%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET928+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 : n008.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 08:57:49 AM UTC 2026
% Result : Theorem 3.16s 3.42s
% Output : Proof 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 88 ( 37 unt; 0 def)
% Number of atoms : 209 ( 54 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 215 ( 94 ~; 78 |; 40 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 87 ( 1 sgn 43 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(t55_zfmisc_1,axiom,
! [A,B,C] :
~ ( in(A,C)
& disjoint(unordered_pair(A,B),C) ),
file('theBenchmark.p',t55_zfmisc_1) ).
fof(t57_zfmisc_1,axiom,
! [A,B,C] :
~ ( ~ disjoint(unordered_pair(A,C),B)
& ~ in(C,B)
& ~ in(A,B) ),
file('theBenchmark.p',t57_zfmisc_1) ).
fof(t72_zfmisc_1,conjecture,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(B,C)
& ~ in(A,C) ) ),
file('theBenchmark.p',t72_zfmisc_1) ).
fof(t83_xboole_1,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_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_6_1,plain,
! [A,B,C] :
( ~ in(A,C)
| ~ disjoint(unordered_pair(A,B),C) ),
inference(fof_nnf,[status(thm)],[t55_zfmisc_1]) ).
fof(f_6_2,plain,
! [U_10,U_9,U_8] :
( ~ in(U_10,U_8)
| ~ disjoint(unordered_pair(U_10,U_9),U_8) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( ~ in(U_10,U_8)
| ~ disjoint(unordered_pair(U_10,U_9),U_8) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B,C] :
( disjoint(unordered_pair(A,C),B)
| in(C,B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[t57_zfmisc_1]) ).
fof(f_7_2,plain,
! [U_13,U_12,U_11] :
( disjoint(unordered_pair(U_13,U_11),U_12)
| in(U_11,U_12)
| in(U_13,U_12) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_13,U_12] :
( ! [U_11] :
( disjoint(unordered_pair(U_13,U_11),U_12)
| in(U_11,U_12) )
| in(U_13,U_12) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( disjoint(unordered_pair(U_13,U_11),U_12)
| in(U_11,U_12)
| in(U_13,U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(B,C)
& ~ in(A,C) ) ),
inference(negate,[status(cth)],[t72_zfmisc_1]) ).
fof(f_8_2,negated_conjecture,
? [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& ~ in(B,C)
& ~ in(A,C) )
| ( ( in(B,C)
| in(A,C) )
& set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[f_8_1]) ).
fof(f_8_3,negated_conjecture,
? [U_16,U_15,U_14] :
( ( set_difference(unordered_pair(U_16,U_15),U_14) != unordered_pair(U_16,U_15)
& ~ in(U_15,U_14)
& ~ in(U_16,U_14) )
| ( ( in(U_15,U_14)
| in(U_16,U_14) )
& set_difference(unordered_pair(U_16,U_15),U_14) = unordered_pair(U_16,U_15) ) ),
inference(variable_rename,[status(thm)],[f_8_2]) ).
fof(f_8_4,negated_conjecture,
( ? [U_22,U_20,U_18] :
( set_difference(unordered_pair(U_22,U_20),U_18) != unordered_pair(U_22,U_20)
& ~ in(U_20,U_18)
& ~ in(U_22,U_18) )
| ? [U_21,U_19,U_17] :
( ( in(U_19,U_17)
| in(U_21,U_17) )
& set_difference(unordered_pair(U_21,U_19),U_17) = unordered_pair(U_21,U_19) ) ),
inference(miniscope,[status(thm)],[f_8_3]) ).
fof(f_8_5,negated_conjecture,
( ? [U_22,U_20,U_18] :
( set_difference(unordered_pair(U_22,U_20),U_18) != unordered_pair(U_22,U_20)
& ~ in(U_20,U_18)
& ~ in(U_22,U_18) )
| ? [U_19,U_17] :
( ( in(U_19,U_17)
| in(sK3,U_17) )
& set_difference(unordered_pair(sK3,U_19),U_17) = unordered_pair(sK3,U_19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_21,sK3)],[f_8_4]) ).
fof(f_8_6,negated_conjecture,
( ? [U_22,U_20,U_18] :
( set_difference(unordered_pair(U_22,U_20),U_18) != unordered_pair(U_22,U_20)
& ~ in(U_20,U_18)
& ~ in(U_22,U_18) )
| ? [U_17] :
( ( in(sK4,U_17)
| in(sK3,U_17) )
& set_difference(unordered_pair(sK3,sK4),U_17) = unordered_pair(sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_19,sK4)],[f_8_5]) ).
fof(f_8_7,negated_conjecture,
( ? [U_22,U_20,U_18] :
( set_difference(unordered_pair(U_22,U_20),U_18) != unordered_pair(U_22,U_20)
& ~ in(U_20,U_18)
& ~ in(U_22,U_18) )
| ( ( in(sK4,sK5)
| in(sK3,sK5) )
& set_difference(unordered_pair(sK3,sK4),sK5) = unordered_pair(sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_17,sK5)],[f_8_6]) ).
