%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE037+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 : n016.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 08:46:55 AM UTC 2026
% Result : Theorem 192.24s 192.57s
% Output : Proof 192.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 45 unt; 0 def)
% Number of atoms : 106 ( 60 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 40 ~; 34 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE002+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('KLE002+0.ax',additive_idempotence) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('KLE002+0.ax',order) ).
fof(star_unfold_right,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('KLE002+0.ax',star_unfold_right) ).
fof(goals,conjecture,
! [X0] : leq(one,star(X0)),
file('theBenchmark.p',goals) ).
fof(f_2_1,plain,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(fof_nnf,[status(thm)],[additive_associativity]) ).
fof(f_2_2,plain,
! [U_4,U_3,U_2] : addition(U_2,addition(U_3,U_4)) = addition(addition(U_2,U_3),U_4),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
addition(U_2,addition(U_3,U_4)) = addition(addition(U_2,U_3),U_4),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_4_1,plain,
! [A] : addition(A,A) = A,
inference(fof_nnf,[status(thm)],[additive_idempotence]) ).
fof(f_4_2,plain,
! [U_6] : addition(U_6,U_6) = U_6,
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
addition(U_6,U_6) = U_6,
inference(clausify,[status(thm)],[f_4_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,plain,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(fof_nnf,[status(thm)],[star_unfold_right]) ).
fof(f_13_2,plain,
! [U_26] : leq(addition(one,multiplication(U_26,star(U_26))),star(U_26)),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
leq(addition(one,multiplication(U_26,star(U_26))),star(U_26)),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_17_1,negated_conjecture,
~ ! [X0] : leq(one,star(X0)),
inference(negate,[status(cth)],[goals]) ).
fof(f_17_2,negated_conjecture,
? [X0] : ~ leq(one,star(X0)),
inference(fof_nnf,[status(thm)],[f_17_1]) ).
fof(f_17_3,negated_conjecture,
? [U_34] : ~ leq(one,star(U_34)),
inference(variable_rename,[status(thm)],[f_17_2]) ).
fof(f_17_4,negated_conjecture,
~ leq(one,star(sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_34,sK1)],[f_17_3]) ).
cnf(f_17_5,negated_conjecture,
~ leq(one,star(sK1)),
inference(clausify,[status(thm)],[f_17_4]) ).
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_7,axiom,
( leq(Eq_y_0,Eq_y_1)
| ~ leq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ leq(one,star(sK1)),
inference(start,[status(thm),parent(0:0)],[f_17_5]) ).
cnf(t2,plain,
( addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))) != star(sK1)
| ~ leq(one,addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))))
| one != one
| leq(one,star(sK1)) ),
inference(extension,[status(thm),parent(t1:1)],[equality_7]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( one != one
| one = one ),
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,
one = one,
inference(extension,[status(thm),parent(t4:2)],[equality_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( addition(one,addition(one,addition(multiplication(sK1,star(sK1)),star(sK1)))) != addition(one,addition(multiplication(sK1,star(sK1)),star(sK1)))
| leq(one,addition(one,addition(multiplication(sK1,star(sK1)),star(sK1)))) ),
inference(extension,[status(thm),parent(t2:3)],[f_12_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))) != addition(one,addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))))
| addition(one,addition(one,addition(multiplication(sK1,star(sK1)),star(sK1)))) = addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))) ),
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,
( addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))) != addition(addition(one,one),addition(multiplication(sK1,star(sK1)),star(sK1)))
| addition(addition(one,one),addition(multiplication(sK1,star(sK1)),star(sK1))) != addition(one,addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))))
| addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))) = addition(one,addition(one,addition(multiplication(sK1,star(sK1)),star(sK1)))) ),
inference(extension,[status(thm),parent(t10:2)],[equality_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( addition(one,addition(one,addition(multiplication(sK1,star(sK1)),star(sK1)))) != addition(addition(one,one),addition(multiplication(sK1,star(sK1)),star(sK1)))
| addition(addition(one,one),addition(multiplication(sK1,star(sK1)),star(sK1))) = addition(one,addition(one,addition(multiplication(sK1,star(sK1)),star(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,
addition(one,addition(one,addition(multiplication(sK1,star(sK1)),star(sK1)))) = addition(addition(one,one),addition(multiplication(sK1,star(sK1)),star(sK1))),
inference(extension,[status(thm),parent(t14:2)],[f_2_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( addition(addition(one,one),addition(multiplication(sK1,star(sK1)),star(sK1))) != addition(one,addition(multiplication(sK1,star(sK1)),star(sK1)))
| addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))) = addition(addition(one,one),addition(multiplication(sK1,star(sK1)),star(sK1))) ),
inference(extension,[status(thm),parent(t12:3)],[equality_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:3]) ).
cnf(t20,plain,
( addition(multiplication(sK1,star(sK1)),star(sK1)) != addition(multiplication(sK1,star(sK1)),star(sK1))
| addition(one,one) != one
| addition(addition(one,one),addition(multiplication(sK1,star(sK1)),star(sK1))) = addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))) ),
inference(extension,[status(thm),parent(t18:2)],[equality_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
addition(one,one) = one,
inference(extension,[status(thm),parent(t20:2)],[f_4_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
addition(multiplication(sK1,star(sK1)),star(sK1)) = addition(multiplication(sK1,star(sK1)),star(sK1)),
inference(extension,[status(thm),parent(t20:3)],[equality_1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
( star(sK1) != addition(one,addition(multiplication(sK1,star(sK1)),star(sK1)))
| addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))) = star(sK1) ),
inference(extension,[status(thm),parent(t2:4)],[equality_2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t2:4]) ).
cnf(t28,plain,
( star(sK1) != addition(addition(one,multiplication(sK1,star(sK1))),star(sK1))
| addition(addition(one,multiplication(sK1,star(sK1))),star(sK1)) != addition(one,addition(multiplication(sK1,star(sK1)),star(sK1)))
| star(sK1) = addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))) ),
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,
( addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))) != addition(addition(one,multiplication(sK1,star(sK1))),star(sK1))
| addition(addition(one,multiplication(sK1,star(sK1))),star(sK1)) = addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))) ),
inference(extension,[status(thm),parent(t28:2)],[equality_2]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
addition(one,addition(multiplication(sK1,star(sK1)),star(sK1))) = addition(addition(one,multiplication(sK1,star(sK1))),star(sK1)),
inference(extension,[status(thm),parent(t30:2)],[f_2_3]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
( addition(addition(one,multiplication(sK1,star(sK1))),star(sK1)) != star(sK1)
| star(sK1) = addition(addition(one,multiplication(sK1,star(sK1))),star(sK1)) ),
inference(extension,[status(thm),parent(t28:3)],[equality_2]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t28:3]) ).
cnf(t36,plain,
( ~ leq(addition(one,multiplication(sK1,star(sK1))),star(sK1))
| addition(addition(one,multiplication(sK1,star(sK1))),star(sK1)) = star(sK1) ),
inference(extension,[status(thm),parent(t34:2)],[f_12_4]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
leq(addition(one,multiplication(sK1,star(sK1))),star(sK1)),
inference(extension,[status(thm),parent(t36:2)],[f_13_3]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE037+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 11:49:05 UTC 2026
% 0.08/0.37 % CPUTime :
% 192.24/192.57 % SZS status Theorem for theBenchmark
% 192.24/192.57 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------