%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE072+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 : n012.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 0.06s 0.33s
% Output : Proof 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 24 unt; 0 def)
% Number of atoms : 34 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 15 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 21 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE001+0.ax',left_distributivity) ).
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('KLE001+5.ax',domain5) ).
fof(goals,conjecture,
! [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) = addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))),
file('theBenchmark.p',goals) ).
fof(f_9_1,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(fof_nnf,[status(thm)],[left_distributivity]) ).
fof(f_9_2,plain,
! [U_17,U_16,U_15] : multiplication(addition(U_17,U_16),U_15) = addition(multiplication(U_17,U_15),multiplication(U_16,U_15)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
multiplication(addition(U_17,U_16),U_15) = addition(multiplication(U_17,U_15),multiplication(U_16,U_15)),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_17_1,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(fof_nnf,[status(thm)],[domain5]) ).
fof(f_17_2,plain,
! [U_31,U_30] : domain(addition(U_31,U_30)) = addition(domain(U_31),domain(U_30)),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
domain(addition(U_31,U_30)) = addition(domain(U_31),domain(U_30)),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,negated_conjecture,
~ ! [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) = addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))),
inference(negate,[status(cth)],[goals]) ).
fof(f_18_2,negated_conjecture,
? [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) != addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))),
inference(fof_nnf,[status(thm)],[f_18_1]) ).
fof(f_18_3,negated_conjecture,
? [U_34,U_33,U_32] : domain(multiplication(addition(U_34,U_33),domain(U_32))) != addition(domain(multiplication(U_34,domain(U_32))),domain(multiplication(U_33,domain(U_32)))),
inference(variable_rename,[status(thm)],[f_18_2]) ).
fof(f_18_4,negated_conjecture,
? [U_33,U_32] : domain(multiplication(addition(sK1,U_33),domain(U_32))) != addition(domain(multiplication(sK1,domain(U_32))),domain(multiplication(U_33,domain(U_32)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_34,sK1)],[f_18_3]) ).
fof(f_18_5,negated_conjecture,
? [U_32] : domain(multiplication(addition(sK1,sK2),domain(U_32))) != addition(domain(multiplication(sK1,domain(U_32))),domain(multiplication(sK2,domain(U_32)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_33,sK2)],[f_18_4]) ).
fof(f_18_6,negated_conjecture,
domain(multiplication(addition(sK1,sK2),domain(sK3))) != addition(domain(multiplication(sK1,domain(sK3))),domain(multiplication(sK2,domain(sK3)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_32,sK3)],[f_18_5]) ).
fof(f_18_7,negated_conjecture,
domain(multiplication(addition(sK1,sK2),domain(sK3))) != addition(domain(multiplication(sK1,domain(sK3))),domain(multiplication(sK2,domain(sK3)))),
inference(definitional_conversion,[status(esa)],[f_18_6]) ).
cnf(f_18_8,negated_conjecture,
domain(multiplication(addition(sK1,sK2),domain(sK3))) != addition(domain(multiplication(sK1,domain(sK3))),domain(multiplication(sK2,domain(sK3)))),
inference(clausify,[status(thm)],[f_18_7]) ).
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_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(addition(sK1,sK2),domain(sK3))) != addition(domain(multiplication(sK1,domain(sK3))),domain(multiplication(sK2,domain(sK3)))),
inference(start,[status(thm),parent(0:0)],[f_18_8]) ).
cnf(t2,plain,
( domain(addition(multiplication(sK1,domain(sK3)),multiplication(sK2,domain(sK3)))) != addition(domain(multiplication(sK1,domain(sK3))),domain(multiplication(sK2,domain(sK3))))
| domain(multiplication(addition(sK1,sK2),domain(sK3))) != domain(addition(multiplication(sK1,domain(sK3)),multiplication(sK2,domain(sK3))))
| domain(multiplication(addition(sK1,sK2),domain(sK3))) = addition(domain(multiplication(sK1,domain(sK3))),domain(multiplication(sK2,domain(sK3)))) ),
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(addition(sK1,sK2),domain(sK3)) != addition(multiplication(sK1,domain(sK3)),multiplication(sK2,domain(sK3)))
| domain(multiplication(addition(sK1,sK2),domain(sK3))) = domain(addition(multiplication(sK1,domain(sK3)),multiplication(sK2,domain(sK3)))) ),
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,
multiplication(addition(sK1,sK2),domain(sK3)) = addition(multiplication(sK1,domain(sK3)),multiplication(sK2,domain(sK3))),
inference(extension,[status(thm),parent(t4:2)],[f_9_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
domain(addition(multiplication(sK1,domain(sK3)),multiplication(sK2,domain(sK3)))) = addition(domain(multiplication(sK1,domain(sK3))),domain(multiplication(sK2,domain(sK3)))),
inference(extension,[status(thm),parent(t2:3)],[f_17_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE072+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 19 11:49:53 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.06/0.33 % SZS status Theorem for theBenchmark
% 0.06/0.33 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------