%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU212+3 : 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 : 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 08:58:31 AM UTC 2026
% Result : Theorem 6.35s 11.62s
% Output : Proof 6.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 126 ( 59 unt; 0 def)
% Number of atoms : 387 ( 75 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 430 ( 169 ~; 165 |; 81 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 159 ( 4 sgn 110 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('theBenchmark.p',d4_funct_1) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('theBenchmark.p',d4_relat_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t8_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t8_funct_1) ).
fof(f_5_1,plain,
! [A] :
( ! [B,C] :
( ( ( ( C = apply(A,B)
| C != empty_set )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_funct_1]) ).
fof(f_5_2,plain,
! [U_8] :
( ! [U_7,U_6] :
( ( ( ( U_6 = apply(U_8,U_7)
| U_6 != empty_set )
& ( U_6 = empty_set
| U_6 != apply(U_8,U_7) ) )
| in(U_7,relation_dom(U_8)) )
& ( ( ( U_6 = apply(U_8,U_7)
| ~ in(ordered_pair(U_7,U_6),U_8) )
& ( in(ordered_pair(U_7,U_6),U_8)
| U_6 != apply(U_8,U_7) ) )
| ~ in(U_7,relation_dom(U_8)) ) )
| ~ function(U_8)
| ~ relation(U_8) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_8] :
( ( ! [U_16] :
( ( ! [U_14] :
( U_14 = apply(U_8,U_16)
| U_14 != empty_set )
& ! [U_13] :
( U_13 = empty_set
| U_13 != apply(U_8,U_16) ) )
| in(U_16,relation_dom(U_8)) )
& ! [U_15] :
( ( ! [U_12] :
( U_12 = apply(U_8,U_15)
| ~ in(ordered_pair(U_15,U_12),U_8) )
& ! [U_11] :
( in(ordered_pair(U_15,U_11),U_8)
| U_11 != apply(U_8,U_15) ) )
| ~ in(U_15,relation_dom(U_8)) ) )
| ~ function(U_8)
| ~ relation(U_8) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( in(ordered_pair(U_15,U_11),U_8)
| U_11 != apply(U_8,U_15)
| ~ in(U_15,relation_dom(U_8))
| ~ function(U_8)
| ~ relation(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( U_12 = apply(U_8,U_15)
| ~ in(ordered_pair(U_15,U_12),U_8)
| ~ in(U_15,relation_dom(U_8))
| ~ function(U_8)
| ~ relation(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A] :
( ! [B] :
( ( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] : in(ordered_pair(C,D),A) )
| ( ! [D] : ~ in(ordered_pair(C,D),A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_relat_1]) ).
fof(f_6_2,plain,
! [U_24] :
( ! [U_23] :
( ( U_23 = relation_dom(U_24)
| ? [U_22] :
( ( ~ in(U_22,U_23)
& ? [U_21] : in(ordered_pair(U_22,U_21),U_24) )
| ( ! [U_20] : ~ in(ordered_pair(U_22,U_20),U_24)
& in(U_22,U_23) ) ) )
& ( ! [U_19] :
( ( in(U_19,U_23)
| ! [U_18] : ~ in(ordered_pair(U_19,U_18),U_24) )
& ( ? [U_17] : in(ordered_pair(U_19,U_17),U_24)
| ~ in(U_19,U_23) ) )
| U_23 != relation_dom(U_24) ) )
| ~ relation(U_24) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_24] :
( ( ! [U_30] :
( U_30 = relation_dom(U_24)
| ? [U_28] :
( ~ in(U_28,U_30)
& ? [U_21] : in(ordered_pair(U_28,U_21),U_24) )
| ? [U_27] :
( ! [U_20] : ~ in(ordered_pair(U_27,U_20),U_24)
& in(U_27,U_30) ) )
& ! [U_29] :
( ( ! [U_26] :
( in(U_26,U_29)
| ! [U_18] : ~ in(ordered_pair(U_26,U_18),U_24) )
& ! [U_25] :
( ? [U_17] : in(ordered_pair(U_25,U_17),U_24)
| ~ in(U_25,U_29) ) )
| U_29 != relation_dom(U_24) ) )
| ~ relation(U_24) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
! [U_24] :
( ( ! [U_30] :
( U_30 = relation_dom(U_24)
| ? [U_28] :
( ~ in(U_28,U_30)
& ? [U_21] : in(ordered_pair(U_28,U_21),U_24) )
| ? [U_27] :
( ! [U_20] : ~ in(ordered_pair(U_27,U_20),U_24)
& in(U_27,U_30) ) )
& ! [U_29] :
( ( ! [U_26] :
( in(U_26,U_29)
| ! [U_18] : ~ in(ordered_pair(U_26,U_18),U_24) )
& ! [U_25] :
( in(ordered_pair(U_25,sK1(U_24,U_29,U_25)),U_24)
| ~ in(U_25,U_29) ) )
| U_29 != relation_dom(U_24) ) )
| ~ relation(U_24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_17,sK1(U_24,U_29,U_25))],[f_6_3]) ).
