%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE054+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 : 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 : Sun Sep 27 07:44:13 AM UTC 2026
% Result : Theorem 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 8 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_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(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('theBenchmark.p',domain2) ).
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,X1] : addition(domain(multiplication(X0,X1)),domain(X0)) = domain(X0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] : addition(domain(multiplication(X0,X1)),domain(X0)) = domain(X0),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0,X1] : domain(X0) != addition(domain(multiplication(X0,X1)),domain(X0)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
domain(sK0) != addition(domain(multiplication(sK0,sK1)),domain(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_17]) ).
cnf(c_20,negated_conjecture,
domain(sK0) != addition(domain(multiplication(sK0,sK1)),domain(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_21,negated_conjecture,
addition(domain(multiplication(sK0,sK1)),domain(sK0)) != domain(sK0),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_22,plain,
domain(addition(A,B)) = addition(domain(A),domain(B)),
inference(clausify,[status(thm)],[domain5]) ).
cnf(c_24,plain,
addition(domain(A),one) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_25,plain,
domain(multiplication(A,domain(B))) = domain(multiplication(A,B)),
inference(clausify,[status(thm)],[domain2]) ).
cnf(c_32,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_33,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_35,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_40,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_41,plain,
addition(one,domain(A)) = one,
inference(paramod,[status(thm)],[c_40,c_24]) ).
cnf(c_42,negated_conjecture,
addition(domain(sK0),domain(multiplication(sK0,sK1))) != domain(sK0),
inference(paramod,[status(thm)],[c_40,c_21]) ).
cnf(c_99,plain,
addition(multiplication(A,one),multiplication(A,domain(B))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_41,c_33]) ).
cnf(c_100,plain,
addition(A,multiplication(A,domain(B))) = multiplication(A,one),
inference(paramod,[status(thm)],[c_35,c_99]) ).
cnf(c_78,plain,
addition(A,multiplication(A,domain(B))) = A,
inference(paramod,[status(thm)],[c_35,c_100]) ).
cnf(c_101,plain,
domain(A) = addition(domain(A),domain(multiplication(A,domain(B)))),
inference(paramod,[status(thm)],[c_78,c_22]) ).
cnf(c_102,plain,
domain(A) = addition(domain(A),domain(multiplication(A,B))),
inference(paramod,[status(thm)],[c_25,c_101]) ).
cnf(c_97,plain,
addition(domain(A),domain(multiplication(A,B))) = domain(A),
inference(copy,[status(thm)],[c_102]) ).
cnf(c_98,plain,
$false,
inference(resolve,[status(thm)],[c_97,c_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE054+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 19:23:44 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3086005 was started by sandbox2 on n016,
% 0.11/0.37 % Fri Sep 25 19:23:44 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.41
% 0.11/0.41 % SZS status Theorem for theBenchmark
% 0.11/0.41
% 0.11/0.41 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.11/0.41 % Length of proof is 21.
% 0.11/0.41 % Level of proof is 5.
% 0.11/0.41 % Maximum clause weight is 13.000.
% 0.11/0.41 % Given clauses 25.
% 0.11/0.41
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------