%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET662+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n010.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 08:57:14 AM UTC 2026
% Result : Theorem 75.25s 75.57s
% Output : Proof 75.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 81 ( 43 unt; 0 def)
% Number of atoms : 230 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 251 ( 102 ~; 92 |; 34 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 1 sgn 54 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('theBenchmark.p',p2) ).
fof(p5a,axiom,
empty(empty_set),
file('theBenchmark.p',p5a) ).
fof(p7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('theBenchmark.p',p7) ).
fof(p11,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('theBenchmark.p',p11) ).
fof(p12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('theBenchmark.p',p12) ).
fof(p13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p13) ).
fof(p14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('theBenchmark.p',p14) ).
fof(p20,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p20) ).
fof(prove_relset_1_25,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ),
file('theBenchmark.p',prove_relset_1_25) ).
fof(f_2_1,plain,
! [B] :
( ! [C] :
( ( ! [E] :
( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ! [D] :
( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p2]) ).
fof(f_2_2,plain,
! [U_5] :
( ! [U_4] :
( ( ! [U_3] :
( ilf_type(U_3,subset_type(cross_product(U_5,U_4)))
| ~ ilf_type(U_3,relation_type(U_5,U_4)) )
& ! [U_2] :
( ilf_type(U_2,relation_type(U_5,U_4))
| ~ ilf_type(U_2,subset_type(cross_product(U_5,U_4))) ) )
| ~ ilf_type(U_4,set_type) )
| ~ ilf_type(U_5,set_type) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ilf_type(U_2,relation_type(U_5,U_4))
| ~ ilf_type(U_2,subset_type(cross_product(U_5,U_4)))
| ~ ilf_type(U_4,set_type)
| ~ ilf_type(U_5,set_type) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_5_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[p5a]) ).
cnf(f_5_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_8_1,plain,
! [B] :
( ! [C] :
( ( ( ilf_type(C,subset_type(B))
| ~ ilf_type(C,member_type(power_set(B))) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p7]) ).
fof(f_8_2,plain,
! [U_13] :
( ! [U_12] :
( ( ( ilf_type(U_12,subset_type(U_13))
| ~ ilf_type(U_12,member_type(power_set(U_13))) )
& ( ilf_type(U_12,member_type(power_set(U_13)))
| ~ ilf_type(U_12,subset_type(U_13)) ) )
| ~ ilf_type(U_12,set_type) )
| ~ ilf_type(U_13,set_type) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_4,plain,
( ilf_type(U_12,subset_type(U_13))
| ~ ilf_type(U_12,member_type(power_set(U_13)))
| ~ ilf_type(U_12,set_type)
| ~ ilf_type(U_13,set_type) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_12_1,plain,
! [B] :
( ( ( empty(B)
| ? [C] :
( member(C,B)
& ilf_type(C,set_type) ) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p11]) ).
fof(f_12_2,plain,
! [U_23] :
( ( ( empty(U_23)
| ? [U_22] :
( member(U_22,U_23)
& ilf_type(U_22,set_type) ) )
& ( ! [U_21] :
( ~ member(U_21,U_23)
| ~ ilf_type(U_21,set_type) )
| ~ empty(U_23) ) )
| ~ ilf_type(U_23,set_type) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_23] :
( ( ( empty(U_23)
| ( member(sK4(U_23),U_23)
& ilf_type(sK4(U_23),set_type) ) )
& ( ! [U_21] :
( ~ member(U_21,U_23)
| ~ ilf_type(U_21,set_type) )
| ~ empty(U_23) ) )
| ~ ilf_type(U_23,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_22,sK4(U_23))],[f_12_2]) ).
cnf(f_12_4,plain,
( ~ member(U_21,U_23)
| ~ ilf_type(U_21,set_type)
| ~ empty(U_23)
| ~ ilf_type(U_23,set_type) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [B] :
( ! [C] :
( ( ( member(B,power_set(C))
| ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) ) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p12]) ).
