%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU044+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 : n001.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 08:57:59 AM UTC 2026
% Result : Theorem 78.02s 78.54s
% Output : Proof 78.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 120 ( 78 unt; 0 def)
% Number of atoms : 378 ( 51 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 424 ( 166 ~; 163 |; 85 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 91 ( 3 sgn 51 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc5_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) ) ),
file('theBenchmark.p',fc5_funct_1) ).
fof(t86_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
<=> ( in(apply(C,B),A)
& in(B,relation_dom(C)) ) ) ),
file('theBenchmark.p',t86_funct_1) ).
fof(t85_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& ! [D] :
( in(D,relation_dom(B))
<=> ( in(apply(C,D),A)
& in(D,relation_dom(C)) ) ) ) ) ) ),
file('theBenchmark.p',t85_funct_1) ).
fof(f_20_1,plain,
! [A,B] :
( ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[fc5_funct_1]) ).
fof(f_20_2,plain,
! [U_32,U_31] :
( ( function(relation_rng_restriction(U_32,U_31))
& relation(relation_rng_restriction(U_32,U_31)) )
| ~ function(U_31)
| ~ relation(U_31) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( relation(relation_rng_restriction(U_32,U_31))
| ~ function(U_31)
| ~ relation(U_31) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( function(relation_rng_restriction(U_32,U_31))
| ~ function(U_31)
| ~ relation(U_31) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_33_1,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
<=> ( in(apply(C,B),A)
& in(B,relation_dom(C)) ) ) ),
inference(negate,[status(cth)],[t86_funct_1]) ).
fof(f_33_2,negated_conjecture,
? [A,B,C] :
( ( ( ~ in(B,relation_dom(relation_rng_restriction(A,C)))
& in(apply(C,B),A)
& in(B,relation_dom(C)) )
| ( ( ~ in(apply(C,B),A)
| ~ in(B,relation_dom(C)) )
& in(B,relation_dom(relation_rng_restriction(A,C))) ) )
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[f_33_1]) ).
fof(f_33_3,negated_conjecture,
? [U_51,U_50,U_49] :
( ( ( ~ in(U_50,relation_dom(relation_rng_restriction(U_51,U_49)))
& in(apply(U_49,U_50),U_51)
& in(U_50,relation_dom(U_49)) )
| ( ( ~ in(apply(U_49,U_50),U_51)
| ~ in(U_50,relation_dom(U_49)) )
& in(U_50,relation_dom(relation_rng_restriction(U_51,U_49))) ) )
& function(U_49)
& relation(U_49) ),
inference(variable_rename,[status(thm)],[f_33_2]) ).
fof(f_33_4,negated_conjecture,
? [U_50,U_49] :
( ( ( ~ in(U_50,relation_dom(relation_rng_restriction(sK12,U_49)))
& in(apply(U_49,U_50),sK12)
& in(U_50,relation_dom(U_49)) )
| ( ( ~ in(apply(U_49,U_50),sK12)
| ~ in(U_50,relation_dom(U_49)) )
& in(U_50,relation_dom(relation_rng_restriction(sK12,U_49))) ) )
& function(U_49)
& relation(U_49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_51,sK12)],[f_33_3]) ).
fof(f_33_5,negated_conjecture,
? [U_49] :
( ( ( ~ in(sK13,relation_dom(relation_rng_restriction(sK12,U_49)))
& in(apply(U_49,sK13),sK12)
& in(sK13,relation_dom(U_49)) )
| ( ( ~ in(apply(U_49,sK13),sK12)
| ~ in(sK13,relation_dom(U_49)) )
& in(sK13,relation_dom(relation_rng_restriction(sK12,U_49))) ) )
& function(U_49)
& relation(U_49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_50,sK13)],[f_33_4]) ).
fof(f_33_6,negated_conjecture,
( ( ( ~ in(sK13,relation_dom(relation_rng_restriction(sK12,sK14)))
& in(apply(sK14,sK13),sK12)
& in(sK13,relation_dom(sK14)) )
| ( ( ~ in(apply(sK14,sK13),sK12)
| ~ in(sK13,relation_dom(sK14)) )
& in(sK13,relation_dom(relation_rng_restriction(sK12,sK14))) ) )
& function(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_49,sK14)],[f_33_5]) ).
