%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE001+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 0.10s 0.40s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 45 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 18 ~; 8 |; 10 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 19 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('KLE001+0.ax',additive_idempotence) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('KLE001+0.ax',order) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( leq(X0,X1)
=> leq(addition(X0,X2),addition(X0,X2)) ),
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_12_1,plain,
! [A,B] :
( ( leq(A,B)
| addition(A,B) != B )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(fof_nnf,[status(thm)],[order]) ).
fof(f_12_2,plain,
! [U_21,U_20] :
( ( leq(U_21,U_20)
| addition(U_21,U_20) != U_20 )
& ( addition(U_21,U_20) = U_20
| ~ leq(U_21,U_20) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_25,U_23] :
( leq(U_25,U_23)
| addition(U_25,U_23) != U_23 )
& ! [U_24,U_22] :
( addition(U_24,U_22) = U_22
| ~ leq(U_24,U_22) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_5,plain,
( leq(U_25,U_23)
| addition(U_25,U_23) != U_23 ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(X0,X1)
=> leq(addition(X0,X2),addition(X0,X2)) ),
inference(negate,[status(cth)],[goals]) ).
fof(f_13_2,negated_conjecture,
? [X0,X1,X2] :
( ~ leq(addition(X0,X2),addition(X0,X2))
& leq(X0,X1) ),
inference(fof_nnf,[status(thm)],[f_13_1]) ).
fof(f_13_3,negated_conjecture,
? [U_28,U_27,U_26] :
( ~ leq(addition(U_28,U_26),addition(U_28,U_26))
& leq(U_28,U_27) ),
inference(variable_rename,[status(thm)],[f_13_2]) ).
fof(f_13_4,negated_conjecture,
? [U_28] :
( ? [U_27] : leq(U_28,U_27)
& ? [U_26] : ~ leq(addition(U_28,U_26),addition(U_28,U_26)) ),
inference(miniscope,[status(thm)],[f_13_3]) ).
fof(f_13_5,negated_conjecture,
( ? [U_27] : leq(sK1,U_27)
& ? [U_26] : ~ leq(addition(sK1,U_26),addition(sK1,U_26)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_28,sK1)],[f_13_4]) ).
fof(f_13_6,negated_conjecture,
( ? [U_27] : leq(sK1,U_27)
& ~ leq(addition(sK1,sK2),addition(sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_26,sK2)],[f_13_5]) ).
fof(f_13_7,negated_conjecture,
( leq(sK1,sK3)
& ~ leq(addition(sK1,sK2),addition(sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_27,sK3)],[f_13_6]) ).
fof(f_13_8,negated_conjecture,
( leq(sK1,sK3)
& ~ leq(addition(sK1,sK2),addition(sK1,sK2)) ),
inference(definitional_conversion,[status(esa)],[f_13_7]) ).
cnf(f_13_9,negated_conjecture,
~ leq(addition(sK1,sK2),addition(sK1,sK2)),
inference(clausify,[status(thm)],[f_13_8]) ).
cnf(t1,plain,
~ leq(addition(sK1,sK2),addition(sK1,sK2)),
inference(start,[status(thm),parent(0:0)],[f_13_9]) ).
cnf(t2,plain,
( addition(addition(sK1,sK2),addition(sK1,sK2)) != addition(sK1,sK2)
| leq(addition(sK1,sK2),addition(sK1,sK2)) ),
inference(extension,[status(thm),parent(t1:1)],[f_12_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
addition(addition(sK1,sK2),addition(sK1,sK2)) = addition(sK1,sK2),
inference(extension,[status(thm),parent(t2:2)],[f_4_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE001+1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 11:45:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------