%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE005+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 0.42s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 34 unt; 0 def)
% Number of atoms : 110 ( 72 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 97 ( 40 ~; 39 |; 14 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 2 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('KLE001+0.ax',additive_commutativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('KLE001+0.ax',additive_identity) ).
fof(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero,
file('KLE001+0.ax',right_annihilation) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('KLE001+0.ax',left_annihilation) ).
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(test_4,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('KLE001+1.ax',test_4) ).
fof(goals,conjecture,
c(one) = zero,
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(A,zero) = zero,
inference(fof_nnf,[status(thm)],[right_annihilation]) ).
fof(f_10_2,plain,
! [U_18] : multiplication(U_18,zero) = zero,
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
multiplication(U_18,zero) = zero,
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] : multiplication(zero,A) = zero,
inference(fof_nnf,[status(thm)],[left_annihilation]) ).
fof(f_11_2,plain,
! [U_19] : multiplication(zero,U_19) = zero,
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
multiplication(zero,U_19) = zero,
inference(clausify,[status(thm)],[f_11_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_7,plain,
( complement(U_34,U_36)
| addition(U_36,U_34) != one
| multiplication(U_34,U_36) != zero
| multiplication(U_36,U_34) != zero ),
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_5,plain,
( c(U_38) = U_40
| ~ complement(U_38,U_40)
| ~ test(U_38) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [X0] :
( c(X0) = zero
| test(X0) ),
inference(fof_nnf,[status(thm)],[test_4]) ).
fof(f_16_2,plain,
! [U_41] :
( c(U_41) = zero
| test(U_41) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( c(U_41) = zero
| test(U_41) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,negated_conjecture,
c(one) != zero,
inference(negate,[status(cth)],[goals]) ).
fof(f_17_2,negated_conjecture,
c(one) != zero,
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,negated_conjecture,
c(one) != zero,
inference(clausify,[status(thm)],[f_17_2]) ).
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,
c(one) != zero,
inference(start,[status(thm),parent(0:0)],[f_17_3]) ).
cnf(t2,plain,
( ~ complement(one,zero)
| ~ test(one)
| c(one) = zero ),
inference(extension,[status(thm),parent(t1:1)],[f_15_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( c(one) = zero
| test(one) ),
inference(extension,[status(thm),parent(t2:2)],[f_16_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
$false,
inference(reduction,[status(thm),parent(t4:2)],[t4:2,t1:1]) ).
cnf(t7,plain,
( multiplication(one,zero) != zero
| addition(zero,one) != one
| multiplication(zero,one) != zero
| complement(one,zero) ),
inference(extension,[status(thm),parent(t2:3)],[f_14_7]) ).
cnf(t8,plain,
$false,
inference(connection,[status(thm),parent(t7:1)],[t7:1,t2:3]) ).
cnf(t9,plain,
multiplication(zero,one) = zero,
inference(extension,[status(thm),parent(t7:2)],[f_11_3]) ).
cnf(t10,plain,
$false,
inference(connection,[status(thm),parent(t9:1)],[t9:1,t7:2]) ).
cnf(t11,plain,
( addition(one,zero) != one
| addition(zero,one) != addition(one,zero)
| addition(zero,one) = one ),
inference(extension,[status(thm),parent(t7:3)],[equality_3]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t7:3]) ).
cnf(t13,plain,
addition(zero,one) = addition(one,zero),
inference(extension,[status(thm),parent(t11:2)],[f_1_3]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t11:2]) ).
cnf(t15,plain,
addition(one,zero) = one,
inference(extension,[status(thm),parent(t11:3)],[f_3_3]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t11:3]) ).
cnf(t17,plain,
multiplication(one,zero) = zero,
inference(extension,[status(thm),parent(t7:4)],[f_10_3]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t7:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE005+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 11:45:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.42 % SZS status Theorem for theBenchmark
% 0.10/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------