%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE067+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 : n011.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 08:46:57 AM UTC 2026
% Result : Theorem 30.15s 30.43s
% Output : Proof 30.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 52 unt; 0 def)
% Number of atoms : 96 ( 75 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 34 ~; 26 |; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 24 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('KLE001+0.ax',multiplicative_left_identity) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('KLE001+5.ax',domain2) ).
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('KLE001+5.ax',domain5) ).
fof(goals,conjecture,
! [X0,X1] : domain(addition(domain(X0),domain(X1))) = addition(domain(X0),domain(X1)),
file('theBenchmark.p',goals) ).
fof(f_7_1,plain,
! [A] : multiplication(one,A) = A,
inference(fof_nnf,[status(thm)],[multiplicative_left_identity]) ).
fof(f_7_2,plain,
! [U_11] : multiplication(one,U_11) = U_11,
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_11] : multiplication(one,U_11) = U_11,
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
multiplication(one,U_11) = U_11,
inference(clausify,[status(thm)],[f_7_3]) ).
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]) ).
fof(f_14_3,plain,
! [U_27,U_28] : domain(multiplication(U_28,U_27)) = domain(multiplication(U_28,domain(U_27))),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
domain(multiplication(U_28,U_27)) = domain(multiplication(U_28,domain(U_27))),
inference(clausify,[status(thm)],[f_14_3]) ).
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]) ).
fof(f_17_3,plain,
! [U_30,U_31] : domain(addition(U_31,U_30)) = addition(domain(U_31),domain(U_30)),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
domain(addition(U_31,U_30)) = addition(domain(U_31),domain(U_30)),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,negated_conjecture,
~ ! [X0,X1] : domain(addition(domain(X0),domain(X1))) = addition(domain(X0),domain(X1)),
inference(negate,[status(cth)],[goals]) ).
fof(f_18_2,negated_conjecture,
? [X0,X1] : domain(addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)),
inference(fof_nnf,[status(thm)],[f_18_1]) ).
fof(f_18_3,negated_conjecture,
? [U_33,U_32] : domain(addition(domain(U_33),domain(U_32))) != addition(domain(U_33),domain(U_32)),
inference(variable_rename,[status(thm)],[f_18_2]) ).
fof(f_18_4,negated_conjecture,
? [U_32] : domain(addition(domain(sK1),domain(U_32))) != addition(domain(sK1),domain(U_32)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_33,sK1)],[f_18_3]) ).
fof(f_18_5,negated_conjecture,
domain(addition(domain(sK1),domain(sK2))) != addition(domain(sK1),domain(sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_32,sK2)],[f_18_4]) ).
fof(f_18_6,negated_conjecture,
domain(addition(domain(sK1),domain(sK2))) != addition(domain(sK1),domain(sK2)),
inference(definitional_conversion,[status(esa)],[f_18_5]) ).
cnf(f_18_7,negated_conjecture,
domain(addition(domain(sK1),domain(sK2))) != addition(domain(sK1),domain(sK2)),
inference(clausify,[status(thm)],[f_18_6]) ).
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_4,axiom,
( addition(Eq_x_0,Eq_x_1) = addition(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(addition(domain(sK1),domain(sK2))) != addition(domain(sK1),domain(sK2)),
inference(start,[status(thm),parent(0:0)],[f_18_7]) ).