fof(f_13_2,plain,
! [U_27] :
( ! [U_26] :
( ( ( member(U_27,power_set(U_26))
| ? [U_25] :
( ~ member(U_25,U_26)
& member(U_25,U_27)
& ilf_type(U_25,set_type) ) )
& ( ! [U_24] :
( member(U_24,U_26)
| ~ member(U_24,U_27)
| ~ ilf_type(U_24,set_type) )
| ~ member(U_27,power_set(U_26)) ) )
| ~ ilf_type(U_26,set_type) )
| ~ ilf_type(U_27,set_type) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_27] :
( ! [U_26] :
( ( ( member(U_27,power_set(U_26))
| ( ~ member(sK5(U_27,U_26),U_26)
& member(sK5(U_27,U_26),U_27)
& ilf_type(sK5(U_27,U_26),set_type) ) )
& ( ! [U_24] :
( member(U_24,U_26)
| ~ member(U_24,U_27)
| ~ ilf_type(U_24,set_type) )
| ~ member(U_27,power_set(U_26)) ) )
| ~ ilf_type(U_26,set_type) )
| ~ ilf_type(U_27,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_25,sK5(U_27,U_26))],[f_13_2]) ).
cnf(f_13_6,plain,
( member(sK5(U_27,U_26),U_27)
| member(U_27,power_set(U_26))
| ~ ilf_type(U_26,set_type)
| ~ ilf_type(U_27,set_type) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p13]) ).
fof(f_14_2,plain,
! [U_28] :
( ( ilf_type(power_set(U_28),set_type)
& ~ empty(power_set(U_28)) )
| ~ ilf_type(U_28,set_type) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( ~ empty(power_set(U_28))
| ~ ilf_type(U_28,set_type) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [B] :
( ! [C] :
( ( ( ilf_type(B,member_type(C))
| ~ member(B,C) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p14]) ).
fof(f_15_2,plain,
! [U_30] :
( ! [U_29] :
( ( ( ilf_type(U_30,member_type(U_29))
| ~ member(U_30,U_29) )
& ( member(U_30,U_29)
| ~ ilf_type(U_30,member_type(U_29)) ) )
| ~ ilf_type(U_29,set_type)
| empty(U_29) )
| ~ ilf_type(U_30,set_type) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_4,plain,
( ilf_type(U_30,member_type(U_29))
| ~ member(U_30,U_29)
| ~ ilf_type(U_29,set_type)
| empty(U_29)
| ~ ilf_type(U_30,set_type) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_21_1,plain,
! [B] : ilf_type(B,set_type),
inference(fof_nnf,[status(thm)],[p20]) ).
fof(f_21_2,plain,
! [U_46] : ilf_type(U_46,set_type),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
ilf_type(U_46,set_type),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ),
inference(negate,[status(cth)],[prove_relset_1_25]) ).
fof(f_22_2,negated_conjecture,
? [B] :
( ? [C] :
( ~ ilf_type(empty_set,relation_type(B,C))
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[f_22_1]) ).
fof(f_22_3,negated_conjecture,
? [U_48] :
( ? [U_47] :
( ~ ilf_type(empty_set,relation_type(U_48,U_47))
& ilf_type(U_47,set_type) )
& ilf_type(U_48,set_type) ),
inference(variable_rename,[status(thm)],[f_22_2]) ).
fof(f_22_4,negated_conjecture,
( ? [U_47] :
( ~ ilf_type(empty_set,relation_type(sK10,U_47))
& ilf_type(U_47,set_type) )
& ilf_type(sK10,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_48,sK10)],[f_22_3]) ).
fof(f_22_5,negated_conjecture,
( ~ ilf_type(empty_set,relation_type(sK10,sK11))
& ilf_type(sK11,set_type)
& ilf_type(sK10,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_47,sK11)],[f_22_4]) ).
cnf(f_22_6,negated_conjecture,
ilf_type(sK10,set_type),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_7,negated_conjecture,
ilf_type(sK11,set_type),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_8,negated_conjecture,
~ ilf_type(empty_set,relation_type(sK10,sK11)),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(t1,plain,
~ ilf_type(empty_set,relation_type(sK10,sK11)),
inference(start,[status(thm),parent(0:0)],[f_22_8]) ).
