%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE093+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 07:44:18 AM UTC 2026
% Result : Theorem 0.21s 0.53s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 49 unt; 0 def)
% Number of atoms : 53 ( 48 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 5 sgn 19 !; 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(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(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(domain1,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('theBenchmark.p',domain1) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one,
file('theBenchmark.p',domain3) ).
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('theBenchmark.p',domain5) ).
fof(goals,conjecture,
! [X0] : domain(star(X0)) = one,
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : domain(star(X0)) = one,
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_22,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_23,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_27,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_28,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_31,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_32,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_35,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_37,plain,
leq(addition(one,multiplication(A,star(A))),star(A)),
inference(clausify,[status(thm)],[star_unfold_right]) ).
cnf(c_41,plain,
multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)),
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_42,plain,
addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_44,plain,
addition(domain(A),one) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_45,plain,
addition(one,domain(A)) = one,
inference(paramod,[status(thm)],[c_22,c_44]) ).
cnf(c_47,plain,
domain(addition(A,B)) = addition(domain(A),domain(B)),
inference(clausify,[status(thm)],[domain5]) ).
fof(nnf_21,plain,
? [X0] : domain(star(X0)) != one,
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
domain(star(sK0)) != one,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_21]) ).
cnf(c_48,negated_conjecture,
domain(star(sK0)) != one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_445,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_22,c_23]) ).
cnf(c_50,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_23,c_445]) ).
cnf(c_446,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_28,c_32]) ).
cnf(c_61,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_446]) ).
cnf(c_447,plain,
addition(addition(one,multiplication(A,star(A))),star(A)) = star(A),
inference(resolve,[status(thm)],[c_35,c_37]) ).
cnf(c_448,plain,
addition(star(A),addition(one,multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_22,c_447]) ).
cnf(c_449,plain,
addition(one,addition(star(A),multiplication(A,star(A)))) = star(A),
inference(paramod,[status(thm)],[c_50,c_448]) ).
cnf(c_69,plain,
addition(one,multiplication(addition(one,A),star(A))) = star(A),
inference(paramod,[status(thm)],[c_61,c_449]) ).
cnf(c_450,plain,
addition(one,domain(one)) = multiplication(domain(one),one),
inference(paramod,[status(thm)],[c_27,c_42]) ).
cnf(c_451,plain,
one = multiplication(domain(one),one),
inference(paramod,[status(thm)],[c_45,c_450]) ).
cnf(c_452,plain,
one = domain(one),
inference(paramod,[status(thm)],[c_27,c_451]) ).
cnf(c_97,plain,
domain(one) = one,
inference(copy,[status(thm)],[c_452]) ).
cnf(c_111,plain,
domain(multiplication(addition(A,B),C)) = addition(domain(multiplication(A,C)),domain(multiplication(B,C))),
inference(paramod,[status(thm)],[c_32,c_47]) ).
cnf(c_453,plain,
addition(A,one) = addition(one,addition(A,domain(B))),
inference(paramod,[status(thm)],[c_45,c_50]) ).
cnf(c_117,plain,
addition(one,addition(A,domain(B))) = addition(A,one),
inference(copy,[status(thm)],[c_453]) ).
cnf(c_454,plain,
domain(star(A)) = addition(domain(one),domain(multiplication(addition(one,A),star(A)))),
inference(paramod,[status(thm)],[c_69,c_47]) ).
cnf(c_455,plain,
domain(star(A)) = addition(one,domain(multiplication(addition(one,A),star(A)))),
inference(paramod,[status(thm)],[c_97,c_454]) ).
cnf(c_456,plain,
domain(star(A)) = addition(one,addition(domain(multiplication(one,star(A))),domain(multiplication(A,star(A))))),
inference(paramod,[status(thm)],[c_111,c_455]) ).
cnf(c_457,plain,
domain(star(A)) = addition(one,addition(domain(star(A)),domain(multiplication(A,star(A))))),
inference(paramod,[status(thm)],[c_28,c_456]) ).
cnf(c_458,plain,
domain(star(A)) = addition(domain(star(A)),one),
inference(paramod,[status(thm)],[c_117,c_457]) ).
cnf(c_459,plain,
domain(star(A)) = addition(one,domain(star(A))),
inference(paramod,[status(thm)],[c_22,c_458]) ).
cnf(c_443,plain,
domain(star(A)) = one,
inference(paramod,[status(thm)],[c_45,c_459]) ).
cnf(c_444,plain,
$false,
inference(resolve,[status(thm)],[c_443,c_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE093+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n002.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 19:23:52 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 3928298 was started by sandbox on n002,
% 0.17/0.44 % Fri Sep 25 19:23:52 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.21/0.53
% 0.21/0.53 % SZS status Theorem for theBenchmark
% 0.21/0.53
% 0.21/0.53 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.21/0.53 % Length of proof is 33.
% 0.21/0.53 % Level of proof is 6.
% 0.21/0.53 % Maximum clause weight is 36.000.
% 0.21/0.53 % Given clauses 69.
% 0.21/0.53
% 0.21/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------