cnf(t2,plain,
( addition(domain(domain(sK1)),domain(domain(sK2))) != addition(domain(sK1),domain(sK2))
| domain(addition(domain(sK1),domain(sK2))) != addition(domain(domain(sK1)),domain(domain(sK2)))
| domain(addition(domain(sK1),domain(sK2))) = addition(domain(sK1),domain(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,
domain(addition(domain(sK1),domain(sK2))) = addition(domain(domain(sK1)),domain(domain(sK2))),
inference(extension,[status(thm),parent(t2:2)],[f_17_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( domain(domain(sK2)) != domain(sK2)
| domain(domain(sK1)) != domain(sK1)
| addition(domain(domain(sK1)),domain(domain(sK2))) = addition(domain(sK1),domain(sK2)) ),
inference(extension,[status(thm),parent(t2:3)],[equality_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( domain(sK1) != domain(domain(sK1))
| domain(domain(sK1)) = domain(sK1) ),
inference(extension,[status(thm),parent(t6:2)],[equality_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( domain(multiplication(one,sK1)) != domain(domain(sK1))
| domain(sK1) != domain(multiplication(one,sK1))
| domain(sK1) = domain(domain(sK1)) ),
inference(extension,[status(thm),parent(t8:2)],[equality_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( sK1 != multiplication(one,sK1)
| domain(sK1) = domain(multiplication(one,sK1)) ),
inference(extension,[status(thm),parent(t10:2)],[equality_6]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( multiplication(one,sK1) != sK1
| sK1 = multiplication(one,sK1) ),
inference(extension,[status(thm),parent(t12:2)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
multiplication(one,sK1) = sK1,
inference(extension,[status(thm),parent(t14:2)],[f_7_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( domain(multiplication(one,domain(sK1))) != domain(domain(sK1))
| domain(multiplication(one,sK1)) != domain(multiplication(one,domain(sK1)))
| domain(multiplication(one,sK1)) = domain(domain(sK1)) ),
inference(extension,[status(thm),parent(t10:3)],[equality_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t10:3]) ).
cnf(t20,plain,
domain(multiplication(one,sK1)) = domain(multiplication(one,domain(sK1))),
inference(extension,[status(thm),parent(t18:2)],[f_14_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( multiplication(one,domain(sK1)) != domain(sK1)
| domain(multiplication(one,domain(sK1))) = domain(domain(sK1)) ),
inference(extension,[status(thm),parent(t18:3)],[equality_6]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
multiplication(one,domain(sK1)) = domain(sK1),
inference(extension,[status(thm),parent(t22:2)],[f_7_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( domain(sK2) != domain(domain(sK2))
| domain(domain(sK2)) = domain(sK2) ),
inference(extension,[status(thm),parent(t6:3)],[equality_2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t6:3]) ).
cnf(t28,plain,
( domain(multiplication(one,sK2)) != domain(domain(sK2))
| domain(sK2) != domain(multiplication(one,sK2))
| domain(sK2) = domain(domain(sK2)) ),
inference(extension,[status(thm),parent(t26:2)],[equality_3]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( sK2 != multiplication(one,sK2)
| domain(sK2) = domain(multiplication(one,sK2)) ),
inference(extension,[status(thm),parent(t28:2)],[equality_6]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( multiplication(one,sK2) != sK2
| sK2 = multiplication(one,sK2) ),
inference(extension,[status(thm),parent(t30:2)],[equality_2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
multiplication(one,sK2) = sK2,
inference(extension,[status(thm),parent(t32:2)],[f_7_4]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( domain(multiplication(one,domain(sK2))) != domain(domain(sK2))
| domain(multiplication(one,sK2)) != domain(multiplication(one,domain(sK2)))
| domain(multiplication(one,sK2)) = domain(domain(sK2)) ),
inference(extension,[status(thm),parent(t28:3)],[equality_3]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t28:3]) ).
cnf(t38,plain,
domain(multiplication(one,sK2)) = domain(multiplication(one,domain(sK2))),
inference(extension,[status(thm),parent(t36:2)],[f_14_4]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( multiplication(one,domain(sK2)) != domain(sK2)
| domain(multiplication(one,domain(sK2))) = domain(domain(sK2)) ),
inference(extension,[status(thm),parent(t36:3)],[equality_6]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t36:3]) ).
cnf(t42,plain,
multiplication(one,domain(sK2)) = domain(sK2),
inference(extension,[status(thm),parent(t40:2)],[f_7_4]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE067+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
% 0.07/0.36 % Computer : n011.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sat Sep 19 11:50:09 UTC 2026
% 0.07/0.36 % CPUTime :
% 30.15/30.43 % SZS status Theorem for theBenchmark
% 30.15/30.43 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------