fof(f_8_8,negated_conjecture,
( ? [U_20,U_18] :
( set_difference(unordered_pair(sK6,U_20),U_18) != unordered_pair(sK6,U_20)
& ~ in(U_20,U_18)
& ~ in(sK6,U_18) )
| ( ( in(sK4,sK5)
| in(sK3,sK5) )
& set_difference(unordered_pair(sK3,sK4),sK5) = unordered_pair(sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_22,sK6)],[f_8_7]) ).
fof(f_8_9,negated_conjecture,
( ? [U_18] :
( set_difference(unordered_pair(sK6,sK7),U_18) != unordered_pair(sK6,sK7)
& ~ in(sK7,U_18)
& ~ in(sK6,U_18) )
| ( ( in(sK4,sK5)
| in(sK3,sK5) )
& set_difference(unordered_pair(sK3,sK4),sK5) = unordered_pair(sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_20,sK7)],[f_8_8]) ).
fof(f_8_10,negated_conjecture,
( ( set_difference(unordered_pair(sK6,sK7),sK8) != unordered_pair(sK6,sK7)
& ~ in(sK7,sK8)
& ~ in(sK6,sK8) )
| ( ( in(sK4,sK5)
| in(sK3,sK5) )
& set_difference(unordered_pair(sK3,sK4),sK5) = unordered_pair(sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_18,sK8)],[f_8_9]) ).
fof(f_8_11,negated_conjecture,
( ( set_difference(unordered_pair(sK6,sK7),sK8) != unordered_pair(sK6,sK7)
| ~ sP1 )
& ( ~ in(sK7,sK8)
| ~ sP1 )
& ( ~ in(sK6,sK8)
| ~ sP1 )
& ( in(sK4,sK5)
| in(sK3,sK5)
| ~ sP0 )
& ( set_difference(unordered_pair(sK3,sK4),sK5) = unordered_pair(sK3,sK4)
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_8_10]) ).
cnf(f_8_12,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_8_11]) ).
cnf(f_8_13,negated_conjecture,
( set_difference(unordered_pair(sK3,sK4),sK5) = unordered_pair(sK3,sK4)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_8_11]) ).
cnf(f_8_14,negated_conjecture,
( in(sK4,sK5)
| in(sK3,sK5)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_8_11]) ).
cnf(f_8_15,negated_conjecture,
( ~ in(sK6,sK8)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_8_11]) ).
cnf(f_8_16,negated_conjecture,
( ~ in(sK7,sK8)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_8_11]) ).
cnf(f_8_17,negated_conjecture,
( set_difference(unordered_pair(sK6,sK7),sK8) != unordered_pair(sK6,sK7)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_8_11]) ).
fof(f_9_1,plain,
! [A,B] :
( ( disjoint(A,B)
| set_difference(A,B) != A )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t83_xboole_1]) ).
fof(f_9_2,plain,
! [U_24,U_23] :
( ( disjoint(U_24,U_23)
| set_difference(U_24,U_23) != U_24 )
& ( set_difference(U_24,U_23) = U_24
| ~ disjoint(U_24,U_23) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_28,U_26] :
( disjoint(U_28,U_26)
| set_difference(U_28,U_26) != U_28 )
& ! [U_27,U_25] :
( set_difference(U_27,U_25) = U_27
| ~ disjoint(U_27,U_25) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( set_difference(U_27,U_25) = U_27
| ~ disjoint(U_27,U_25) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( disjoint(U_28,U_26)
| set_difference(U_28,U_26) != U_28 ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_8,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(t1,plain,
( ~ in(sK6,sK8)
| ~ sP1 ),
inference(start,[status(thm),parent(0:0)],[f_8_15]) ).
cnf(t2,plain,
( sP0
| sP1 ),
inference(extension,[status(thm),parent(t1:1)],[f_8_12]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( in(sK3,sK5)
| in(sK4,sK5)
| ~ sP0 ),
inference(extension,[status(thm),parent(t2:2)],[f_8_14]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ disjoint(unordered_pair(sK4,sK3),sK5)
| ~ in(sK4,sK5) ),
inference(extension,[status(thm),parent(t4:2)],[f_6_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( sK5 != sK5
| ~ disjoint(unordered_pair(sK3,sK4),sK5)
| unordered_pair(sK3,sK4) != unordered_pair(sK4,sK3)
| disjoint(unordered_pair(sK4,sK3),sK5) ),
inference(extension,[status(thm),parent(t6:2)],[equality_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
unordered_pair(sK3,sK4) = unordered_pair(sK4,sK3),
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_difference(unordered_pair(sK3,sK4),sK5) != unordered_pair(sK3,sK4)
| disjoint(unordered_pair(sK3,sK4),sK5) ),
inference(extension,[status(thm),parent(t8:3)],[f_9_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( ~ sP0
| set_difference(unordered_pair(sK3,sK4),sK5) = unordered_pair(sK3,sK4) ),
inference(extension,[status(thm),parent(t12:2)],[f_8_13]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
$false,
inference(reduction,[status(thm),parent(t14:2)],[t14:2,t2:2]) ).
