,U_35] :
( ! [U_34,U_33] : ordered_pair(U_34,U_33) != U_37
& in(U_37,cartesian_product2(U_36,U_35)) ),
inference(variable_rename,[status(thm)],[f_8_2]) ).
fof(f_8_4,negated_conjecture,
? [U_37] :
( ? [U_36,U_35] : in(U_37,cartesian_product2(U_36,U_35))
& ! [U_34,U_33] : ordered_pair(U_34,U_33) != U_37 ),
inference(miniscope,[status(thm)],[f_8_3]) ).
fof(f_8_5,negated_conjecture,
( ? [U_36,U_35] : in(sK9,cartesian_product2(U_36,U_35))
& ! [U_34,U_33] : ordered_pair(U_34,U_33) != sK9 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_37,sK9)],[f_8_4]) ).
fof(f_8_6,negated_conjecture,
( ? [U_35] : in(sK9,cartesian_product2(sK10,U_35))
& ! [U_34,U_33] : ordered_pair(U_34,U_33) != sK9 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_36,sK10)],[f_8_5]) ).
fof(f_8_7,negated_conjecture,
( in(sK9,cartesian_product2(sK10,sK11))
& ! [U_34,U_33] : ordered_pair(U_34,U_33) != sK9 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_35,sK11)],[f_8_6]) ).
fof(f_8_8,negated_conjecture,
( in(sK9,cartesian_product2(sK10,sK11))
& ! [U_34,U_33] : ordered_pair(U_34,U_33) != sK9 ),
inference(definitional_conversion,[status(esa)],[f_8_7]) ).
cnf(f_8_9,negated_conjecture,
ordered_pair(U_34,U_33) != sK9,
inference(clausify,[status(thm)],[f_8_8]) ).
cnf(f_8_10,negated_conjecture,
in(sK9,cartesian_product2(sK10,sK11)),
inference(clausify,[status(thm)],[f_8_8]) ).
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(t1,plain,
ordered_pair(sK1(sK10,sK11,cartesian_product2(sK10,sK11),sK9),sK2(sK10,sK11,cartesian_product2(sK10,sK11),sK9)) != sK9,
inference(start,[status(thm),parent(0:0)],[f_8_9]) ).
cnf(t2,plain,
( sK9 != ordered_pair(sK1(sK10,sK11,cartesian_product2(sK10,sK11),sK9),sK2(sK10,sK11,cartesian_product2(sK10,sK11),sK9))
| ordered_pair(sK1(sK10,sK11,cartesian_product2(sK10,sK11),sK9),sK2(sK10,sK11,cartesian_product2(sK10,sK11),sK9)) = sK9 ),
inference(extension,[status(thm),parent(t1:1)],[equality_2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ in(sK9,cartesian_product2(sK10,sK11))
| cartesian_product2(sK10,sK11) != cartesian_product2(sK10,sK11)
| sK9 = ordered_pair(sK1(sK10,sK11,cartesian_product2(sK10,sK11),sK9),sK2(sK10,sK11,cartesian_product2(sK10,sK11),sK9)) ),
inference(extension,[status(thm),parent(t2:2)],[f_3_12]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
cartesian_product2(sK10,sK11) = cartesian_product2(sK10,sK11),
inference(extension,[status(thm),parent(t4:2)],[equality_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
in(sK9,cartesian_product2(sK10,sK11)),
inference(extension,[status(thm),parent(t4:3)],[f_8_10]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET949+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
% 0.10/0.57 % Computer : n015.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Sat Sep 19 23:11:34 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.14/0.67 % SZS status Theorem for theBenchmark
% 0.14/0.67 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------