%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE003+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 : n001.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 08:46:50 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 10 unt; 0 def)
% Number of atoms : 48 ( 30 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 47 ( 21 ~; 14 |; 10 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 4 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('KLE001+0.ax',additive_idempotence) ).
fof(goals,conjecture,
( ! [X0] : addition(X0,X0) = X0
<=> addition(one,one) = one ),
file('theBenchmark.p',goals) ).
fof(f_4_1,plain,
! [A] : addition(A,A) = A,
inference(fof_nnf,[status(thm)],[additive_idempotence]) ).
fof(f_4_2,plain,
! [U_6] : addition(U_6,U_6) = U_6,
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
addition(U_6,U_6) = U_6,
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_13_1,negated_conjecture,
~ ( ! [X0] : addition(X0,X0) = X0
<=> addition(one,one) = one ),
inference(negate,[status(cth)],[goals]) ).
fof(f_13_2,negated_conjecture,
( ( ? [X0] : addition(X0,X0) != X0
& addition(one,one) = one )
| ( addition(one,one) != one
& ! [X0] : addition(X0,X0) = X0 ) ),
inference(fof_nnf,[status(thm)],[f_13_1]) ).
fof(f_13_3,negated_conjecture,
( ( ? [U_27] : addition(U_27,U_27) != U_27
& addition(one,one) = one )
| ( addition(one,one) != one
& ! [U_26] : addition(U_26,U_26) = U_26 ) ),
inference(variable_rename,[status(thm)],[f_13_2]) ).
fof(f_13_4,negated_conjecture,
( ( addition(sK1,sK1) != sK1
& addition(one,one) = one )
| ( addition(one,one) != one
& ! [U_26] : addition(U_26,U_26) = U_26 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_27,sK1)],[f_13_3]) ).
fof(f_13_5,negated_conjecture,
( ( addition(sK1,sK1) != sK1
| ~ sP1 )
& ( addition(one,one) = one
| ~ sP1 )
& ! [U_26] :
( addition(one,one) != one
| ~ sP0(U_26) )
& ! [U_26] :
( addition(U_26,U_26) = U_26
| ~ sP0(U_26) )
& ! [U_26] :
( sP1
| sP0(U_26) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_13_4]) ).
cnf(f_13_6,negated_conjecture,
( sP1
| sP0(U_26) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_8,negated_conjecture,
( addition(one,one) != one
| ~ sP0(U_26) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_10,negated_conjecture,
( addition(sK1,sK1) != sK1
| ~ sP1 ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(t1,plain,
( addition(one,one) != one
| ~ sP0(U_264) ),
inference(start,[status(thm),parent(0:0)],[f_13_8]) ).
cnf(t2,plain,
( sP1
| sP0(U_264) ),
inference(extension,[status(thm),parent(t1:1)],[f_13_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( addition(sK1,sK1) != sK1
| ~ sP1 ),
inference(extension,[status(thm),parent(t2:2)],[f_13_10]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
addition(sK1,sK1) = sK1,
inference(extension,[status(thm),parent(t4:2)],[f_4_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
addition(one,one) = one,
inference(extension,[status(thm),parent(t1:2)],[f_4_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t1:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE003+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 11:45:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------