%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE141+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 : n014.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 07:44:23 AM UTC 2026
% Result : Theorem 2.98s 0.85s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 83 ( 73 unt; 0 def)
% Number of atoms : 93 ( 70 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 7 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 125 ( 7 sgn 30 !; 1 ?)
% 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(idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',idempotence) ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('theBenchmark.p',multiplicative_associativity) ).
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(distributivity1,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',distributivity1) ).
fof(distributivity2,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',distributivity2) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(star_unfold1,axiom,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
file('theBenchmark.p',star_unfold1) ).
fof(star_induction1,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,C),B),C)
=> leq(multiplication(star(A),B),C) ),
file('theBenchmark.p',star_induction1) ).
fof(infty_coinduction,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('theBenchmark.p',infty_coinduction) ).
fof(isolation,axiom,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
file('theBenchmark.p',isolation) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(goals,conjecture,
! [X0] : multiplication(strong_iteration(one),X0) = strong_iteration(one),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : multiplication(strong_iteration(one),X0) = strong_iteration(one),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_20,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_21,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_23,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[idempotence]) ).
cnf(c_24,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_25,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_26,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_27,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[distributivity1]) ).
cnf(c_28,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_29,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[distributivity2]) ).
cnf(c_30,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_31,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_32,plain,
star(A) = addition(one,multiplication(A,star(A))),
inference(clausify,[status(thm)],[star_unfold1]) ).
cnf(c_33,plain,
addition(one,multiplication(A,star(A))) = star(A),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_36,plain,
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(clausify,[status(thm)],[star_induction1]) ).
cnf(c_40,plain,
( leq(A,multiplication(strong_iteration(B),C))
| ~ leq(A,addition(multiplication(B,A),C)) ),
inference(clausify,[status(thm)],[infty_coinduction]) ).
cnf(c_41,plain,
strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
inference(clausify,[status(thm)],[isolation]) ).
cnf(c_42,plain,
addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_43,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_44,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
fof(nnf_19,plain,
? [X0] : strong_iteration(one) != multiplication(strong_iteration(one),X0),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
strong_iteration(one) != multiplication(strong_iteration(one),sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_19]) ).
cnf(c_45,negated_conjecture,
strong_iteration(one) != multiplication(strong_iteration(one),sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_46,negated_conjecture,
multiplication(strong_iteration(one),sK0) != strong_iteration(one),
inference(copy,[status(thm)],[c_45]) ).
cnf(c_1208,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_20,c_21]) ).
cnf(c_48,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_21,c_1208]) ).
cnf(c_1209,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_23,c_21]) ).
cnf(c_50,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_1209]) ).
cnf(c_1210,plain,
addition(addition(A,B),B) = addition(A,B),
inference(paramod,[status(thm)],[c_23,c_21]) ).
cnf(c_52,plain,
addition(A,addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_20,c_1210]) ).
cnf(c_1211,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_25,c_28]) ).
cnf(c_54,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_1211]) ).
cnf(c_1212,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_26,c_30]) ).
cnf(c_59,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_1212]) ).
cnf(c_75,plain,
( leq(multiplication(star(one),B),A)
| ~ leq(addition(A,B),A) ),
inference(paramod,[status(thm)],[c_26,c_36]) ).
cnf(c_98,plain,
( leq(A,multiplication(strong_iteration(one),B))
| ~ leq(A,addition(A,B)) ),
inference(paramod,[status(thm)],[c_26,c_40]) ).
cnf(c_103,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_44,c_23]) ).
cnf(c_124,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_50,c_44]) ).
cnf(c_1213,plain,
addition(one,star(A)) = addition(one,multiplication(A,star(A))),
inference(paramod,[status(thm)],[c_33,c_50]) ).
cnf(c_127,plain,
addition(one,star(A)) = star(A),
inference(paramod,[status(thm)],[c_33,c_1213]) ).
cnf(c_133,plain,
leq(A,multiplication(strong_iteration(one),B)),
inference(resolve,[status(thm)],[c_124,c_98]) ).
cnf(c_1214,plain,
addition(multiplication(A,star(A)),star(A)) = addition(one,multiplication(A,star(A))),
inference(paramod,[status(thm)],[c_33,c_52]) ).
cnf(c_1215,plain,
addition(star(A),multiplication(A,star(A))) = addition(one,multiplication(A,star(A))),
inference(paramod,[status(thm)],[c_20,c_1214]) ).
