%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU219+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 : n002.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 08:58:33 AM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 29 unt; 0 def)
% Number of atoms : 127 ( 55 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 114 ( 47 ~; 40 |; 20 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 22 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d9_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> function_inverse(A) = relation_inverse(A) ) ),
file('theBenchmark.p',d9_funct_1) ).
fof(t37_relat_1,axiom,
! [A] :
( relation(A)
=> ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
file('theBenchmark.p',t37_relat_1) ).
fof(t55_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('theBenchmark.p',t55_funct_1) ).
fof(f_1_1,plain,
! [A] :
( function_inverse(A) = relation_inverse(A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d9_funct_1]) ).
fof(f_1_2,plain,
! [U_0] :
( function_inverse(U_0) = relation_inverse(U_0)
| ~ one_to_one(U_0)
| ~ function(U_0)
| ~ relation(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( function_inverse(U_0) = relation_inverse(U_0)
| ~ one_to_one(U_0)
| ~ function(U_0)
| ~ relation(U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_10_1,plain,
! [A] :
( ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t37_relat_1]) ).
fof(f_10_2,plain,
! [U_7] :
( ( relation_dom(U_7) = relation_rng(relation_inverse(U_7))
& relation_rng(U_7) = relation_dom(relation_inverse(U_7)) )
| ~ relation(U_7) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( relation_rng(U_7) = relation_dom(relation_inverse(U_7))
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( relation_dom(U_7) = relation_rng(relation_inverse(U_7))
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
inference(negate,[status(cth)],[t55_funct_1]) ).
fof(f_11_2,negated_conjecture,
? [A] :
( ( relation_dom(A) != relation_rng(function_inverse(A))
| relation_rng(A) != relation_dom(function_inverse(A)) )
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_8] :
( ( relation_dom(U_8) != relation_rng(function_inverse(U_8))
| relation_rng(U_8) != relation_dom(function_inverse(U_8)) )
& one_to_one(U_8)
& function(U_8)
& relation(U_8) ),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
( ( relation_dom(sK3) != relation_rng(function_inverse(sK3))
| relation_rng(sK3) != relation_dom(function_inverse(sK3)) )
& one_to_one(sK3)
& function(sK3)
& relation(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_8,sK3)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
( ( relation_dom(sK3) != relation_rng(function_inverse(sK3))
| relation_rng(sK3) != relation_dom(function_inverse(sK3)) )
& one_to_one(sK3)
& function(sK3)
& relation(sK3) ),
inference(definitional_conversion,[status(esa)],[f_11_4]) ).
cnf(f_11_6,negated_conjecture,
relation(sK3),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_7,negated_conjecture,
function(sK3),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_8,negated_conjecture,
one_to_one(sK3),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_9,negated_conjecture,
( relation_dom(sK3) != relation_rng(function_inverse(sK3))
| relation_rng(sK3) != relation_dom(function_inverse(sK3)) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_6,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
( relation_dom(sK3) != relation_rng(function_inverse(sK3))
| relation_rng(sK3) != relation_dom(function_inverse(sK3)) ),
inference(start,[status(thm),parent(0:0)],[f_11_9]) ).
cnf(t2,plain,
( relation_dom(relation_inverse(sK3)) != relation_dom(function_inverse(sK3))
| relation_rng(sK3) != relation_dom(relation_inverse(sK3))
| relation_rng(sK3) = relation_dom(function_inverse(sK3)) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ relation(sK3)
| relation_rng(sK3) = relation_dom(relation_inverse(sK3)) ),
inference(extension,[status(thm),parent(t2:2)],[f_10_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
relation(sK3),
inference(extension,[status(thm),parent(t4:2)],[f_11_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( relation_inverse(sK3) != function_inverse(sK3)
| relation_dom(relation_inverse(sK3)) = relation_dom(function_inverse(sK3)) ),
inference(extension,[status(thm),parent(t2:3)],[equality_7]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( function_inverse(sK3) != relation_inverse(sK3)
| relation_inverse(sK3) = function_inverse(sK3) ),
inference(extension,[status(thm),parent(t8:2)],[equality_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ function(sK3)
| ~ one_to_one(sK3)
| ~ relation(sK3)
| function_inverse(sK3) = relation_inverse(sK3) ),
inference(extension,[status(thm),parent(t10:2)],[f_1_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
relation(sK3),
inference(extension,[status(thm),parent(t12:2)],[f_11_6]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
one_to_one(sK3),
inference(extension,[status(thm),parent(t12:3)],[f_11_8]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
function(sK3),
inference(extension,[status(thm),parent(t12:4)],[f_11_7]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:4]) ).
cnf(t20,plain,
( relation_rng(relation_inverse(sK3)) != relation_rng(function_inverse(sK3))
| relation_dom(sK3) != relation_rng(relation_inverse(sK3))
| relation_dom(sK3) = relation_rng(function_inverse(sK3)) ),
inference(extension,[status(thm),parent(t1:2)],[equality_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t1:2]) ).
cnf(t22,plain,
( ~ relation(sK3)
| relation_dom(sK3) = relation_rng(relation_inverse(sK3)) ),
inference(extension,[status(thm),parent(t20:2)],[f_10_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
relation(sK3),
inference(extension,[status(thm),parent(t22:2)],[f_11_6]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( relation_inverse(sK3) != function_inverse(sK3)
| relation_rng(relation_inverse(sK3)) = relation_rng(function_inverse(sK3)) ),
inference(extension,[status(thm),parent(t20:3)],[equality_6]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t20:3]) ).
cnf(t28,plain,
( function_inverse(sK3) != relation_inverse(sK3)
| relation_inverse(sK3) = function_inverse(sK3) ),
inference(extension,[status(thm),parent(t26:2)],[equality_2]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( ~ function(sK3)
| ~ one_to_one(sK3)
| ~ relation(sK3)
| function_inverse(sK3) = relation_inverse(sK3) ),
inference(extension,[status(thm),parent(t28:2)],[f_1_3]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
relation(sK3),
inference(extension,[status(thm),parent(t30:2)],[f_11_6]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
one_to_one(sK3),
inference(extension,[status(thm),parent(t30:3)],[f_11_8]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t30:3]) ).
cnf(t36,plain,
function(sK3),
inference(extension,[status(thm),parent(t30:4)],[f_11_7]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t30:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU219+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.08/0.37 % Computer : n002.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 19 23:36:16 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------