cnf(f_33_7,negated_conjecture,
relation(sK14),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_8,negated_conjecture,
function(sK14),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_9,negated_conjecture,
( in(sK13,relation_dom(sK14))
| in(sK13,relation_dom(relation_rng_restriction(sK12,sK14))) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_10,negated_conjecture,
( in(apply(sK14,sK13),sK12)
| in(sK13,relation_dom(relation_rng_restriction(sK12,sK14))) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_14,negated_conjecture,
( ~ in(sK13,relation_dom(relation_rng_restriction(sK12,sK14)))
| ~ in(apply(sK14,sK13),sK12)
| ~ in(sK13,relation_dom(sK14)) ),
inference(clausify,[status(thm)],[f_33_6]) ).
fof(f_34_1,plain,
! [A,B] :
( ! [C] :
( ( ( B = relation_rng_restriction(A,C)
| ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| ? [D] :
( ( ~ in(D,relation_dom(B))
& in(apply(C,D),A)
& in(D,relation_dom(C)) )
| ( ( ~ in(apply(C,D),A)
| ~ in(D,relation_dom(C)) )
& in(D,relation_dom(B)) ) ) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( ( in(D,relation_dom(B))
| ~ in(apply(C,D),A)
| ~ in(D,relation_dom(C)) )
& ( ( in(apply(C,D),A)
& in(D,relation_dom(C)) )
| ~ in(D,relation_dom(B)) ) ) )
| B != relation_rng_restriction(A,C) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t85_funct_1]) ).
fof(f_34_2,plain,
! [U_58,U_57] :
( ! [U_56] :
( ( ( U_57 = relation_rng_restriction(U_58,U_56)
| ? [U_55] :
( apply(U_57,U_55) != apply(U_56,U_55)
& in(U_55,relation_dom(U_57)) )
| ? [U_54] :
( ( ~ in(U_54,relation_dom(U_57))
& in(apply(U_56,U_54),U_58)
& in(U_54,relation_dom(U_56)) )
| ( ( ~ in(apply(U_56,U_54),U_58)
| ~ in(U_54,relation_dom(U_56)) )
& in(U_54,relation_dom(U_57)) ) ) )
& ( ( ! [U_53] :
( apply(U_57,U_53) = apply(U_56,U_53)
| ~ in(U_53,relation_dom(U_57)) )
& ! [U_52] :
( ( in(U_52,relation_dom(U_57))
| ~ in(apply(U_56,U_52),U_58)
| ~ in(U_52,relation_dom(U_56)) )
& ( ( in(apply(U_56,U_52),U_58)
& in(U_52,relation_dom(U_56)) )
| ~ in(U_52,relation_dom(U_57)) ) ) )
| U_57 != relation_rng_restriction(U_58,U_56) ) )
| ~ function(U_56)
| ~ relation(U_56) )
| ~ function(U_57)
| ~ relation(U_57) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_58,U_57] :
( ! [U_56] :
( ( ( U_57 = relation_rng_restriction(U_58,U_56)
| ? [U_55] :
( apply(U_57,U_55) != apply(U_56,U_55)
& in(U_55,relation_dom(U_57)) )
| ? [U_62] :
( ~ in(U_62,relation_dom(U_57))
& in(apply(U_56,U_62),U_58)
& in(U_62,relation_dom(U_56)) )
| ? [U_61] :
( ( ~ in(apply(U_56,U_61),U_58)
| ~ in(U_61,relation_dom(U_56)) )
& in(U_61,relation_dom(U_57)) ) )
& ( ( ! [U_53] :
( apply(U_57,U_53) = apply(U_56,U_53)
| ~ in(U_53,relation_dom(U_57)) )
& ! [U_60] :
( in(U_60,relation_dom(U_57))
| ~ in(apply(U_56,U_60),U_58)
| ~ in(U_60,relation_dom(U_56)) )
& ! [U_59] :
( ( in(apply(U_56,U_59),U_58)
& in(U_59,relation_dom(U_56)) )
| ~ in(U_59,relation_dom(U_57)) ) )
| U_57 != relation_rng_restriction(U_58,U_56) ) )
| ~ function(U_56)
| ~ relation(U_56) )
| ~ function(U_57)
