%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU223+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : n013.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 96.79s 97.10s
% Output : Proof 96.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 32 unt; 0 def)
% Number of atoms : 156 ( 39 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 160 ( 62 ~; 54 |; 34 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 66 ( 6 sgn 44 !; 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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t68_funct_1,lemma,
! [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(t6_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_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(f_91_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_91_2,plain,
! [U_444,U_443] :
( ( function(relation_dom_restriction(U_444,U_443))
& relation(relation_dom_restriction(U_444,U_443)) )
| ~ function(U_444)
| ~ relation(U_444) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
! [U_444] :
( ( ! [U_446] : function(relation_dom_restriction(U_444,U_446))
& ! [U_445] : relation(relation_dom_restriction(U_444,U_445)) )
| ~ function(U_444)
| ~ relation(U_444) ),
inference(miniscope,[status(thm)],[f_91_2]) ).
cnf(f_91_4,plain,
( relation(relation_dom_restriction(U_444,U_445))
| ~ function(U_444)
| ~ relation(U_444) ),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_5,plain,
( function(relation_dom_restriction(U_444,U_446))
| ~ function(U_444)
| ~ relation(U_444) ),
inference(clausify,[status(thm)],[f_91_3]) ).
fof(f_130_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_130_2,plain,
! [U_534,U_533] : subset(U_534,U_534),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_534] : subset(U_534,U_534),
inference(miniscope,[status(thm)],[f_130_2]) ).
cnf(f_130_4,plain,
subset(U_534,U_534),
inference(clausify,[status(thm)],[f_130_3]) ).
fof(f_216_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_216_2,plain,
! [U_796,U_795] :
( ! [U_794] :
( ( ( U_795 = relation_dom_restriction(U_794,U_796)
| ? [U_793] :
( apply(U_795,U_793) != apply(U_794,U_793)
& in(U_793,relation_dom(U_795)) )
| relation_dom(U_795) != set_intersection2(relation_dom(U_794),U_796) )
& ( ( ! [U_792] :
( apply(U_795,U_792) = apply(U_794,U_792)
| ~ in(U_792,relation_dom(U_795)) )
& relation_dom(U_795) = set_intersection2(relation_dom(U_794),U_796) )
| U_795 != relation_dom_restriction(U_794,U_796) ) )
| ~ function(U_794)
| ~ relation(U_794) )
| ~ function(U_795)
| ~ relation(U_795) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_796,U_795] :
( ! [U_794] :
( ( ( U_795 = relation_dom_restriction(U_794,U_796)
| ( apply(U_795,sK105(U_796,U_795,U_794)) != apply(U_794,sK105(U_796,U_795,U_794))
& in(sK105(U_796,U_795,U_794),relation_dom(U_795)) )
| relation_dom(U_795) != set_intersection2(relation_dom(U_794),U_796) )
& ( ( ! [U_792] :
( apply(U_795,U_792) = apply(U_794,U_792)
| ~ in(U_792,relation_dom(U_795)) )
& relation_dom(U_795) = set_intersection2(relation_dom(U_794),U_796) )
| U_795 != relation_dom_restriction(U_794,U_796) ) )
| ~ function(U_794)
| ~ relation(U_794) )
| ~ function(U_795)
| ~ relation(U_795) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_793,sK105(U_796,U_795,U_794))],[f_216_2]) ).
cnf(f_216_5,plain,
( apply(U_795,U_792) = apply(U_794,U_792)
| ~ in(U_792,relation_dom(U_795))
| U_795 != relation_dom_restriction(U_794,U_796)
| ~ function(U_794)
| ~ relation(U_794)
| ~ function(U_795)
| ~ relation(U_795) ),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_219_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_219_2,plain,
! [U_800,U_799] :
( U_800 = U_799
| ~ subset(singleton(U_800),singleton(U_799)) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( U_800 = U_799
| ~ subset(singleton(U_800),singleton(U_799)) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_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_220_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_220_1]) ).
fof(f_220_3,negated_conjecture,
? [U_803,U_802,U_801] :
( apply(relation_dom_restriction(U_801,U_803),U_802) != apply(U_801,U_802)
& in(U_802,relation_dom(relation_dom_restriction(U_801,U_803)))
& function(U_801)
& relation(U_801) ),
inference(variable_rename,[status(thm)],[f_220_2]) ).
fof(f_220_4,negated_conjecture,
? [U_802,U_801] :
( apply(relation_dom_restriction(U_801,sK106),U_802) != apply(U_801,U_802)
& in(U_802,relation_dom(relation_dom_restriction(U_801,sK106)))
& function(U_801)
& relation(U_801) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_803,sK106)],[f_220_3]) ).
