%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE041+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 : Sun Sep 27 07:44:10 AM UTC 2026
% Result : Theorem 50.82s 6.90s
% Output : CNFRefutation 50.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 77 ( 65 unt; 0 def)
% Number of atoms : 89 ( 54 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 6 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 112 ( 6 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('theBenchmark.p',additive_associativity) ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_idempotence) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',right_distributivity) ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',left_distributivity) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(star_unfold_right,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('theBenchmark.p',star_unfold_right) ).
fof(star_induction_left,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('theBenchmark.p',star_induction_left) ).
fof(goals,conjecture,
! [X0,X1] :
( leq(X0,X1)
=> leq(star(X0),star(X1)) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,X1)
=> leq(star(X0),star(X1)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_18,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_19,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_21,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_23,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_24,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_25,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_26,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_27,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_28,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_31,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_32,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_33,plain,
leq(addition(one,multiplication(A,star(A))),star(A)),
inference(clausify,[status(thm)],[star_unfold_right]) ).
cnf(c_35,plain,
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(clausify,[status(thm)],[star_induction_left]) ).
fof(nnf_17,plain,
? [X0,X1] :
( ~ leq(star(X0),star(X1))
& leq(X0,X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(star(sK0),star(sK1))
& leq(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_17]) ).
cnf(c_37,negated_conjecture,
leq(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_38,negated_conjecture,
~ leq(star(sK0),star(sK1)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_15995,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_40,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_19,c_15995]) ).
cnf(c_15996,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_42,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_15996]) ).
cnf(c_15997,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_23,c_26]) ).
cnf(c_46,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_15997]) ).
cnf(c_15998,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_51,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_15998]) ).
cnf(c_15999,plain,
addition(multiplication(A,B),B) = multiplication(addition(A,one),B),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_16000,plain,
addition(B,multiplication(A,B)) = multiplication(addition(A,one),B),
inference(paramod,[status(thm)],[c_18,c_15999]) ).
cnf(c_52,plain,
multiplication(addition(A,one),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_16000]) ).
cnf(c_53,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_32,c_21]) ).
cnf(c_16001,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = star(A),
inference(resolve,[status(thm)],[c_33,c_31]) ).
cnf(c_59,plain,
addition(star(A),addition(one,multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_18,c_16001]) ).
cnf(c_64,plain,
( leq(multiplication(star(B),A),C)
| ~ leq(addition(A,multiplication(B,C)),C) ),
inference(paramod,[status(thm)],[c_18,c_35]) ).
cnf(c_84,plain,
addition(sK0,sK1) = sK1,
inference(resolve,[status(thm)],[c_37,c_31]) ).
cnf(c_85,negated_conjecture,
addition(star(sK0),star(sK1)) != star(sK1),
inference(resolve,[status(thm)],[c_32,c_38]) ).
cnf(c_16002,plain,
addition(sK1,A) = addition(sK0,addition(sK1,A)),
inference(paramod,[status(thm)],[c_84,c_19]) ).
cnf(c_93,plain,
addition(sK0,addition(sK1,A)) = addition(sK1,A),
inference(copy,[status(thm)],[c_16002]) ).
cnf(c_96,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_42,c_32]) ).
cnf(c_104,plain,
leq(multiplication(A,B),multiplication(addition(A,C),B)),
inference(paramod,[status(thm)],[c_28,c_96]) ).
cnf(c_105,plain,
leq(A,addition(B,addition(A,C))),
inference(paramod,[status(thm)],[c_40,c_96]) ).
cnf(c_16003,plain,
star(A) = addition(one,addition(star(A),multiplication(A,star(A)))),
inference(paramod,[status(thm)],[c_59,c_40]) ).
cnf(c_655,plain,
addition(one,addition(star(A),multiplication(A,star(A)))) = star(A),
inference(copy,[status(thm)],[c_16003]) ).
cnf(c_710,plain,
leq(one,star(A)),
inference(paramod,[status(thm)],[c_59,c_105]) ).
cnf(c_711,plain,
addition(one,star(A)) = star(A),
inference(resolve,[status(thm)],[c_710,c_31]) ).
cnf(c_16004,plain,
addition(star(A),B) = addition(one,addition(star(A),B)),
inference(paramod,[status(thm)],[c_711,c_19]) ).
cnf(c_721,plain,
addition(one,addition(star(A),B)) = addition(star(A),B),
inference(copy,[status(thm)],[c_16004]) ).
