%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU223+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 : n020.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 08:58:34 AM UTC 2026
% Result : Theorem 0.66s 0.95s
% Output : Proof 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 30 unt; 0 def)
% Number of atoms : 154 ( 44 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 163 ( 63 ~; 54 |; 37 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 55 ( 3 sgn 31 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc4_funct_1,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc4_funct_1) ).
fof(t70_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t70_funct_1) ).
fof(t68_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('theBenchmark.p',t68_funct_1) ).
fof(f_24_1,plain,
! [A,B] :
( ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc4_funct_1]) ).
fof(f_24_2,plain,
! [U_41,U_40] :
( ( function(relation_dom_restriction(U_41,U_40))
& relation(relation_dom_restriction(U_41,U_40)) )
| ~ function(U_41)
| ~ relation(U_41) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_41] :
( ( ! [U_43] : function(relation_dom_restriction(U_41,U_43))
& ! [U_42] : relation(relation_dom_restriction(U_41,U_42)) )
| ~ function(U_41)
| ~ relation(U_41) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( relation(relation_dom_restriction(U_41,U_42))
| ~ function(U_41)
| ~ relation(U_41) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
( function(relation_dom_restriction(U_41,U_43))
| ~ function(U_41)
| ~ relation(U_41) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_38_1,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
inference(negate,[status(cth)],[t70_funct_1]) ).
fof(f_38_2,negated_conjecture,
? [A,B,C] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,relation_dom(relation_dom_restriction(C,A)))
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[f_38_1]) ).
fof(f_38_3,negated_conjecture,
? [U_64,U_63,U_62] :
( apply(relation_dom_restriction(U_62,U_64),U_63) != apply(U_62,U_63)
& in(U_63,relation_dom(relation_dom_restriction(U_62,U_64)))
& function(U_62)
& relation(U_62) ),
inference(variable_rename,[status(thm)],[f_38_2]) ).
fof(f_38_4,negated_conjecture,
? [U_63,U_62] :
( apply(relation_dom_restriction(U_62,sK12),U_63) != apply(U_62,U_63)
& in(U_63,relation_dom(relation_dom_restriction(U_62,sK12)))
& function(U_62)
& relation(U_62) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_64,sK12)],[f_38_3]) ).
fof(f_38_5,negated_conjecture,
? [U_62] :
( apply(relation_dom_restriction(U_62,sK12),sK13) != apply(U_62,sK13)
& in(sK13,relation_dom(relation_dom_restriction(U_62,sK12)))
& function(U_62)
& relation(U_62) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_63,sK13)],[f_38_4]) ).
fof(f_38_6,negated_conjecture,
( apply(relation_dom_restriction(sK14,sK12),sK13) != apply(sK14,sK13)
& in(sK13,relation_dom(relation_dom_restriction(sK14,sK12)))
& function(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_62,sK14)],[f_38_5]) ).
fof(f_38_7,negated_conjecture,
( apply(relation_dom_restriction(sK14,sK12),sK13) != apply(sK14,sK13)
& in(sK13,relation_dom(relation_dom_restriction(sK14,sK12)))
& function(sK14)
& relation(sK14) ),
inference(definitional_conversion,[status(esa)],[f_38_6]) ).
cnf(f_38_8,negated_conjecture,
relation(sK14),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_9,negated_conjecture,
function(sK14),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_10,negated_conjecture,
in(sK13,relation_dom(relation_dom_restriction(sK14,sK12))),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_11,negated_conjecture,
apply(relation_dom_restriction(sK14,sK12),sK13) != apply(sK14,sK13),
inference(clausify,[status(thm)],[f_38_7]) ).
fof(f_39_1,plain,
! [A,B] :
( ! [C] :
( ( ( B = relation_dom_restriction(C,A)
| ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t68_funct_1]) ).