| ~ relation(U_57) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
fof(f_34_4,plain,
! [U_58,U_57] :
( ! [U_56] :
( ( ( U_57 = relation_rng_restriction(U_58,U_56)
| ? [U_55] :
( apply(U_57,U_55) != apply(U_56,U_55)
& in(U_55,relation_dom(U_57)) )
| ? [U_62] :
( ~ in(U_62,relation_dom(U_57))
& in(apply(U_56,U_62),U_58)
& in(U_62,relation_dom(U_56)) )
| ( ( ~ in(apply(U_56,sK15(U_58,U_57,U_56)),U_58)
| ~ in(sK15(U_58,U_57,U_56),relation_dom(U_56)) )
& in(sK15(U_58,U_57,U_56),relation_dom(U_57)) ) )
& ( ( ! [U_53] :
( apply(U_57,U_53) = apply(U_56,U_53)
| ~ in(U_53,relation_dom(U_57)) )
& ! [U_60] :
( in(U_60,relation_dom(U_57))
| ~ in(apply(U_56,U_60),U_58)
| ~ in(U_60,relation_dom(U_56)) )
& ! [U_59] :
( ( in(apply(U_56,U_59),U_58)
& in(U_59,relation_dom(U_56)) )
| ~ in(U_59,relation_dom(U_57)) ) )
| U_57 != relation_rng_restriction(U_58,U_56) ) )
| ~ function(U_56)
| ~ relation(U_56) )
| ~ function(U_57)
| ~ relation(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_61,sK15(U_58,U_57,U_56))],[f_34_3]) ).
fof(f_34_5,plain,
! [U_58,U_57] :
( ! [U_56] :
( ( ( U_57 = relation_rng_restriction(U_58,U_56)
| ? [U_55] :
( apply(U_57,U_55) != apply(U_56,U_55)
& in(U_55,relation_dom(U_57)) )
| ( ~ in(sK16(U_58,U_57,U_56),relation_dom(U_57))
& in(apply(U_56,sK16(U_58,U_57,U_56)),U_58)
& in(sK16(U_58,U_57,U_56),relation_dom(U_56)) )
| ( ( ~ in(apply(U_56,sK15(U_58,U_57,U_56)),U_58)
| ~ in(sK15(U_58,U_57,U_56),relation_dom(U_56)) )
& in(sK15(U_58,U_57,U_56),relation_dom(U_57)) ) )
& ( ( ! [U_53] :
( apply(U_57,U_53) = apply(U_56,U_53)
| ~ in(U_53,relation_dom(U_57)) )
& ! [U_60] :
( in(U_60,relation_dom(U_57))
| ~ in(apply(U_56,U_60),U_58)
| ~ in(U_60,relation_dom(U_56)) )
& ! [U_59] :
( ( in(apply(U_56,U_59),U_58)
& in(U_59,relation_dom(U_56)) )
| ~ in(U_59,relation_dom(U_57)) ) )
| U_57 != relation_rng_restriction(U_58,U_56) ) )
| ~ function(U_56)
| ~ relation(U_56) )
| ~ function(U_57)
| ~ relation(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_62,sK16(U_58,U_57,U_56))],[f_34_4]) ).
fof(f_34_6,plain,
! [U_58,U_57] :
( ! [U_56] :
( ( ( U_57 = relation_rng_restriction(U_58,U_56)
| ( apply(U_57,sK17(U_58,U_57,U_56)) != apply(U_56,sK17(U_58,U_57,U_56))
& in(sK17(U_58,U_57,U_56),relation_dom(U_57)) )
| ( ~ in(sK16(U_58,U_57,U_56),relation_dom(U_57))
& in(apply(U_56,sK16(U_58,U_57,U_56)),U_58)
& in(sK16(U_58,U_57,U_56),relation_dom(U_56)) )
| ( ( ~ in(apply(U_56,sK15(U_58,U_57,U_56)),U_58)
| ~ in(sK15(U_58,U_57,U_56),relation_dom(U_56)) )
& in(sK15(U_58,U_57,U_56),relation_dom(U_57)) ) )
& ( ( ! [U_53] :
( apply(U_57,U_53) = apply(U_56,U_53)
| ~ in(U_53,relation_dom(U_57)) )
& ! [U_60] :
( in(U_60,relation_dom(U_57))
| ~ in(apply(U_56,U_60),U_58)
| ~ in(U_60,relation_dom(U_56)) )
& ! [U_59] :
( ( in(apply(U_56,U_59),U_58)
& in(U_59,relation_dom(U_56)) )
| ~ in(U_59,relation_dom(U_57)) ) )
| U_57 != relation_rng_restriction(U_58,U_56) ) )
| ~ function(U_56)
| ~ relation(U_56) )
| ~ function(U_57)
| ~ relation(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_55,sK17(U_58,U_57,U_56))],[f_34_5]) ).