cnf(c_16005,plain,
addition(multiplication(one,A),multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_711,c_28]) ).
cnf(c_723,plain,
addition(A,multiplication(star(B),A)) = multiplication(star(B),A),
inference(paramod,[status(thm)],[c_24,c_16005]) ).
cnf(c_736,plain,
addition(star(A),multiplication(A,star(A))) = star(A),
inference(paramod,[status(thm)],[c_721,c_655]) ).
cnf(c_779,plain,
( leq(multiplication(star(A),B),B)
| ~ leq(multiplication(addition(one,A),B),B) ),
inference(paramod,[status(thm)],[c_51,c_64]) ).
cnf(c_1643,plain,
leq(multiplication(sK0,A),multiplication(addition(sK1,B),A)),
inference(paramod,[status(thm)],[c_93,c_104]) ).
cnf(c_1840,plain,
leq(multiplication(sK0,A),addition(A,multiplication(sK1,A))),
inference(paramod,[status(thm)],[c_52,c_1643]) ).
cnf(c_12376,plain,
leq(multiplication(sK0,star(sK1)),star(sK1)),
inference(paramod,[status(thm)],[c_736,c_1840]) ).
cnf(c_16006,plain,
addition(multiplication(sK0,star(sK1)),star(sK1)) = star(sK1),
inference(resolve,[status(thm)],[c_12376,c_31]) ).
cnf(c_16007,plain,
addition(star(sK1),multiplication(sK0,star(sK1))) = star(sK1),
inference(paramod,[status(thm)],[c_18,c_16006]) ).
cnf(c_12437,plain,
multiplication(addition(one,sK0),star(sK1)) = star(sK1),
inference(paramod,[status(thm)],[c_51,c_16007]) ).
cnf(c_16008,plain,
( leq(multiplication(star(sK0),star(sK1)),star(sK1))
| ~ leq(star(sK1),star(sK1)) ),
inference(paramod,[status(thm)],[c_12437,c_779]) ).
cnf(c_15942,plain,
leq(multiplication(star(sK0),star(sK1)),star(sK1)),
inference(resolve,[status(thm)],[c_53,c_16008]) ).
cnf(c_16009,plain,
addition(multiplication(star(sK0),star(sK1)),star(sK1)) = star(sK1),
inference(resolve,[status(thm)],[c_15942,c_31]) ).
cnf(c_16010,plain,
addition(star(sK1),multiplication(star(sK0),star(sK1))) = star(sK1),
inference(paramod,[status(thm)],[c_18,c_16009]) ).
cnf(c_15968,plain,
multiplication(star(sK0),star(sK1)) = star(sK1),
inference(paramod,[status(thm)],[c_723,c_16010]) ).
cnf(c_16011,plain,
multiplication(star(sK0),addition(one,star(sK1))) = addition(star(sK0),star(sK1)),
inference(paramod,[status(thm)],[c_15968,c_46]) ).
cnf(c_16012,plain,
multiplication(star(sK0),star(sK1)) = addition(star(sK0),star(sK1)),
inference(paramod,[status(thm)],[c_711,c_16011]) ).
cnf(c_16013,plain,
star(sK1) = addition(star(sK0),star(sK1)),
inference(paramod,[status(thm)],[c_15968,c_16012]) ).
cnf(c_16014,plain,
addition(star(sK0),star(sK1)) = star(sK1),
inference(copy,[status(thm)],[c_16013]) ).
cnf(c_15994,plain,
$false,
inference(resolve,[status(thm)],[c_85,c_16014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE041+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.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 : Fri Sep 25 19:18:38 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 859675 was started by sandbox2 on n003,
% 0.08/0.37 % Fri Sep 25 19:18:38 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 50.82/6.90
% 50.82/6.90 % Assigning unary symbol star kb_weight 0 and highest precedence (9).
% 50.82/6.90
% 50.82/6.90 % given #500 (T,wt=24): 4944 leq(multiplication(c1,A),multiplication(c2,addition(A,B))). [para(84(a,1),4900(a,2,1))].
% 50.82/6.90
% 50.82/6.90 % SZS status Theorem for theBenchmark
% 50.82/6.90
% 50.82/6.90 % Proof 1 at 5.12 (+ 1.36) seconds.
% 50.82/6.90 % Length of proof is 54.
% 50.82/6.90 % Level of proof is 13.
% 50.82/6.90 % Maximum clause weight is 42.000.
% 50.82/6.90 % Given clauses 796.
% 50.82/6.90
% 50.82/6.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------