fof(f_39_2,plain,
! [U_69,U_68] :
( ! [U_67] :
( ( ( U_68 = relation_dom_restriction(U_67,U_69)
| ? [U_66] :
( apply(U_68,U_66) != apply(U_67,U_66)
& in(U_66,relation_dom(U_68)) )
| relation_dom(U_68) != set_intersection2(relation_dom(U_67),U_69) )
& ( ( ! [U_65] :
( apply(U_68,U_65) = apply(U_67,U_65)
| ~ in(U_65,relation_dom(U_68)) )
& relation_dom(U_68) = set_intersection2(relation_dom(U_67),U_69) )
| U_68 != relation_dom_restriction(U_67,U_69) ) )
| ~ function(U_67)
| ~ relation(U_67) )
| ~ function(U_68)
| ~ relation(U_68) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_69,U_68] :
( ! [U_67] :
( ( ( U_68 = relation_dom_restriction(U_67,U_69)
| ( apply(U_68,sK15(U_69,U_68,U_67)) != apply(U_67,sK15(U_69,U_68,U_67))
& in(sK15(U_69,U_68,U_67),relation_dom(U_68)) )
| relation_dom(U_68) != set_intersection2(relation_dom(U_67),U_69) )
& ( ( ! [U_65] :
( apply(U_68,U_65) = apply(U_67,U_65)
| ~ in(U_65,relation_dom(U_68)) )
& relation_dom(U_68) = set_intersection2(relation_dom(U_67),U_69) )
| U_68 != relation_dom_restriction(U_67,U_69) ) )
| ~ function(U_67)
| ~ relation(U_67) )
| ~ function(U_68)
| ~ relation(U_68) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_66,sK15(U_69,U_68,U_67))],[f_39_2]) ).
cnf(f_39_5,plain,
( apply(U_68,U_65) = apply(U_67,U_65)
| ~ in(U_65,relation_dom(U_68))
| U_68 != relation_dom_restriction(U_67,U_69)
| ~ function(U_67)
| ~ relation(U_67)
| ~ function(U_68)
| ~ relation(U_68) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_7,axiom,
( relation_dom_restriction(Eq_x_0,Eq_x_1) = relation_dom_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_dom_restriction(sK14,sK12),sK13) != apply(sK14,sK13),
inference(start,[status(thm),parent(0:0)],[f_38_11]) ).
cnf(t2,plain,
( ~ function(relation_dom_restriction(sK14,sK12))
| ~ relation(sK14)
| ~ function(sK14)
| relation_dom_restriction(sK14,sK12) != relation_dom_restriction(sK14,sK12)
| ~ in(sK13,relation_dom(relation_dom_restriction(sK14,sK12)))
| ~ relation(relation_dom_restriction(sK14,sK12))
| apply(relation_dom_restriction(sK14,sK12),sK13) = apply(sK14,sK13) ),
inference(extension,[status(thm),parent(t1:1)],[f_39_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ function(sK14)
| ~ relation(sK14)
| relation(relation_dom_restriction(sK14,sK12)) ),
inference(extension,[status(thm),parent(t2:2)],[f_24_4]) ).
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_38_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_38_9]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
in(sK13,relation_dom(relation_dom_restriction(sK14,sK12))),
inference(extension,[status(thm),parent(t2:3)],[f_38_10]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( sK12 != sK12
| sK14 != sK14
| relation_dom_restriction(sK14,sK12) = relation_dom_restriction(sK14,sK12) ),
inference(extension,[status(thm),parent(t2:4)],[equality_7]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
cnf(t14,plain,
sK14 = sK14,
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,
sK12 = sK12,
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_38_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_38_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_dom_restriction(sK14,sK12)) ),
inference(extension,[status(thm),parent(t2:7)],[f_24_5]) ).
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
% 0.00/0.03 % Problem : SEU223+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
% 0.11/0.38 % Computer : n020.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 19 23:35:47 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.66/0.95 % SZS status Theorem for theBenchmark
% 0.66/0.95 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------