%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE058+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 : n003.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 0.22s 0.54s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 41 unt; 0 def)
% Number of atoms : 68 ( 55 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 21 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 30 ( 1 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('KLE001+0.ax',additive_commutativity) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('KLE001+0.ax',multiplicative_right_identity) ).
fof(domain1,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('KLE001+5.ax',domain1) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one,
file('KLE001+5.ax',domain3) ).
fof(goals,conjecture,
domain(one) = 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_6_1,plain,
! [A] : multiplication(A,one) = A,
inference(fof_nnf,[status(thm)],[multiplicative_right_identity]) ).
fof(f_6_2,plain,
! [U_10] : multiplication(U_10,one) = U_10,
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
multiplication(U_10,one) = U_10,
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_13_1,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(fof_nnf,[status(thm)],[domain1]) ).
fof(f_13_2,plain,
! [U_26] : addition(U_26,multiplication(domain(U_26),U_26)) = multiplication(domain(U_26),U_26),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
addition(U_26,multiplication(domain(U_26),U_26)) = multiplication(domain(U_26),U_26),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_15_1,plain,
! [X0] : addition(domain(X0),one) = one,
inference(fof_nnf,[status(thm)],[domain3]) ).
fof(f_15_2,plain,
! [U_29] : addition(domain(U_29),one) = one,
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
addition(domain(U_29),one) = one,
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_18_1,negated_conjecture,
domain(one) != one,
inference(negate,[status(cth)],[goals]) ).
fof(f_18_2,negated_conjecture,
domain(one) != one,
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,negated_conjecture,
domain(one) != one,
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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_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,
domain(one) != one,
inference(start,[status(thm),parent(0:0)],[f_18_3]) ).
cnf(t2,plain,
( addition(one,multiplication(domain(one),one)) != one
| domain(one) != addition(one,multiplication(domain(one),one))
| domain(one) = 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,
( multiplication(domain(one),one) != addition(one,multiplication(domain(one),one))
| domain(one) != multiplication(domain(one),one)
| domain(one) = addition(one,multiplication(domain(one),one)) ),
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,
( multiplication(domain(one),one) != domain(one)
| domain(one) = multiplication(domain(one),one) ),
inference(extension,[status(thm),parent(t4:2)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
multiplication(domain(one),one) = domain(one),
inference(extension,[status(thm),parent(t6:2)],[f_6_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( addition(one,multiplication(domain(one),one)) != multiplication(domain(one),one)
| multiplication(domain(one),one) = addition(one,multiplication(domain(one),one)) ),
inference(extension,[status(thm),parent(t4:3)],[equality_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
addition(one,multiplication(domain(one),one)) = multiplication(domain(one),one),
inference(extension,[status(thm),parent(t10:2)],[f_13_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( addition(one,domain(one)) != one
| addition(one,multiplication(domain(one),one)) != addition(one,domain(one))
| addition(one,multiplication(domain(one),one)) = one ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).
cnf(t16,plain,
( multiplication(domain(one),one) != domain(one)
| one != one
| addition(one,multiplication(domain(one),one)) = addition(one,domain(one)) ),
inference(extension,[status(thm),parent(t14:2)],[equality_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
one = one,
inference(extension,[status(thm),parent(t16:2)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
multiplication(domain(one),one) = domain(one),
inference(extension,[status(thm),parent(t16:3)],[f_6_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
( addition(domain(one),one) != one
| addition(one,domain(one)) != addition(domain(one),one)
| addition(one,domain(one)) = one ),
inference(extension,[status(thm),parent(t14:3)],[equality_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t14:3]) ).
cnf(t24,plain,
addition(one,domain(one)) = addition(domain(one),one),
inference(extension,[status(thm),parent(t22:2)],[f_1_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
addition(domain(one),one) = one,
inference(extension,[status(thm),parent(t22:3)],[f_15_3]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE058+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
% 0.08/0.36 % Computer : n003.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 11:51:43 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.22/0.54 % SZS status Theorem for theBenchmark
% 0.22/0.54 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------