cnf(t2,plain,
( ~ ilf_type(sK11,set_type)
| ~ ilf_type(empty_set,subset_type(cross_product(sK10,sK11)))
| ~ ilf_type(sK10,set_type)
| ilf_type(empty_set,relation_type(sK10,sK11)) ),
inference(extension,[status(thm),parent(t1:1)],[f_2_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
ilf_type(sK10,set_type),
inference(extension,[status(thm),parent(t2:2)],[f_22_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ ilf_type(empty_set,set_type)
| ~ ilf_type(empty_set,member_type(power_set(cross_product(sK10,sK11))))
| ~ ilf_type(cross_product(sK10,sK11),set_type)
| ilf_type(empty_set,subset_type(cross_product(sK10,sK11))) ),
inference(extension,[status(thm),parent(t2:3)],[f_8_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
ilf_type(cross_product(sK10,sK11),set_type),
inference(extension,[status(thm),parent(t6:2)],[f_21_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(l4,lemma,
ilf_type(cross_product(sK10,sK11),set_type),
inference(lemma,[status(cth),parent(t6:2),below(t2:3)],[t6:2]) ).
cnf(t10,plain,
( empty(power_set(cross_product(sK10,sK11)))
| ~ ilf_type(power_set(cross_product(sK10,sK11)),set_type)
| ~ member(empty_set,power_set(cross_product(sK10,sK11)))
| ~ ilf_type(empty_set,set_type)
| ilf_type(empty_set,member_type(power_set(cross_product(sK10,sK11)))) ),
inference(extension,[status(thm),parent(t6:3)],[f_15_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
ilf_type(empty_set,set_type),
inference(extension,[status(thm),parent(t10:2)],[f_21_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(l6,lemma,
ilf_type(empty_set,set_type),
inference(lemma,[status(cth),parent(t10:2),below(t6:3)],[t10:2]) ).
cnf(t14,plain,
( ~ ilf_type(cross_product(sK10,sK11),set_type)
| member(sK5(empty_set,cross_product(sK10,sK11)),empty_set)
| ~ ilf_type(empty_set,set_type)
| member(empty_set,power_set(cross_product(sK10,sK11))) ),
inference(extension,[status(thm),parent(t10:3)],[f_13_6]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
ilf_type(empty_set,set_type),
inference(lemma_extension,[status(thm),parent(t14:2)],[l6:1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ empty(empty_set)
| ~ ilf_type(sK5(empty_set,cross_product(sK10,sK11)),set_type)
| ~ ilf_type(empty_set,set_type)
| ~ member(sK5(empty_set,cross_product(sK10,sK11)),empty_set) ),
inference(extension,[status(thm),parent(t14:3)],[f_12_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
ilf_type(empty_set,set_type),
inference(lemma_extension,[status(thm),parent(t18:2)],[l6:1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
ilf_type(sK5(empty_set,cross_product(sK10,sK11)),set_type),
inference(extension,[status(thm),parent(t18:3)],[f_21_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
empty(empty_set),
inference(extension,[status(thm),parent(t18:4)],[f_5_2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t18:4]) ).
cnf(t26,plain,
ilf_type(cross_product(sK10,sK11),set_type),
inference(lemma_extension,[status(thm),parent(t14:4)],[l4:1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t14:4]) ).
cnf(t28,plain,
ilf_type(power_set(cross_product(sK10,sK11)),set_type),
inference(extension,[status(thm),parent(t10:4)],[f_21_3]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t10:4]) ).
cnf(t30,plain,
( ~ ilf_type(cross_product(sK10,sK11),set_type)
| ~ empty(power_set(cross_product(sK10,sK11))) ),
inference(extension,[status(thm),parent(t10:5)],[f_14_3]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t10:5]) ).
cnf(t32,plain,
ilf_type(cross_product(sK10,sK11),set_type),
inference(lemma_extension,[status(thm),parent(t30:2)],[l4:1]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
ilf_type(empty_set,set_type),
inference(extension,[status(thm),parent(t6:4)],[f_21_3]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t6:4]) ).
cnf(t36,plain,
ilf_type(sK11,set_type),
inference(extension,[status(thm),parent(t2:4)],[f_22_7]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET662+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % 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 : n010.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 22:45:42 UTC 2026
% 0.08/0.37 % CPUTime :
% 75.25/75.57 % SZS status Theorem for theBenchmark
% 75.25/75.57 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------