cnf(f_34_7,plain,
( in(U_59,relation_dom(U_56))
| ~ in(U_59,relation_dom(U_57))
| U_57 != relation_rng_restriction(U_58,U_56)
| ~ function(U_56)
| ~ relation(U_56)
| ~ function(U_57)
| ~ relation(U_57) ),
inference(clausify,[status(thm)],[f_34_6]) ).
cnf(f_34_8,plain,
( in(apply(U_56,U_59),U_58)
| ~ in(U_59,relation_dom(U_57))
| U_57 != relation_rng_restriction(U_58,U_56)
| ~ function(U_56)
| ~ relation(U_56)
| ~ function(U_57)
| ~ relation(U_57) ),
inference(clausify,[status(thm)],[f_34_6]) ).
cnf(f_34_9,plain,
( in(U_60,relation_dom(U_57))
| ~ in(apply(U_56,U_60),U_58)
| ~ in(U_60,relation_dom(U_56))
| U_57 != relation_rng_restriction(U_58,U_56)
| ~ function(U_56)
| ~ relation(U_56)
| ~ function(U_57)
| ~ relation(U_57) ),
inference(clausify,[status(thm)],[f_34_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_6,axiom,
( relation_rng_restriction(Eq_x_0,Eq_x_1) = relation_rng_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
( ~ in(apply(sK14,sK13),sK12)
| ~ in(sK13,relation_dom(relation_rng_restriction(sK12,sK14)))
| ~ in(sK13,relation_dom(sK14)) ),
inference(start,[status(thm),parent(0:0)],[f_33_14]) ).
cnf(t2,plain,
( in(sK13,relation_dom(relation_rng_restriction(sK12,sK14)))
| in(sK13,relation_dom(sK14)) ),
inference(extension,[status(thm),parent(t1:1)],[f_33_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ function(relation_rng_restriction(sK12,sK14))
| ~ relation(sK14)
| ~ function(sK14)
| relation_rng_restriction(sK12,sK14) != relation_rng_restriction(sK12,sK14)
| in(sK13,relation_dom(sK14))
| ~ relation(relation_rng_restriction(sK12,sK14))
| ~ in(sK13,relation_dom(relation_rng_restriction(sK12,sK14))) ),
inference(extension,[status(thm),parent(t2:2)],[f_34_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ function(sK14)
| ~ relation(sK14)
| relation(relation_rng_restriction(sK12,sK14)) ),
inference(extension,[status(thm),parent(t4:2)],[f_20_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
relation(sK14),
inference(extension,[status(thm),parent(t6:2)],[f_33_7]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
function(sK14),
inference(extension,[status(thm),parent(t6:3)],[f_33_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
$false,
inference(reduction,[status(thm),parent(t4:3)],[t4:3,t1:1]) ).
cnf(t13,plain,
( sK14 != sK14
| sK12 != sK12
| relation_rng_restriction(sK12,sK14) = relation_rng_restriction(sK12,sK14) ),
inference(extension,[status(thm),parent(t4:4)],[equality_6]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t4:4]) ).
cnf(t15,plain,
sK12 = sK12,
inference(extension,[status(thm),parent(t13:2)],[equality_1]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
sK14 = sK14,
inference(extension,[status(thm),parent(t13:3)],[equality_1]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t13:3]) ).
cnf(t19,plain,
function(sK14),
inference(extension,[status(thm),parent(t4:5)],[f_33_8]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t4:5]) ).
cnf(l10,lemma,
function(sK14),
inference(lemma,[status(cth),parent(t4:5),below(t2:2)],[t4:5]) ).
cnf(t21,plain,
relation(sK14),
inference(extension,[status(thm),parent(t4:6)],[f_33_7]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t4:6]) ).
cnf(l11,lemma,
relation(sK14),
inference(lemma,[status(cth),parent(t4:6),below(t2:2)],[t4:6]) ).
