%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE072+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 : n013.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 07:44:15 AM UTC 2026
% Result : Theorem 0.07s 0.38s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 29 ( 0 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('theBenchmark.p',domain2) ).
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('theBenchmark.p',domain5) ).
fof(goals,conjecture,
! [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) = addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) = addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) != addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
domain(multiplication(addition(sK0,sK1),domain(sK2))) != addition(domain(multiplication(sK0,domain(sK2))),domain(multiplication(sK1,domain(sK2)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_17]) ).
cnf(c_20,negated_conjecture,
domain(multiplication(addition(sK0,sK1),domain(sK2))) != addition(domain(multiplication(sK0,domain(sK2))),domain(multiplication(sK1,domain(sK2)))),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_21,plain,
domain(addition(A,B)) = addition(domain(A),domain(B)),
inference(clausify,[status(thm)],[domain5]) ).
cnf(c_24,plain,
domain(multiplication(A,domain(B))) = domain(multiplication(A,B)),
inference(clausify,[status(thm)],[domain2]) ).
cnf(c_29,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_30,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_50,negated_conjecture,
domain(multiplication(addition(sK0,sK1),sK2)) != addition(domain(multiplication(sK0,domain(sK2))),domain(multiplication(sK1,domain(sK2)))),
inference(paramod,[status(thm)],[c_24,c_20]) ).
cnf(c_51,negated_conjecture,
domain(multiplication(addition(sK0,sK1),sK2)) != addition(domain(multiplication(sK0,sK2)),domain(multiplication(sK1,domain(sK2)))),
inference(paramod,[status(thm)],[c_24,c_50]) ).
cnf(c_40,negated_conjecture,
domain(multiplication(addition(sK0,sK1),sK2)) != addition(domain(multiplication(sK0,sK2)),domain(multiplication(sK1,sK2))),
inference(paramod,[status(thm)],[c_24,c_51]) ).
cnf(c_48,plain,
domain(multiplication(addition(A,B),C)) = addition(domain(multiplication(A,C)),domain(multiplication(B,C))),
inference(paramod,[status(thm)],[c_30,c_21]) ).
cnf(c_49,plain,
$false,
inference(resolve,[status(thm)],[c_48,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE072+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n013.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 19:19:06 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 992173 was started by sandbox2 on n013,
% 0.07/0.35 % Fri Sep 25 19:19:06 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.07/0.38
% 0.07/0.38 % SZS status Theorem for theBenchmark
% 0.07/0.38
% 0.07/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.07/0.38 % Length of proof is 12.
% 0.07/0.38 % Level of proof is 4.
% 0.07/0.38 % Maximum clause weight is 19.000.
% 0.07/0.38 % Given clauses 7.
% 0.07/0.38
% 0.07/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------