%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU217+3 : 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 : n008.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 08:58:32 AM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 83 ( 36 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 85 ( 34 ~; 26 |; 20 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn 21 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc2_funct_1,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('theBenchmark.p',fc2_funct_1) ).
fof(t35_funct_1,conjecture,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('theBenchmark.p',t35_funct_1) ).
fof(t34_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('theBenchmark.p',t34_funct_1) ).
fof(f_19_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_19_2,plain,
! [U_29] :
( function(identity_relation(U_29))
& relation(identity_relation(U_29)) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_31] : function(identity_relation(U_31))
& ! [U_30] : relation(identity_relation(U_30)) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
relation(identity_relation(U_30)),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
function(identity_relation(U_31)),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_30_1,negated_conjecture,
~ ! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
inference(negate,[status(cth)],[t35_funct_1]) ).
fof(f_30_2,negated_conjecture,
? [A,B] :
( apply(identity_relation(A),B) != B
& in(B,A) ),
inference(fof_nnf,[status(thm)],[f_30_1]) ).
fof(f_30_3,negated_conjecture,
? [U_47,U_46] :
( apply(identity_relation(U_47),U_46) != U_46
& in(U_46,U_47) ),
inference(variable_rename,[status(thm)],[f_30_2]) ).
fof(f_30_4,negated_conjecture,
? [U_46] :
( apply(identity_relation(sK10),U_46) != U_46
& in(U_46,sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_47,sK10)],[f_30_3]) ).
fof(f_30_5,negated_conjecture,
( apply(identity_relation(sK10),sK11) != sK11
& in(sK11,sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_46,sK11)],[f_30_4]) ).
fof(f_30_6,negated_conjecture,
( apply(identity_relation(sK10),sK11) != sK11
& in(sK11,sK10) ),
inference(definitional_conversion,[status(esa)],[f_30_5]) ).
cnf(f_30_7,negated_conjecture,
in(sK11,sK10),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_8,negated_conjecture,
apply(identity_relation(sK10),sK11) != sK11,
inference(clausify,[status(thm)],[f_30_6]) ).
fof(f_31_1,plain,
! [A,B] :
( ( ( B = identity_relation(A)
| ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t34_funct_1]) ).
fof(f_31_2,plain,
! [U_51,U_50] :
( ( ( U_50 = identity_relation(U_51)
| ? [U_49] :
( apply(U_50,U_49) != U_49
& in(U_49,U_51) )
| relation_dom(U_50) != U_51 )
& ( ( ! [U_48] :
( apply(U_50,U_48) = U_48
| ~ in(U_48,U_51) )
& relation_dom(U_50) = U_51 )
| U_50 != identity_relation(U_51) ) )
| ~ function(U_50)
| ~ relation(U_50) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_51,U_50] :
( ( ( U_50 = identity_relation(U_51)
| ( apply(U_50,sK12(U_51,U_50)) != sK12(U_51,U_50)
& in(sK12(U_51,U_50),U_51) )
| relation_dom(U_50) != U_51 )
& ( ( ! [U_48] :
( apply(U_50,U_48) = U_48
| ~ in(U_48,U_51) )
& relation_dom(U_50) = U_51 )
| U_50 != identity_relation(U_51) ) )
| ~ function(U_50)
| ~ relation(U_50) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_49,sK12(U_51,U_50))],[f_31_2]) ).
cnf(f_31_5,plain,
( apply(U_50,U_48) = U_48
| ~ in(U_48,U_51)
| U_50 != identity_relation(U_51)
| ~ function(U_50)
| ~ relation(U_50) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
apply(identity_relation(sK10),sK11) != sK11,
inference(start,[status(thm),parent(0:0)],[f_30_8]) ).
cnf(t2,plain,
( ~ function(identity_relation(sK10))
| identity_relation(sK10) != identity_relation(sK10)
| ~ in(sK11,sK10)
| ~ relation(identity_relation(sK10))
| apply(identity_relation(sK10),sK11) = sK11 ),
inference(extension,[status(thm),parent(t1:1)],[f_31_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
relation(identity_relation(sK10)),
inference(extension,[status(thm),parent(t2:2)],[f_19_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
in(sK11,sK10),
inference(extension,[status(thm),parent(t2:3)],[f_30_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
identity_relation(sK10) = identity_relation(sK10),
inference(extension,[status(thm),parent(t2:4)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
function(identity_relation(sK10)),
inference(extension,[status(thm),parent(t2:5)],[f_19_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU217+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 23:33:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.14/0.45 % SZS status Theorem for theBenchmark
% 0.14/0.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------