%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE076+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 : n015.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 08:46:58 AM UTC 2026
% Result : Theorem 0.14s 5.45s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 29 unt; 0 def)
% Number of atoms : 50 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 20 ~; 13 |; 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; 2 con; 0-2 aty)
% Number of variables : 18 ( 1 sgn 5 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero,
file('KLE001+0.ax',right_annihilation) ).
fof(domain4,axiom,
domain(zero) = zero,
file('KLE001+5.ax',domain4) ).
fof(goals,conjecture,
! [X0] : domain(multiplication(X0,domain(zero))) = zero,
file('theBenchmark.p',goals) ).
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_16_1,plain,
domain(zero) = zero,
inference(fof_nnf,[status(thm)],[domain4]) ).
cnf(f_16_2,plain,
domain(zero) = zero,
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_18_1,negated_conjecture,
~ ! [X0] : domain(multiplication(X0,domain(zero))) = zero,
inference(negate,[status(cth)],[goals]) ).
fof(f_18_2,negated_conjecture,
? [X0] : domain(multiplication(X0,domain(zero))) != zero,
inference(fof_nnf,[status(thm)],[f_18_1]) ).
fof(f_18_3,negated_conjecture,
? [U_32] : domain(multiplication(U_32,domain(zero))) != zero,
inference(variable_rename,[status(thm)],[f_18_2]) ).
fof(f_18_4,negated_conjecture,
domain(multiplication(sK1,domain(zero))) != zero,
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_32,sK1)],[f_18_3]) ).
fof(f_18_5,negated_conjecture,
domain(multiplication(sK1,domain(zero))) != zero,
inference(definitional_conversion,[status(esa)],[f_18_4]) ).
cnf(f_18_6,negated_conjecture,
domain(multiplication(sK1,domain(zero))) != zero,
inference(clausify,[status(thm)],[f_18_5]) ).
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_5,axiom,
( multiplication(Eq_x_0,Eq_x_1) = multiplication(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( domain(Eq_x_0) = domain(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
domain(multiplication(sK1,domain(zero))) != zero,
inference(start,[status(thm),parent(0:0)],[f_18_6]) ).
cnf(t2,plain,
( domain(multiplication(sK1,zero)) != zero
| domain(multiplication(sK1,domain(zero))) != domain(multiplication(sK1,zero))
| domain(multiplication(sK1,domain(zero))) = zero ),
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(sK1,domain(zero)) != multiplication(sK1,zero)
| domain(multiplication(sK1,domain(zero))) = domain(multiplication(sK1,zero)) ),
inference(extension,[status(thm),parent(t2:2)],[equality_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( domain(zero) != zero
| sK1 != sK1
| multiplication(sK1,domain(zero)) = multiplication(sK1,zero) ),
inference(extension,[status(thm),parent(t4:2)],[equality_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
sK1 = sK1,
inference(extension,[status(thm),parent(t6:2)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
domain(zero) = zero,
inference(extension,[status(thm),parent(t6:3)],[f_16_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( domain(zero) != zero
| domain(multiplication(sK1,zero)) != domain(zero)
| domain(multiplication(sK1,zero)) = zero ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:3]) ).
cnf(t14,plain,
( multiplication(sK1,zero) != zero
| domain(multiplication(sK1,zero)) = domain(zero) ),
inference(extension,[status(thm),parent(t12:2)],[equality_6]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
multiplication(sK1,zero) = zero,
inference(extension,[status(thm),parent(t14:2)],[f_10_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
domain(zero) = zero,
inference(extension,[status(thm),parent(t12:3)],[f_16_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE076+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
% 0.09/5.38 % Computer : n015.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sat Sep 19 11:52:53 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.14/5.45 % SZS status Theorem for theBenchmark
% 0.14/5.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------