%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE074+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 : n005.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 0.32s 0.57s
% Output : Proof 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 25 unt; 0 def)
% Number of atoms : 39 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 17 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 21 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('KLE001+0.ax',multiplicative_associativity) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('KLE001+5.ax',domain2) ).
fof(goals,conjecture,
! [X0,X1,X2] : domain(multiplication(multiplication(X0,X1),domain(X2))) = domain(multiplication(X0,domain(multiplication(X1,domain(X2))))),
file('theBenchmark.p',goals) ).
fof(f_5_1,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(fof_nnf,[status(thm)],[multiplicative_associativity]) ).
fof(f_5_2,plain,
! [U_9,U_8,U_7] : multiplication(U_9,multiplication(U_8,U_7)) = multiplication(multiplication(U_9,U_8),U_7),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
multiplication(U_9,multiplication(U_8,U_7)) = multiplication(multiplication(U_9,U_8),U_7),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_14_1,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(fof_nnf,[status(thm)],[domain2]) ).
fof(f_14_2,plain,
! [U_28,U_27] : domain(multiplication(U_28,U_27)) = domain(multiplication(U_28,domain(U_27))),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
domain(multiplication(U_28,U_27)) = domain(multiplication(U_28,domain(U_27))),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_18_1,negated_conjecture,
~ ! [X0,X1,X2] : domain(multiplication(multiplication(X0,X1),domain(X2))) = domain(multiplication(X0,domain(multiplication(X1,domain(X2))))),
inference(negate,[status(cth)],[goals]) ).
fof(f_18_2,negated_conjecture,
? [X0,X1,X2] : domain(multiplication(multiplication(X0,X1),domain(X2))) != domain(multiplication(X0,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(multiplication(U_34,U_33),domain(U_32))) != domain(multiplication(U_34,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(multiplication(sK1,U_33),domain(U_32))) != domain(multiplication(sK1,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(multiplication(sK1,sK2),domain(U_32))) != domain(multiplication(sK1,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(multiplication(sK1,sK2),domain(sK3))) != domain(multiplication(sK1,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(multiplication(sK1,sK2),domain(sK3))) != domain(multiplication(sK1,domain(multiplication(sK2,domain(sK3))))),
inference(definitional_conversion,[status(esa)],[f_18_6]) ).
cnf(f_18_8,negated_conjecture,
domain(multiplication(multiplication(sK1,sK2),domain(sK3))) != domain(multiplication(sK1,domain(multiplication(sK2,domain(sK3))))),
inference(clausify,[status(thm)],[f_18_7]) ).
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_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(multiplication(sK1,sK2),domain(sK3))) != domain(multiplication(sK1,domain(multiplication(sK2,domain(sK3))))),
inference(start,[status(thm),parent(0:0)],[f_18_8]) ).
cnf(t2,plain,
( domain(multiplication(sK1,multiplication(sK2,domain(sK3)))) != domain(multiplication(sK1,domain(multiplication(sK2,domain(sK3)))))
| domain(multiplication(multiplication(sK1,sK2),domain(sK3))) != domain(multiplication(sK1,multiplication(sK2,domain(sK3))))
| domain(multiplication(multiplication(sK1,sK2),domain(sK3))) = domain(multiplication(sK1,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(multiplication(sK1,sK2),domain(sK3)) != multiplication(sK1,multiplication(sK2,domain(sK3)))
| domain(multiplication(multiplication(sK1,sK2),domain(sK3))) = domain(multiplication(sK1,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(sK1,multiplication(sK2,domain(sK3))) != multiplication(multiplication(sK1,sK2),domain(sK3))
| multiplication(multiplication(sK1,sK2),domain(sK3)) = multiplication(sK1,multiplication(sK2,domain(sK3))) ),
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(sK1,multiplication(sK2,domain(sK3))) = multiplication(multiplication(sK1,sK2),domain(sK3)),
inference(extension,[status(thm),parent(t6:2)],[f_5_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
domain(multiplication(sK1,multiplication(sK2,domain(sK3)))) = domain(multiplication(sK1,domain(multiplication(sK2,domain(sK3))))),
inference(extension,[status(thm),parent(t2:3)],[f_14_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE074+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
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 11:49:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.32/0.57 % SZS status Theorem for theBenchmark
% 0.32/0.57 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------