%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU045+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 : n009.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 3.95s 4.27s
% Output : Proof 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 30 unt; 0 def)
% Number of atoms : 248 ( 49 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 307 ( 115 ~; 106 |; 76 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 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 : 83 ( 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(t87_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
=> apply(relation_rng_restriction(A,C),B) = apply(C,B) ) ),
file('theBenchmark.p',t87_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)))
=> apply(relation_rng_restriction(A,C),B) = apply(C,B) ) ),
inference(negate,[status(cth)],[t87_funct_1]) ).
fof(f_33_2,negated_conjecture,
? [A,B,C] :
( apply(relation_rng_restriction(A,C),B) != apply(C,B)
& 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] :
( apply(relation_rng_restriction(U_51,U_49),U_50) != apply(U_49,U_50)
& 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] :
( apply(relation_rng_restriction(sK12,U_49),U_50) != apply(U_49,U_50)
& 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] :
( apply(relation_rng_restriction(sK12,U_49),sK13) != apply(U_49,sK13)
& 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,
( apply(relation_rng_restriction(sK12,sK14),sK13) != apply(sK14,sK13)
& 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]) ).
fof(f_33_7,negated_conjecture,
( apply(relation_rng_restriction(sK12,sK14),sK13) != apply(sK14,sK13)
& in(sK13,relation_dom(relation_rng_restriction(sK12,sK14)))
& function(sK14)
& relation(sK14) ),
inference(definitional_conversion,[status(esa)],[f_33_6]) ).
cnf(f_33_8,negated_conjecture,
relation(sK14),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_9,negated_conjecture,
function(sK14),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_10,negated_conjecture,
in(sK13,relation_dom(relation_rng_restriction(sK12,sK14))),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_11,negated_conjecture,
apply(relation_rng_restriction(sK12,sK14),sK13) != apply(sK14,sK13),
inference(clausify,[status(thm)],[f_33_7]) ).
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_10,plain,
( apply(U_57,U_53) = apply(U_56,U_53)
| ~ in(U_53,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(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,
apply(relation_rng_restriction(sK12,sK14),sK13) != apply(sK14,sK13),
inference(start,[status(thm),parent(0:0)],[f_33_11]) ).
cnf(t2,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(relation_rng_restriction(sK12,sK14)))
| ~ relation(relation_rng_restriction(sK12,sK14))
| apply(relation_rng_restriction(sK12,sK14),sK13) = apply(sK14,sK13) ),
inference(extension,[status(thm),parent(t1:1)],[f_34_10]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ function(sK14)
| ~ relation(sK14)
| relation(relation_rng_restriction(sK12,sK14)) ),
inference(extension,[status(thm),parent(t2:2)],[f_20_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
relation(sK14),
inference(extension,[status(thm),parent(t4:2)],[f_33_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
function(sK14),
inference(extension,[status(thm),parent(t4:3)],[f_33_9]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
in(sK13,relation_dom(relation_rng_restriction(sK12,sK14))),
inference(extension,[status(thm),parent(t2:3)],[f_33_10]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( sK14 != sK14
| sK12 != sK12
| relation_rng_restriction(sK12,sK14) = relation_rng_restriction(sK12,sK14) ),
inference(extension,[status(thm),parent(t2:4)],[equality_6]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
cnf(t14,plain,
sK12 = sK12,
inference(extension,[status(thm),parent(t12:2)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
sK14 = sK14,
inference(extension,[status(thm),parent(t12:3)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
function(sK14),
inference(extension,[status(thm),parent(t2:5)],[f_33_9]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:5]) ).
cnf(l9,lemma,
function(sK14),
inference(lemma,[status(cth),parent(t2:5),below(t1:1)],[t2:5]) ).
cnf(t20,plain,
relation(sK14),
inference(extension,[status(thm),parent(t2:6)],[f_33_8]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:6]) ).
cnf(l10,lemma,
relation(sK14),
inference(lemma,[status(cth),parent(t2:6),below(t1:1)],[t2:6]) ).
cnf(t22,plain,
( ~ function(sK14)
| ~ relation(sK14)
| function(relation_rng_restriction(sK12,sK14)) ),
inference(extension,[status(thm),parent(t2:7)],[f_20_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:7]) ).
cnf(t24,plain,
relation(sK14),
inference(lemma_extension,[status(thm),parent(t22:2)],[l10:1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
function(sK14),
inference(lemma_extension,[status(thm),parent(t22:3)],[l9:1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU045+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
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % 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 23:14:12 UTC 2026
% 0.11/0.36 % CPUTime :
% 3.95/4.27 % SZS status Theorem for theBenchmark
% 3.95/4.27 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------