cnf(t23,plain,
( ~ function(sK14)
| ~ relation(sK14)
| function(relation_rng_restriction(sK12,sK14)) ),
inference(extension,[status(thm),parent(t4:7)],[f_20_4]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t4:7]) ).
cnf(t25,plain,
relation(sK14),
inference(lemma_extension,[status(thm),parent(t23:2)],[l11:1]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t23:2]) ).
cnf(t27,plain,
function(sK14),
inference(lemma_extension,[status(thm),parent(t23:3)],[l10:1]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t23:3]) ).
cnf(l1,lemma,
in(sK13,relation_dom(sK14)),
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t29,plain,
( ~ function(relation_rng_restriction(sK12,sK14))
| ~ relation(sK14)
| ~ function(sK14)
| relation_rng_restriction(sK12,sK14) != relation_rng_restriction(sK12,sK14)
| ~ in(sK13,relation_dom(sK14))
| ~ in(apply(sK14,sK13),sK12)
| ~ relation(relation_rng_restriction(sK12,sK14))
| in(sK13,relation_dom(relation_rng_restriction(sK12,sK14))) ),
inference(extension,[status(thm),parent(t1:2)],[f_34_9]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t1:2]) ).
cnf(t31,plain,
( ~ function(sK14)
| ~ relation(sK14)
| relation(relation_rng_restriction(sK12,sK14)) ),
inference(extension,[status(thm),parent(t29:2)],[f_20_3]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t29:2]) ).
cnf(t33,plain,
relation(sK14),
inference(extension,[status(thm),parent(t31:2)],[f_33_7]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t31:2]) ).
cnf(t35,plain,
function(sK14),
inference(extension,[status(thm),parent(t31:3)],[f_33_8]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t31:3]) ).
cnf(t37,plain,
( in(sK13,relation_dom(relation_rng_restriction(sK12,sK14)))
| in(apply(sK14,sK13),sK12) ),
inference(extension,[status(thm),parent(t29:3)],[f_33_10]) ).
cnf(t38,plain,
$false,
inference(connection,[status(thm),parent(t37:1)],[t37:1,t29:3]) ).
cnf(t39,plain,
$false,
inference(reduction,[status(thm),parent(t37:2)],[t37:2,t1:2]) ).
cnf(t40,plain,
in(sK13,relation_dom(sK14)),
inference(lemma_extension,[status(thm),parent(t29:4)],[l1:1]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t29:4]) ).
cnf(t42,plain,
( sK14 != sK14
| sK12 != sK12
| relation_rng_restriction(sK12,sK14) = relation_rng_restriction(sK12,sK14) ),
inference(extension,[status(thm),parent(t29:5)],[equality_6]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t29:5]) ).
cnf(t44,plain,
sK12 = sK12,
inference(extension,[status(thm),parent(t42:2)],[equality_1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
sK14 = sK14,
inference(extension,[status(thm),parent(t42:3)],[equality_1]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).
cnf(t48,plain,
function(sK14),
inference(extension,[status(thm),parent(t29:6)],[f_33_8]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t29:6]) ).
cnf(l22,lemma,
function(sK14),
inference(lemma,[status(cth),parent(t29:6),below(t1:2)],[t29:6]) ).
cnf(t50,plain,
relation(sK14),
inference(extension,[status(thm),parent(t29:7)],[f_33_7]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t29:7]) ).
cnf(l23,lemma,
relation(sK14),
inference(lemma,[status(cth),parent(t29:7),below(t1:2)],[t29:7]) ).
cnf(t52,plain,
( ~ function(sK14)
| ~ relation(sK14)
| function(relation_rng_restriction(sK12,sK14)) ),
inference(extension,[status(thm),parent(t29:8)],[f_20_4]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t29:8]) ).
cnf(t54,plain,
relation(sK14),
inference(lemma_extension,[status(thm),parent(t52:2)],[l23:1]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
function(sK14),
inference(lemma_extension,[status(thm),parent(t52:3)],[l22:1]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t52:3]) ).
cnf(t58,plain,
( in(sK13,relation_dom(relation_rng_restriction(sK12,sK14)))
| in(apply(sK14,sK13),sK12) ),
inference(extension,[status(thm),parent(t1:3)],[f_33_10]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t1:3]) ).
