%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE006+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 08:46:51 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 18 unt; 0 def)
% Number of atoms : 96 ( 57 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 96 ( 40 ~; 33 |; 18 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('KLE001+0.ax',additive_commutativity) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('KLE001+1.ax',test_2) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('KLE001+1.ax',test_3) ).
fof(goals,conjecture,
! [X0] :
( test(X0)
=> one = addition(X0,c(X0)) ),
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_14_1,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(fof_nnf,[status(thm)],[test_2]) ).
fof(f_14_2,plain,
! [U_32,U_31] :
( ( complement(U_31,U_32)
| addition(U_32,U_31) != one
| multiplication(U_31,U_32) != zero
| multiplication(U_32,U_31) != zero )
& ( ( addition(U_32,U_31) = one
& multiplication(U_31,U_32) = zero
& multiplication(U_32,U_31) = zero )
| ~ complement(U_31,U_32) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_36,U_34] :
( complement(U_34,U_36)
| addition(U_36,U_34) != one
| multiplication(U_34,U_36) != zero
| multiplication(U_36,U_34) != zero )
& ! [U_35,U_33] :
( ( addition(U_35,U_33) = one
& multiplication(U_33,U_35) = zero
& multiplication(U_35,U_33) = zero )
| ~ complement(U_33,U_35) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_6,plain,
( addition(U_35,U_33) = one
| ~ complement(U_33,U_35) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(fof_nnf,[status(thm)],[test_3]) ).
fof(f_15_2,plain,
! [U_38,U_37] :
( ( ( c(U_38) = U_37
| ~ complement(U_38,U_37) )
& ( complement(U_38,U_37)
| c(U_38) != U_37 ) )
| ~ test(U_38) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_38] :
( ( ! [U_40] :
( c(U_38) = U_40
| ~ complement(U_38,U_40) )
& ! [U_39] :
( complement(U_38,U_39)
| c(U_38) != U_39 ) )
| ~ test(U_38) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( complement(U_38,U_39)
| c(U_38) != U_39
| ~ test(U_38) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_17_1,negated_conjecture,
~ ! [X0] :
( test(X0)
=> one = addition(X0,c(X0)) ),
inference(negate,[status(cth)],[goals]) ).
fof(f_17_2,negated_conjecture,
? [X0] :
( one != addition(X0,c(X0))
& test(X0) ),
inference(fof_nnf,[status(thm)],[f_17_1]) ).
fof(f_17_3,negated_conjecture,
? [U_42] :
( one != addition(U_42,c(U_42))
& test(U_42) ),
inference(variable_rename,[status(thm)],[f_17_2]) ).
fof(f_17_4,negated_conjecture,
( one != addition(sK2,c(sK2))
& test(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_42,sK2)],[f_17_3]) ).
fof(f_17_5,negated_conjecture,
( one != addition(sK2,c(sK2))
& test(sK2) ),
inference(definitional_conversion,[status(esa)],[f_17_4]) ).
cnf(f_17_6,negated_conjecture,
test(sK2),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_7,negated_conjecture,
one != addition(sK2,c(sK2)),
inference(clausify,[status(thm)],[f_17_5]) ).
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(t1,plain,
one != addition(sK2,c(sK2)),
inference(start,[status(thm),parent(0:0)],[f_17_7]) ).
cnf(t2,plain,
( addition(c(sK2),sK2) != addition(sK2,c(sK2))
| one != addition(c(sK2),sK2)
| one = addition(sK2,c(sK2)) ),
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,
( addition(c(sK2),sK2) != one
| one = addition(c(sK2),sK2) ),
inference(extension,[status(thm),parent(t2:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ complement(sK2,c(sK2))
| addition(c(sK2),sK2) = one ),
inference(extension,[status(thm),parent(t4:2)],[f_14_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( c(sK2) != c(sK2)
| ~ test(sK2)
| complement(sK2,c(sK2)) ),
inference(extension,[status(thm),parent(t6:2)],[f_15_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
test(sK2),
inference(extension,[status(thm),parent(t8:2)],[f_17_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
c(sK2) = c(sK2),
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(c(sK2),sK2) = addition(sK2,c(sK2)),
inference(extension,[status(thm),parent(t2:3)],[f_1_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE006+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 11:39:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------