%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE059+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 08:46:57 AM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 15 unt; 0 def)
% Number of atoms : 45 ( 39 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 17 ~; 9 |; 5 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 10 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('KLE001+5.ax',domain5) ).
fof(goals,conjecture,
! [X0,X1] :
( addition(X0,X1) = X1
=> addition(domain(X0),domain(X1)) = domain(X1) ),
file('theBenchmark.p',goals) ).
fof(f_17_1,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(fof_nnf,[status(thm)],[domain5]) ).
fof(f_17_2,plain,
! [U_31,U_30] : domain(addition(U_31,U_30)) = addition(domain(U_31),domain(U_30)),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
domain(addition(U_31,U_30)) = addition(domain(U_31),domain(U_30)),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,negated_conjecture,
~ ! [X0,X1] :
( addition(X0,X1) = X1
=> addition(domain(X0),domain(X1)) = domain(X1) ),
inference(negate,[status(cth)],[goals]) ).
fof(f_18_2,negated_conjecture,
? [X0,X1] :
( addition(domain(X0),domain(X1)) != domain(X1)
& addition(X0,X1) = X1 ),
inference(fof_nnf,[status(thm)],[f_18_1]) ).
fof(f_18_3,negated_conjecture,
? [U_33,U_32] :
( addition(domain(U_33),domain(U_32)) != domain(U_32)
& addition(U_33,U_32) = U_32 ),
inference(variable_rename,[status(thm)],[f_18_2]) ).
fof(f_18_4,negated_conjecture,
? [U_32] :
( addition(domain(sK1),domain(U_32)) != domain(U_32)
& addition(sK1,U_32) = U_32 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_33,sK1)],[f_18_3]) ).
fof(f_18_5,negated_conjecture,
( addition(domain(sK1),domain(sK2)) != domain(sK2)
& addition(sK1,sK2) = sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_32,sK2)],[f_18_4]) ).
fof(f_18_6,negated_conjecture,
( addition(domain(sK1),domain(sK2)) != domain(sK2)
& addition(sK1,sK2) = sK2 ),
inference(definitional_conversion,[status(esa)],[f_18_5]) ).
cnf(f_18_7,negated_conjecture,
addition(sK1,sK2) = sK2,
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_8,negated_conjecture,
addition(domain(sK1),domain(sK2)) != domain(sK2),
inference(clausify,[status(thm)],[f_18_6]) ).
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,
( domain(Eq_x_0) = domain(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
addition(domain(sK1),domain(sK2)) != domain(sK2),
inference(start,[status(thm),parent(0:0)],[f_18_8]) ).
cnf(t2,plain,
( domain(sK2) != addition(domain(sK1),domain(sK2))
| addition(domain(sK1),domain(sK2)) = domain(sK2) ),
inference(extension,[status(thm),parent(t1:1)],[equality_2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( domain(addition(sK1,sK2)) != addition(domain(sK1),domain(sK2))
| domain(sK2) != domain(addition(sK1,sK2))
| domain(sK2) = addition(domain(sK1),domain(sK2)) ),
inference(extension,[status(thm),parent(t2:2)],[equality_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( sK2 != addition(sK1,sK2)
| domain(sK2) = domain(addition(sK1,sK2)) ),
inference(extension,[status(thm),parent(t4:2)],[equality_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( addition(sK1,sK2) != sK2
| sK2 = addition(sK1,sK2) ),
inference(extension,[status(thm),parent(t6:2)],[equality_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
addition(sK1,sK2) = sK2,
inference(extension,[status(thm),parent(t8:2)],[f_18_7]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
domain(addition(sK1,sK2)) = addition(domain(sK1),domain(sK2)),
inference(extension,[status(thm),parent(t4:3)],[f_17_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE059+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 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
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 11:51:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------