cnf(t60,plain,
( ~ function(relation_rng_restriction(sK12,sK14))
| ~ relation(sK14)
| ~ function(sK14)
| relation_rng_restriction(sK12,sK14) != relation_rng_restriction(sK12,sK14)
| in(apply(sK14,sK13),sK12)
| ~ relation(relation_rng_restriction(sK12,sK14))
| ~ in(sK13,relation_dom(relation_rng_restriction(sK12,sK14))) ),
inference(extension,[status(thm),parent(t58:2)],[f_34_8]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
( ~ function(sK14)
| ~ relation(sK14)
| relation(relation_rng_restriction(sK12,sK14)) ),
inference(extension,[status(thm),parent(t60:2)],[f_20_3]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
relation(sK14),
inference(extension,[status(thm),parent(t62:2)],[f_33_7]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t62:2]) ).
cnf(t66,plain,
function(sK14),
inference(extension,[status(thm),parent(t62:3)],[f_33_8]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t62:3]) ).
cnf(t68,plain,
$false,
inference(reduction,[status(thm),parent(t60:3)],[t60:3,t1:3]) ).
cnf(t69,plain,
( sK14 != sK14
| sK12 != sK12
| relation_rng_restriction(sK12,sK14) = relation_rng_restriction(sK12,sK14) ),
inference(extension,[status(thm),parent(t60:4)],[equality_6]) ).
cnf(t70,plain,
$false,
inference(connection,[status(thm),parent(t69:1)],[t69:1,t60:4]) ).
cnf(t71,plain,
sK12 = sK12,
inference(extension,[status(thm),parent(t69:2)],[equality_1]) ).
cnf(t72,plain,
$false,
inference(connection,[status(thm),parent(t71:1)],[t71:1,t69:2]) ).
cnf(t73,plain,
sK14 = sK14,
inference(extension,[status(thm),parent(t69:3)],[equality_1]) ).
cnf(t74,plain,
$false,
inference(connection,[status(thm),parent(t73:1)],[t73:1,t69:3]) ).
cnf(t75,plain,
function(sK14),
inference(extension,[status(thm),parent(t60:5)],[f_33_8]) ).
cnf(t76,plain,
$false,
inference(connection,[status(thm),parent(t75:1)],[t75:1,t60:5]) ).
cnf(l34,lemma,
function(sK14),
inference(lemma,[status(cth),parent(t60:5),below(t58:2)],[t60:5]) ).
cnf(t77,plain,
relation(sK14),
inference(extension,[status(thm),parent(t60:6)],[f_33_7]) ).
cnf(t78,plain,
$false,
inference(connection,[status(thm),parent(t77:1)],[t77:1,t60:6]) ).
cnf(l35,lemma,
relation(sK14),
inference(lemma,[status(cth),parent(t60:6),below(t58:2)],[t60:6]) ).
cnf(t79,plain,
( ~ function(sK14)
| ~ relation(sK14)
| function(relation_rng_restriction(sK12,sK14)) ),
inference(extension,[status(thm),parent(t60:7)],[f_20_4]) ).
cnf(t80,plain,
$false,
inference(connection,[status(thm),parent(t79:1)],[t79:1,t60:7]) ).
cnf(t81,plain,
relation(sK14),
inference(lemma_extension,[status(thm),parent(t79:2)],[l35:1]) ).
cnf(t82,plain,
$false,
inference(connection,[status(thm),parent(t81:1)],[t81:1,t79:2]) ).
cnf(t83,plain,
function(sK14),
inference(lemma_extension,[status(thm),parent(t79:3)],[l34:1]) ).
cnf(t84,plain,
$false,
inference(connection,[status(thm),parent(t83:1)],[t83:1,t79:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU044+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.57 % Computer : n001.cluster.edu
% 0.08/0.57 % Model : x86_64 x86_64
% 0.08/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.57 % Memory : 8046.5625MB
% 0.08/0.57 % OS : Linux 6.8.0-71-generic
% 0.08/0.57 % CPULimit : 300
% 0.08/0.57 % WCLimit : 300
% 0.08/0.57 % DateTime : Sat Sep 19 23:19:42 UTC 2026
% 0.08/0.57 % CPUTime :
% 78.02/78.54 % SZS status Theorem for theBenchmark
% 78.02/78.54 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------