%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU217+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : 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 08:58:32 AM UTC 2026
% Result : Theorem 0.13s 20.65s
% Output : Proof 0.13s
% 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_24_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_24_2,plain,
! [U_20] :
( function(identity_relation(U_20))
& relation(identity_relation(U_20)) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_22] : function(identity_relation(U_22))
& ! [U_21] : relation(identity_relation(U_21)) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
relation(identity_relation(U_21)),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
function(identity_relation(U_22)),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_27_1,negated_conjecture,
~ ! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
inference(negate,[status(cth)],[t35_funct_1]) ).
fof(f_27_2,negated_conjecture,
? [A,B] :
( apply(identity_relation(A),B) != B
& in(B,A) ),
inference(fof_nnf,[status(thm)],[f_27_1]) ).
fof(f_27_3,negated_conjecture,
? [U_28,U_27] :
( apply(identity_relation(U_28),U_27) != U_27
& in(U_27,U_28) ),
inference(variable_rename,[status(thm)],[f_27_2]) ).
fof(f_27_4,negated_conjecture,
? [U_27] :
( apply(identity_relation(sK8),U_27) != U_27
& in(U_27,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_28,sK8)],[f_27_3]) ).
fof(f_27_5,negated_conjecture,
( apply(identity_relation(sK8),sK9) != sK9
& in(sK9,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_27,sK9)],[f_27_4]) ).
fof(f_27_6,negated_conjecture,
( apply(identity_relation(sK8),sK9) != sK9
& in(sK9,sK8) ),
inference(definitional_conversion,[status(esa)],[f_27_5]) ).
cnf(f_27_7,negated_conjecture,
in(sK9,sK8),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_8,negated_conjecture,
apply(identity_relation(sK8),sK9) != sK9,
inference(clausify,[status(thm)],[f_27_6]) ).
fof(f_28_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_28_2,plain,
! [U_32,U_31] :
( ( ( U_31 = identity_relation(U_32)
| ? [U_30] :
( apply(U_31,U_30) != U_30
& in(U_30,U_32) )
| relation_dom(U_31) != U_32 )
& ( ( ! [U_29] :
( apply(U_31,U_29) = U_29
| ~ in(U_29,U_32) )
& relation_dom(U_31) = U_32 )
| U_31 != identity_relation(U_32) ) )
| ~ function(U_31)
| ~ relation(U_31) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_32,U_31] :
( ( ( U_31 = identity_relation(U_32)
| ( apply(U_31,sK10(U_32,U_31)) != sK10(U_32,U_31)
& in(sK10(U_32,U_31),U_32) )
| relation_dom(U_31) != U_32 )
& ( ( ! [U_29] :
( apply(U_31,U_29) = U_29
| ~ in(U_29,U_32) )
& relation_dom(U_31) = U_32 )
| U_31 != identity_relation(U_32) ) )
| ~ function(U_31)
| ~ relation(U_31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_30,sK10(U_32,U_31))],[f_28_2]) ).
cnf(f_28_5,plain,
( apply(U_31,U_29) = U_29
| ~ in(U_29,U_32)
| U_31 != identity_relation(U_32)
| ~ function(U_31)
| ~ relation(U_31) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
apply(identity_relation(sK8),sK9) != sK9,
inference(start,[status(thm),parent(0:0)],[f_27_8]) ).
cnf(t2,plain,
( ~ function(identity_relation(sK8))
| identity_relation(sK8) != identity_relation(sK8)
| ~ in(sK9,sK8)
| ~ relation(identity_relation(sK8))
| apply(identity_relation(sK8),sK9) = sK9 ),
inference(extension,[status(thm),parent(t1:1)],[f_28_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
relation(identity_relation(sK8)),
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,
in(sK9,sK8),
inference(extension,[status(thm),parent(t2:3)],[f_27_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
identity_relation(sK8) = identity_relation(sK8),
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(sK8)),
inference(extension,[status(thm),parent(t2:5)],[f_24_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+1 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/20.59 % Computer : n013.cluster.edu
% 0.09/20.59 % Model : x86_64 x86_64
% 0.09/20.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/20.59 % Memory : 8046.5625MB
% 0.09/20.59 % OS : Linux 6.8.0-71-generic
% 0.09/20.59 % CPULimit : 300
% 0.09/20.59 % WCLimit : 300
% 0.09/20.59 % DateTime : Sat Sep 19 23:32:46 UTC 2026
% 0.09/20.60 % CPUTime :
% 0.13/20.65 % SZS status Theorem for theBenchmark
% 0.13/20.65 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------