fof(f_6_5,plain,
! [U_24] :
( ( ! [U_30] :
( U_30 = relation_dom(U_24)
| ? [U_28] :
( ~ in(U_28,U_30)
& ? [U_21] : in(ordered_pair(U_28,U_21),U_24) )
| ( ! [U_20] : ~ in(ordered_pair(sK2(U_24,U_30),U_20),U_24)
& in(sK2(U_24,U_30),U_30) ) )
& ! [U_29] :
( ( ! [U_26] :
( in(U_26,U_29)
| ! [U_18] : ~ in(ordered_pair(U_26,U_18),U_24) )
& ! [U_25] :
( in(ordered_pair(U_25,sK1(U_24,U_29,U_25)),U_24)
| ~ in(U_25,U_29) ) )
| U_29 != relation_dom(U_24) ) )
| ~ relation(U_24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_27,sK2(U_24,U_30))],[f_6_4]) ).
fof(f_6_6,plain,
! [U_24] :
( ( ! [U_30] :
( U_30 = relation_dom(U_24)
| ( ~ in(sK3(U_24,U_30),U_30)
& ? [U_21] : in(ordered_pair(sK3(U_24,U_30),U_21),U_24) )
| ( ! [U_20] : ~ in(ordered_pair(sK2(U_24,U_30),U_20),U_24)
& in(sK2(U_24,U_30),U_30) ) )
& ! [U_29] :
( ( ! [U_26] :
( in(U_26,U_29)
| ! [U_18] : ~ in(ordered_pair(U_26,U_18),U_24) )
& ! [U_25] :
( in(ordered_pair(U_25,sK1(U_24,U_29,U_25)),U_24)
| ~ in(U_25,U_29) ) )
| U_29 != relation_dom(U_24) ) )
| ~ relation(U_24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_28,sK3(U_24,U_30))],[f_6_5]) ).
fof(f_6_7,plain,
! [U_24] :
( ( ! [U_30] :
( U_30 = relation_dom(U_24)
| ( ~ in(sK3(U_24,U_30),U_30)
& in(ordered_pair(sK3(U_24,U_30),sK4(U_24,U_30)),U_24) )
| ( ! [U_20] : ~ in(ordered_pair(sK2(U_24,U_30),U_20),U_24)
& in(sK2(U_24,U_30),U_30) ) )
& ! [U_29] :
( ( ! [U_26] :
( in(U_26,U_29)
| ! [U_18] : ~ in(ordered_pair(U_26,U_18),U_24) )
& ! [U_25] :
( in(ordered_pair(U_25,sK1(U_24,U_29,U_25)),U_24)
| ~ in(U_25,U_29) ) )
| U_29 != relation_dom(U_24) ) )
| ~ relation(U_24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_21,sK4(U_24,U_30))],[f_6_6]) ).
cnf(f_6_9,plain,
( in(U_26,U_29)
| ~ in(ordered_pair(U_26,U_18),U_24)
| U_29 != relation_dom(U_24)
| ~ relation(U_24) ),
inference(clausify,[status(thm)],[f_6_7]) ).