cnf(t17,plain,
sK5 = sK5,
inference(extension,[status(thm),parent(t8:4)],[equality_1]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t8:4]) ).
cnf(t19,plain,
( ~ disjoint(unordered_pair(sK3,sK4),sK5)
| ~ in(sK3,sK5) ),
inference(extension,[status(thm),parent(t4:3)],[f_6_3]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t4:3]) ).
cnf(t21,plain,
( set_difference(unordered_pair(sK3,sK4),sK5) != unordered_pair(sK3,sK4)
| disjoint(unordered_pair(sK3,sK4),sK5) ),
inference(extension,[status(thm),parent(t19:2)],[f_9_5]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(t23,plain,
( ~ sP0
| set_difference(unordered_pair(sK3,sK4),sK5) = unordered_pair(sK3,sK4) ),
inference(extension,[status(thm),parent(t21:2)],[f_8_13]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t21:2]) ).
cnf(t25,plain,
$false,
inference(reduction,[status(thm),parent(t23:2)],[t23:2,t2:2]) ).
cnf(l1,lemma,
sP1,
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t26,plain,
( disjoint(unordered_pair(sK6,sK6),sK8)
| in(sK6,sK8)
| in(sK6,sK8) ),
inference(extension,[status(thm),parent(t1:2)],[f_7_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t1:2]) ).
cnf(t28,plain,
$false,
inference(reduction,[status(thm),parent(t26:2)],[t26:2,t1:2]) ).
cnf(t29,plain,
( sK8 != sK8
| disjoint(unordered_pair(sK6,sK6),sK8)
| unordered_pair(sK6,sK6) != unordered_pair(sK6,sK6)
| ~ disjoint(unordered_pair(sK6,sK6),sK8) ),
inference(extension,[status(thm),parent(t26:3)],[equality_8]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t26:3]) ).
cnf(t31,plain,
unordered_pair(sK6,sK6) = unordered_pair(sK6,sK6),
inference(extension,[status(thm),parent(t29:2)],[f_2_3]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t29:2]) ).
cnf(t33,plain,
( ~ in(sK6,sK8)
| ~ disjoint(unordered_pair(sK6,sK6),sK8) ),
inference(extension,[status(thm),parent(t29:3)],[f_6_3]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t29:3]) ).
cnf(t35,plain,
( in(sK7,sK8)
| disjoint(unordered_pair(sK6,sK7),sK8)
| in(sK6,sK8) ),
inference(extension,[status(thm),parent(t33:2)],[f_7_4]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t33:2]) ).
cnf(t37,plain,
( set_difference(unordered_pair(sK6,sK7),sK8) = unordered_pair(sK6,sK7)
| ~ disjoint(unordered_pair(sK6,sK7),sK8) ),
inference(extension,[status(thm),parent(t35:2)],[f_9_4]) ).
cnf(t38,plain,
$false,
inference(connection,[status(thm),parent(t37:1)],[t37:1,t35:2]) ).
cnf(t39,plain,
( ~ sP1
| set_difference(unordered_pair(sK6,sK7),sK8) != unordered_pair(sK6,sK7) ),
inference(extension,[status(thm),parent(t37:2)],[f_8_17]) ).
cnf(t40,plain,
$false,
inference(connection,[status(thm),parent(t39:1)],[t39:1,t37:2]) ).
cnf(t41,plain,
sP1,
inference(lemma_extension,[status(thm),parent(t39:2)],[l1:1]) ).
cnf(t42,plain,
$false,
inference(connection,[status(thm),parent(t41:1)],[t41:1,t39:2]) ).
cnf(t43,plain,
( ~ sP1
| ~ in(sK7,sK8) ),
inference(extension,[status(thm),parent(t35:3)],[f_8_16]) ).
cnf(t44,plain,
$false,
inference(connection,[status(thm),parent(t43:1)],[t43:1,t35:3]) ).
cnf(t45,plain,
sP1,
inference(lemma_extension,[status(thm),parent(t43:2)],[l1:1]) ).
cnf(t46,plain,
$false,
inference(connection,[status(thm),parent(t45:1)],[t45:1,t43:2]) ).
cnf(t47,plain,
sK8 = sK8,
inference(extension,[status(thm),parent(t29:4)],[equality_1]) ).
cnf(t48,plain,
$false,
inference(connection,[status(thm),parent(t47:1)],[t47:1,t29:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET928+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 23:08:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 3.16/3.42 % SZS status Theorem for theBenchmark
% 3.16/3.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------