%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE138+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 : 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 08:47:02 AM UTC 2026
% Result : Theorem 0.08s 0.45s
% Output : Proof 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 36 unt; 0 def)
% Number of atoms : 54 ( 45 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 1 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('KLE004+0.ax',additive_commutativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('KLE004+0.ax',additive_identity) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('KLE004+0.ax',left_annihilation) ).
fof(infty_unfold1,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('KLE004+0.ax',infty_unfold1) ).
fof(goals,conjecture,
strong_iteration(zero) = one,
file('theBenchmark.p',goals) ).
fof(f_1_1,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(fof_nnf,[status(thm)],[additive_commutativity]) ).
fof(f_1_2,plain,
! [U_1,U_0] : addition(U_1,U_0) = addition(U_0,U_1),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
addition(U_1,U_0) = addition(U_0,U_1),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_3_1,plain,
! [A] : addition(A,zero) = A,
inference(fof_nnf,[status(thm)],[additive_identity]) ).
fof(f_3_2,plain,
! [U_5] : addition(U_5,zero) = U_5,
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
addition(U_5,zero) = U_5,
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_10_1,plain,
! [A] : multiplication(zero,A) = zero,
inference(fof_nnf,[status(thm)],[left_annihilation]) ).
fof(f_10_2,plain,
! [U_18] : multiplication(zero,U_18) = zero,
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
multiplication(zero,U_18) = zero,
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_15_1,plain,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
inference(fof_nnf,[status(thm)],[infty_unfold1]) ).
fof(f_15_2,plain,
! [U_27] : strong_iteration(U_27) = addition(multiplication(U_27,strong_iteration(U_27)),one),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
strong_iteration(U_27) = addition(multiplication(U_27,strong_iteration(U_27)),one),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_19_1,negated_conjecture,
strong_iteration(zero) != one,
inference(negate,[status(cth)],[goals]) ).
fof(f_19_2,negated_conjecture,
strong_iteration(zero) != one,
inference(definitional_conversion,[status(esa)],[f_19_1]) ).
cnf(f_19_3,negated_conjecture,
strong_iteration(zero) != one,
inference(clausify,[status(thm)],[f_19_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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_4,axiom,
( addition(Eq_x_0,Eq_x_1) = addition(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
strong_iteration(zero) != one,
inference(start,[status(thm),parent(0:0)],[f_19_3]) ).
cnf(t2,plain,
( addition(multiplication(zero,strong_iteration(zero)),one) != one
| strong_iteration(zero) != addition(multiplication(zero,strong_iteration(zero)),one)
| strong_iteration(zero) = one ),
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,
strong_iteration(zero) = addition(multiplication(zero,strong_iteration(zero)),one),
inference(extension,[status(thm),parent(t2:2)],[f_15_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( addition(zero,one) != one
| addition(multiplication(zero,strong_iteration(zero)),one) != addition(zero,one)
| addition(multiplication(zero,strong_iteration(zero)),one) = one ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( one != one
| multiplication(zero,strong_iteration(zero)) != zero
| addition(multiplication(zero,strong_iteration(zero)),one) = addition(zero,one) ),
inference(extension,[status(thm),parent(t6:2)],[equality_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
multiplication(zero,strong_iteration(zero)) = zero,
inference(extension,[status(thm),parent(t8:2)],[f_10_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
one = one,
inference(extension,[status(thm),parent(t8:3)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( addition(one,zero) != one
| addition(zero,one) != addition(one,zero)
| addition(zero,one) = one ),
inference(extension,[status(thm),parent(t6:3)],[equality_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
cnf(t16,plain,
addition(zero,one) = addition(one,zero),
inference(extension,[status(thm),parent(t14:2)],[f_1_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
addition(one,zero) = one,
inference(extension,[status(thm),parent(t14:3)],[f_3_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE138+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
% 0.08/0.37 % 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 12:03:00 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.45 % SZS status Theorem for theBenchmark
% 0.08/0.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------