fof(f_26_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_26_2,plain,
! [U_54,U_53] : subset(U_54,U_54),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_54] : subset(U_54,U_54),
inference(miniscope,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
subset(U_54,U_54),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_28_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_28_2,plain,
! [U_58,U_57] :
( in(U_58,U_57)
| empty(U_57)
| ~ element(U_58,U_57) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( in(U_58,U_57)
| empty(U_57)
| ~ element(U_58,U_57) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_29_2,plain,
! [U_60,U_59] :
( ( element(U_60,powerset(U_59))
| ~ subset(U_60,U_59) )
& ( subset(U_60,U_59)
| ~ element(U_60,powerset(U_59)) ) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_64,U_62] :
( element(U_64,powerset(U_62))
| ~ subset(U_64,U_62) )
& ! [U_63,U_61] :
( subset(U_63,U_61)
| ~ element(U_63,powerset(U_61)) ) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
cnf(f_29_5,plain,
( element(U_64,powerset(U_62))
| ~ subset(U_64,U_62) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_30_2,plain,
! [U_67,U_66,U_65] :
( element(U_67,U_65)
| ~ element(U_66,powerset(U_65))
| ~ in(U_67,U_66) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( element(U_67,U_65)
| ~ element(U_66,powerset(U_65))
| ~ in(U_67,U_66) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_34_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_34_2,plain,
! [U_75,U_74] :
( ~ empty(U_74)
| U_75 = U_74
| ~ empty(U_75) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_75] :
( ! [U_74] :
( ~ empty(U_74)
| U_75 = U_74 )
| ~ empty(U_75) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( ~ empty(U_74)
| U_75 = U_74
| ~ empty(U_75) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
inference(negate,[status(cth)],[t8_funct_1]) ).
fof(f_35_2,negated_conjecture,
? [A,B,C] :
( ( ( ~ in(ordered_pair(A,B),C)
& B = apply(C,A)
& in(A,relation_dom(C)) )
| ( ( B != apply(C,A)
| ~ in(A,relation_dom(C)) )
& in(ordered_pair(A,B),C) ) )
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[f_35_1]) ).
fof(f_35_3,negated_conjecture,
? [U_78,U_77,U_76] :
( ( ( ~ in(ordered_pair(U_78,U_77),U_76)
& U_77 = apply(U_76,U_78)
& in(U_78,relation_dom(U_76)) )
| ( ( U_77 != apply(U_76,U_78)
| ~ in(U_78,relation_dom(U_76)) )
& in(ordered_pair(U_78,U_77),U_76) ) )
& function(U_76)
& relation(U_76) ),
inference(variable_rename,[status(thm)],[f_35_2]) ).
fof(f_35_4,negated_conjecture,
? [U_77,U_76] :
( ( ( ~ in(ordered_pair(sK14,U_77),U_76)
& U_77 = apply(U_76,sK14)
& in(sK14,relation_dom(U_76)) )
| ( ( U_77 != apply(U_76,sK14)
| ~ in(sK14,relation_dom(U_76)) )
& in(ordered_pair(sK14,U_77),U_76) ) )
& function(U_76)
& relation(U_76) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_78,sK14)],[f_35_3]) ).
fof(f_35_5,negated_conjecture,
? [U_76] :
( ( ( ~ in(ordered_pair(sK14,sK15),U_76)
& sK15 = apply(U_76,sK14)
& in(sK14,relation_dom(U_76)) )
| ( ( sK15 != apply(U_76,sK14)
| ~ in(sK14,relation_dom(U_76)) )
& in(ordered_pair(sK14,sK15),U_76) ) )
& function(U_76)
& relation(U_76) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_77,sK15)],[f_35_4]) ).
fof(f_35_6,negated_conjecture,
( ( ( ~ in(ordered_pair(sK14,sK15),sK16)
& sK15 = apply(sK16,sK14)
& in(sK14,relation_dom(sK16)) )
| ( ( sK15 != apply(sK16,sK14)
| ~ in(sK14,relation_dom(sK16)) )
& in(ordered_pair(sK14,sK15),sK16) ) )
& function(sK16)
& relation(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_76,sK16)],[f_35_5]) ).