fof(f_220_5,negated_conjecture,
? [U_801] :
( apply(relation_dom_restriction(U_801,sK106),sK107) != apply(U_801,sK107)
& in(sK107,relation_dom(relation_dom_restriction(U_801,sK106)))
& function(U_801)
& relation(U_801) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_802,sK107)],[f_220_4]) ).
fof(f_220_6,negated_conjecture,
( apply(relation_dom_restriction(sK108,sK106),sK107) != apply(sK108,sK107)
& in(sK107,relation_dom(relation_dom_restriction(sK108,sK106)))
& function(sK108)
& relation(sK108) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_801,sK108)],[f_220_5]) ).
cnf(f_220_7,negated_conjecture,
relation(sK108),
inference(clausify,[status(thm)],[f_220_6]) ).
cnf(f_220_8,negated_conjecture,
function(sK108),
inference(clausify,[status(thm)],[f_220_6]) ).
cnf(f_220_9,negated_conjecture,
in(sK107,relation_dom(relation_dom_restriction(sK108,sK106))),
inference(clausify,[status(thm)],[f_220_6]) ).
cnf(f_220_10,negated_conjecture,
apply(relation_dom_restriction(sK108,sK106),sK107) != apply(sK108,sK107),
inference(clausify,[status(thm)],[f_220_6]) ).
cnf(t1,plain,
apply(relation_dom_restriction(sK108,sK106),sK107) != apply(sK108,sK107),
inference(start,[status(thm),parent(0:0)],[f_220_10]) ).
cnf(t2,plain,
( ~ function(relation_dom_restriction(sK108,sK106))
| ~ relation(sK108)
| ~ function(sK108)
| relation_dom_restriction(sK108,sK106) != relation_dom_restriction(sK108,sK106)
| ~ in(sK107,relation_dom(relation_dom_restriction(sK108,sK106)))
| ~ relation(relation_dom_restriction(sK108,sK106))
| apply(relation_dom_restriction(sK108,sK106),sK107) = apply(sK108,sK107) ),
inference(extension,[status(thm),parent(t1:1)],[f_216_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ function(sK108)
| ~ relation(sK108)
| relation(relation_dom_restriction(sK108,sK106)) ),
inference(extension,[status(thm),parent(t2:2)],[f_91_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
relation(sK108),
inference(extension,[status(thm),parent(t4:2)],[f_220_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
function(sK108),
inference(extension,[status(thm),parent(t4:3)],[f_220_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
in(sK107,relation_dom(relation_dom_restriction(sK108,sK106))),
inference(extension,[status(thm),parent(t2:3)],[f_220_9]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( ~ subset(singleton(relation_dom_restriction(sK108,sK106)),singleton(relation_dom_restriction(sK108,sK106)))
| relation_dom_restriction(sK108,sK106) = relation_dom_restriction(sK108,sK106) ),
inference(extension,[status(thm),parent(t2:4)],[f_219_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
cnf(t14,plain,
subset(singleton(relation_dom_restriction(sK108,sK106)),singleton(relation_dom_restriction(sK108,sK106))),
inference(extension,[status(thm),parent(t12:2)],[f_130_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
function(sK108),
inference(extension,[status(thm),parent(t2:5)],[f_220_8]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:5]) ).
cnf(l8,lemma,
function(sK108),
inference(lemma,[status(cth),parent(t2:5),below(t1:1)],[t2:5]) ).
cnf(t18,plain,
relation(sK108),
inference(extension,[status(thm),parent(t2:6)],[f_220_7]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:6]) ).
cnf(l9,lemma,
relation(sK108),
inference(lemma,[status(cth),parent(t2:6),below(t1:1)],[t2:6]) ).
cnf(t20,plain,
( ~ function(sK108)
| ~ relation(sK108)
| function(relation_dom_restriction(sK108,sK106)) ),
inference(extension,[status(thm),parent(t2:7)],[f_91_5]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:7]) ).
cnf(t22,plain,
relation(sK108),
inference(lemma_extension,[status(thm),parent(t20:2)],[l9:1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
function(sK108),
inference(lemma_extension,[status(thm),parent(t20:3)],[l8:1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU223+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 19 23:34:05 UTC 2026
% 0.10/0.35 % CPUTime :
% 96.79/97.10 % SZS status Theorem for theBenchmark
% 96.79/97.10 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------