%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE002+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 : n013.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 75.15s 75.43s
% Output : Proof 75.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 66 ( 37 unt; 0 def)
% Number of atoms : 110 ( 61 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 85 ( 41 ~; 32 |; 9 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 28 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('KLE001+0.ax',multiplicative_left_identity) ).
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(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('KLE001+0.ax',order) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ),
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]) ).
cnf(f_7_3,plain,
multiplication(one,U_11) = U_11,
inference(clausify,[status(thm)],[f_7_2]) ).
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_12_1,plain,
! [A,B] :
( ( leq(A,B)
| addition(A,B) != B )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(fof_nnf,[status(thm)],[order]) ).
fof(f_12_2,plain,
! [U_21,U_20] :
( ( leq(U_21,U_20)
| addition(U_21,U_20) != U_20 )
& ( addition(U_21,U_20) = U_20
| ~ leq(U_21,U_20) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_25,U_23] :
( leq(U_25,U_23)
| addition(U_25,U_23) != U_23 )
& ! [U_24,U_22] :
( addition(U_24,U_22) = U_22
| ~ leq(U_24,U_22) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( addition(U_24,U_22) = U_22
| ~ leq(U_24,U_22) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( leq(U_25,U_23)
| addition(U_25,U_23) != U_23 ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ),
inference(negate,[status(cth)],[goals]) ).
fof(f_13_2,negated_conjecture,
? [X0,X1,X2] :
( ~ leq(multiplication(X0,X2),multiplication(X1,X2))
& leq(X0,X1) ),
inference(fof_nnf,[status(thm)],[f_13_1]) ).
fof(f_13_3,negated_conjecture,
? [U_28,U_27,U_26] :
( ~ leq(multiplication(U_28,U_26),multiplication(U_27,U_26))
& leq(U_28,U_27) ),
inference(variable_rename,[status(thm)],[f_13_2]) ).
fof(f_13_4,negated_conjecture,
? [U_28,U_27] :
( ? [U_26] : ~ leq(multiplication(U_28,U_26),multiplication(U_27,U_26))
& leq(U_28,U_27) ),
inference(miniscope,[status(thm)],[f_13_3]) ).
fof(f_13_5,negated_conjecture,
? [U_27] :
( ? [U_26] : ~ leq(multiplication(sK1,U_26),multiplication(U_27,U_26))
& leq(sK1,U_27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_28,sK1)],[f_13_4]) ).
fof(f_13_6,negated_conjecture,
( ? [U_26] : ~ leq(multiplication(sK1,U_26),multiplication(sK2,U_26))
& leq(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_27,sK2)],[f_13_5]) ).
fof(f_13_7,negated_conjecture,
( ~ leq(multiplication(sK1,sK3),multiplication(sK2,sK3))
& leq(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_26,sK3)],[f_13_6]) ).
cnf(f_13_8,negated_conjecture,
leq(sK1,sK2),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_9,negated_conjecture,
~ leq(multiplication(sK1,sK3),multiplication(sK2,sK3)),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
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_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(t1,plain,
~ leq(multiplication(sK1,sK3),multiplication(sK2,sK3)),
inference(start,[status(thm),parent(0:0)],[f_13_9]) ).