fof(f_35_7,negated_conjecture,
( ( ~ in(ordered_pair(sK14,sK15),sK16)
| ~ sP1 )
& ( sK15 = apply(sK16,sK14)
| ~ sP1 )
& ( in(sK14,relation_dom(sK16))
| ~ sP1 )
& ( sK15 != apply(sK16,sK14)
| ~ in(sK14,relation_dom(sK16))
| ~ sP0 )
& ( in(ordered_pair(sK14,sK15),sK16)
| ~ sP0 )
& ( sP1
| sP0 )
& function(sK16)
& relation(sK16) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_35_6]) ).
cnf(f_35_8,negated_conjecture,
relation(sK16),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_9,negated_conjecture,
function(sK16),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_10,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_11,negated_conjecture,
( in(ordered_pair(sK14,sK15),sK16)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_12,negated_conjecture,
( sK15 != apply(sK16,sK14)
| ~ in(sK14,relation_dom(sK16))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_13,negated_conjecture,
( in(sK14,relation_dom(sK16))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_14,negated_conjecture,
( sK15 = apply(sK16,sK14)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_15,negated_conjecture,
( ~ in(ordered_pair(sK14,sK15),sK16)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_5,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
( ~ in(sK14,relation_dom(sK16))
| sK15 != apply(sK16,sK14)
| ~ sP0 ),
inference(start,[status(thm),parent(0:0)],[f_35_12]) ).
cnf(t2,plain,
( sP1
| sP0 ),
inference(extension,[status(thm),parent(t1:1)],[f_35_10]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ in(ordered_pair(sK14,sK15),sK16)
| ~ sP1 ),
inference(extension,[status(thm),parent(t2:2)],[f_35_15]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ function(sK16)
| ~ in(sK14,relation_dom(sK16))
| sK15 != apply(sK16,sK14)
| ~ relation(sK16)
| in(ordered_pair(sK14,sK15),sK16) ),
inference(extension,[status(thm),parent(t4:2)],[f_5_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
relation(sK16),
inference(extension,[status(thm),parent(t6:2)],[f_35_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ sP1
| sK15 = apply(sK16,sK14) ),
inference(extension,[status(thm),parent(t6:3)],[f_35_14]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
$false,
inference(reduction,[status(thm),parent(t10:2)],[t10:2,t2:2]) ).
cnf(t13,plain,
( ~ sP1
| in(sK14,relation_dom(sK16)) ),
inference(extension,[status(thm),parent(t6:4)],[f_35_13]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t6:4]) ).
cnf(t15,plain,
$false,
inference(reduction,[status(thm),parent(t13:2)],[t13:2,t2:2]) ).
cnf(t16,plain,
function(sK16),
inference(extension,[status(thm),parent(t6:5)],[f_35_9]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t6:5]) ).
cnf(l1,lemma,
sP0,
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t18,plain,
( ~ function(sK16)
| ~ in(sK14,relation_dom(sK16))
| ~ in(ordered_pair(sK14,sK15),sK16)
| ~ relation(sK16)
| sK15 = apply(sK16,sK14) ),
inference(extension,[status(thm),parent(t1:2)],[f_5_5]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t1:2]) ).
cnf(t20,plain,
relation(sK16),
inference(extension,[status(thm),parent(t18:2)],[f_35_8]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ sP0
| in(ordered_pair(sK14,sK15),sK16) ),
inference(extension,[status(thm),parent(t18:3)],[f_35_11]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
sP0,
inference(lemma_extension,[status(thm),parent(t22:2)],[l1:1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( relation_dom(sK16) != relation_dom(sK16)
| ~ in(ordered_pair(sK14,sK15),sK16)
| ~ relation(sK16)
| in(sK14,relation_dom(sK16)) ),
inference(extension,[status(thm),parent(t18:4)],[f_6_9]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t18:4]) ).
cnf(t28,plain,
relation(sK16),
inference(extension,[status(thm),parent(t26:2)],[f_35_8]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( ~ sP0
| in(ordered_pair(sK14,sK15),sK16) ),
inference(extension,[status(thm),parent(t26:3)],[f_35_11]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t26:3]) ).
cnf(t32,plain,
sP0,
inference(lemma_extension,[status(thm),parent(t30:2)],[l1:1]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
( sK16 != sK16
| relation_dom(sK16) = relation_dom(sK16) ),
inference(extension,[status(thm),parent(t26:4)],[equality_5]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t26:4]) ).