cnf(c_1216,plain,
multiplication(addition(one,A),star(A)) = addition(one,multiplication(A,star(A))),
inference(paramod,[status(thm)],[c_59,c_1215]) ).
cnf(c_162,plain,
multiplication(addition(one,A),star(A)) = star(A),
inference(paramod,[status(thm)],[c_33,c_1216]) ).
cnf(c_212,plain,
addition(A,multiplication(strong_iteration(one),B)) = multiplication(strong_iteration(one),B),
inference(resolve,[status(thm)],[c_133,c_43]) ).
cnf(c_1217,plain,
addition(A,star(B)) = addition(one,addition(A,star(B))),
inference(paramod,[status(thm)],[c_127,c_48]) ).
cnf(c_219,plain,
addition(one,addition(A,star(B))) = addition(A,star(B)),
inference(copy,[status(thm)],[c_1217]) ).
cnf(c_1218,plain,
multiplication(addition(one,A),addition(one,star(A))) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_162,c_54]) ).
cnf(c_1219,plain,
multiplication(addition(one,A),star(A)) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_127,c_1218]) ).
cnf(c_1220,plain,
star(A) = addition(addition(one,A),star(A)),
inference(paramod,[status(thm)],[c_162,c_1219]) ).
cnf(c_1221,plain,
star(A) = addition(star(A),addition(one,A)),
inference(paramod,[status(thm)],[c_20,c_1220]) ).
cnf(c_1222,plain,
star(A) = addition(one,addition(star(A),A)),
inference(paramod,[status(thm)],[c_48,c_1221]) ).
cnf(c_1223,plain,
star(A) = addition(one,addition(A,star(A))),
inference(paramod,[status(thm)],[c_20,c_1222]) ).
cnf(c_1224,plain,
star(A) = addition(A,star(A)),
inference(paramod,[status(thm)],[c_219,c_1223]) ).
cnf(c_462,plain,
addition(A,star(A)) = star(A),
inference(copy,[status(thm)],[c_1224]) ).
cnf(c_1225,plain,
( leq(multiplication(star(one),A),A)
| ~ leq(A,A) ),
inference(paramod,[status(thm)],[c_23,c_75]) ).
cnf(c_1110,plain,
leq(multiplication(star(one),A),A),
inference(resolve,[status(thm)],[c_103,c_1225]) ).
cnf(c_1133,plain,
leq(star(one),one),
inference(paramod,[status(thm)],[c_25,c_1110]) ).
cnf(c_1226,plain,
addition(star(one),one) = one,
inference(resolve,[status(thm)],[c_1133,c_43]) ).
cnf(c_1227,plain,
addition(one,star(one)) = one,
inference(paramod,[status(thm)],[c_20,c_1226]) ).
cnf(c_1155,plain,
star(one) = one,
inference(paramod,[status(thm)],[c_462,c_1227]) ).
cnf(c_1228,plain,
addition(one,multiplication(strong_iteration(one),zero)) = strong_iteration(one),
inference(paramod,[status(thm)],[c_1155,c_42]) ).
cnf(c_1157,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(one),
inference(paramod,[status(thm)],[c_212,c_1228]) ).
cnf(c_1229,plain,
multiplication(strong_iteration(one),A) = multiplication(strong_iteration(one),multiplication(zero,A)),
inference(paramod,[status(thm)],[c_1157,c_24]) ).
cnf(c_1230,plain,
multiplication(strong_iteration(one),A) = multiplication(strong_iteration(one),zero),
inference(paramod,[status(thm)],[c_31,c_1229]) ).
cnf(c_1206,plain,
multiplication(strong_iteration(one),A) = strong_iteration(one),
inference(paramod,[status(thm)],[c_1157,c_1230]) ).
cnf(c_1207,plain,
$false,
inference(resolve,[status(thm)],[c_1206,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE141+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n014.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Fri Sep 25 19:26:02 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 891351 was started by sandbox2 on n014,
% 0.19/0.44 % Fri Sep 25 19:26:02 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 2.98/0.85
% 2.98/0.85 % SZS status Theorem for theBenchmark
% 2.98/0.85
% 2.98/0.85 % Proof 1 at 0.25 (+ 0.13) seconds.
% 2.98/0.85 % Length of proof is 57.
% 2.98/0.85 % Level of proof is 9.
% 2.98/0.85 % Maximum clause weight is 36.000.
% 2.98/0.85 % Given clauses 162.
% 2.98/0.85
% 2.98/0.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------