cnf(t2,plain,
( addition(multiplication(sK1,sK3),multiplication(sK2,sK3)) != multiplication(sK2,sK3)
| leq(multiplication(sK1,sK3),multiplication(sK2,sK3)) ),
inference(extension,[status(thm),parent(t1:1)],[f_12_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( multiplication(sK2,sK3) != addition(multiplication(sK1,sK3),multiplication(sK2,sK3))
| addition(multiplication(sK1,sK3),multiplication(sK2,sK3)) = multiplication(sK2,sK3) ),
inference(extension,[status(thm),parent(t2:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( multiplication(addition(sK1,sK2),multiplication(one,sK3)) != addition(multiplication(sK1,sK3),multiplication(sK2,sK3))
| multiplication(sK2,sK3) != multiplication(addition(sK1,sK2),multiplication(one,sK3))
| multiplication(sK2,sK3) = addition(multiplication(sK1,sK3),multiplication(sK2,sK3)) ),
inference(extension,[status(thm),parent(t4:2)],[equality_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( sK3 != multiplication(one,sK3)
| sK2 != addition(sK1,sK2)
| multiplication(sK2,sK3) = multiplication(addition(sK1,sK2),multiplication(one,sK3)) ),
inference(extension,[status(thm),parent(t6:2)],[equality_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( addition(sK1,sK2) != sK2
| sK2 = addition(sK1,sK2) ),
inference(extension,[status(thm),parent(t8:2)],[equality_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ leq(sK1,sK2)
| addition(sK1,sK2) = sK2 ),
inference(extension,[status(thm),parent(t10:2)],[f_12_4]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
leq(sK1,sK2),
inference(extension,[status(thm),parent(t12:2)],[f_13_8]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( multiplication(one,sK3) != sK3
| sK3 = multiplication(one,sK3) ),
inference(extension,[status(thm),parent(t8:3)],[equality_2]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t8:3]) ).
cnf(t18,plain,
multiplication(one,sK3) = sK3,
inference(extension,[status(thm),parent(t16:2)],[f_7_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( addition(multiplication(sK1,multiplication(one,sK3)),multiplication(sK2,multiplication(one,sK3))) != addition(multiplication(sK1,sK3),multiplication(sK2,sK3))
| multiplication(addition(sK1,sK2),multiplication(one,sK3)) != addition(multiplication(sK1,multiplication(one,sK3)),multiplication(sK2,multiplication(one,sK3)))
| multiplication(addition(sK1,sK2),multiplication(one,sK3)) = addition(multiplication(sK1,sK3),multiplication(sK2,sK3)) ),
inference(extension,[status(thm),parent(t6:3)],[equality_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t6:3]) ).
cnf(t22,plain,
multiplication(addition(sK1,sK2),multiplication(one,sK3)) = addition(multiplication(sK1,multiplication(one,sK3)),multiplication(sK2,multiplication(one,sK3))),
inference(extension,[status(thm),parent(t20:2)],[f_9_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( multiplication(sK2,multiplication(one,sK3)) != multiplication(sK2,sK3)
| multiplication(sK1,multiplication(one,sK3)) != multiplication(sK1,sK3)
| addition(multiplication(sK1,multiplication(one,sK3)),multiplication(sK2,multiplication(one,sK3))) = addition(multiplication(sK1,sK3),multiplication(sK2,sK3)) ),
inference(extension,[status(thm),parent(t20:3)],[equality_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
( multiplication(one,sK3) != sK3
| sK1 != sK1
| multiplication(sK1,multiplication(one,sK3)) = multiplication(sK1,sK3) ),
inference(extension,[status(thm),parent(t24:2)],[equality_5]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
sK1 = sK1,
inference(extension,[status(thm),parent(t26:2)],[equality_1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
multiplication(one,sK3) = sK3,
inference(extension,[status(thm),parent(t26:3)],[f_7_3]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t26:3]) ).
cnf(t32,plain,
( multiplication(one,sK3) != sK3
| sK2 != sK2
| multiplication(sK2,multiplication(one,sK3)) = multiplication(sK2,sK3) ),
inference(extension,[status(thm),parent(t24:3)],[equality_5]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t24:3]) ).
cnf(t34,plain,
sK2 = sK2,
inference(extension,[status(thm),parent(t32:2)],[equality_1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
multiplication(one,sK3) = sK3,
inference(extension,[status(thm),parent(t32:3)],[f_7_3]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t32:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE002+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
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 11:39:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 75.15/75.43 % SZS status Theorem for theBenchmark
% 75.15/75.43 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------