cnf(t36,plain,
sK16 = sK16,
inference(extension,[status(thm),parent(t34:2)],[equality_1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
function(sK16),
inference(extension,[status(thm),parent(t18:5)],[f_35_9]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t18:5]) ).
cnf(t40,plain,
( empty(relation_dom(sK16))
| ~ element(sK14,relation_dom(sK16))
| in(sK14,relation_dom(sK16)) ),
inference(extension,[status(thm),parent(t1:3)],[f_28_3]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t1:3]) ).
cnf(t42,plain,
( ~ element(relation_dom(sK16),powerset(relation_dom(sK16)))
| ~ in(sK14,relation_dom(sK16))
| element(sK14,relation_dom(sK16)) ),
inference(extension,[status(thm),parent(t40:2)],[f_30_3]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( relation_dom(sK16) != relation_dom(sK16)
| ~ in(ordered_pair(sK14,sK15),sK16)
| ~ relation(sK16)
| in(sK14,relation_dom(sK16)) ),
inference(extension,[status(thm),parent(t42:2)],[f_6_9]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
relation(sK16),
inference(extension,[status(thm),parent(t44:2)],[f_35_8]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
( ~ sP0
| in(ordered_pair(sK14,sK15),sK16) ),
inference(extension,[status(thm),parent(t44:3)],[f_35_11]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t44:3]) ).
cnf(t50,plain,
sP0,
inference(lemma_extension,[status(thm),parent(t48:2)],[l1:1]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
relation_dom(sK16) = relation_dom(sK16),
inference(extension,[status(thm),parent(t44:4)],[equality_1]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t44:4]) ).
cnf(t54,plain,
( ~ subset(relation_dom(sK16),relation_dom(sK16))
| element(relation_dom(sK16),powerset(relation_dom(sK16))) ),
inference(extension,[status(thm),parent(t42:3)],[f_29_5]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t42:3]) ).
cnf(t56,plain,
subset(relation_dom(sK16),relation_dom(sK16)),
inference(extension,[status(thm),parent(t54:2)],[f_26_4]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
( relation_dom(sK16) = relation_dom(sK16)
| ~ empty(relation_dom(sK16))
| ~ empty(relation_dom(sK16)) ),
inference(extension,[status(thm),parent(t40:3)],[f_34_4]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t40:3]) ).
cnf(t60,plain,
$false,
inference(reduction,[status(thm),parent(t58:2)],[t58:2,t40:3]) ).
cnf(t61,plain,
( in(sK14,relation_dom(sK16))
| ~ in(ordered_pair(sK14,sK15),sK16)
| ~ relation(sK16)
| relation_dom(sK16) != relation_dom(sK16) ),
inference(extension,[status(thm),parent(t58:3)],[f_6_9]) ).
cnf(t62,plain,
$false,
inference(connection,[status(thm),parent(t61:1)],[t61:1,t58:3]) ).
cnf(t63,plain,
relation(sK16),
inference(extension,[status(thm),parent(t61:2)],[f_35_8]) ).
cnf(t64,plain,
$false,
inference(connection,[status(thm),parent(t63:1)],[t63:1,t61:2]) ).
cnf(t65,plain,
( ~ sP0
| in(ordered_pair(sK14,sK15),sK16) ),
inference(extension,[status(thm),parent(t61:3)],[f_35_11]) ).
cnf(t66,plain,
$false,
inference(connection,[status(thm),parent(t65:1)],[t65:1,t61:3]) ).
cnf(t67,plain,
sP0,
inference(lemma_extension,[status(thm),parent(t65:2)],[l1:1]) ).
cnf(t68,plain,
$false,
inference(connection,[status(thm),parent(t67:1)],[t67:1,t65:2]) ).
cnf(t69,plain,
$false,
inference(reduction,[status(thm),parent(t61:4)],[t61:4,t1:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU212+3 : 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
% 0.12/5.38 % Computer : n015.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Sat Sep 19 23:35:09 UTC 2026
% 0.12/5.38 % CPUTime :
% 6.35/11.62 % SZS status Theorem for theBenchmark
% 6.35/11.62 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------