%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE067+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 : 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 07:44:14 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% 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 : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 18 ( 0 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
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] : domain(addition(domain(X0),domain(X1))) = addition(domain(X0),domain(X1)),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] : domain(addition(domain(X0),domain(X1))) = addition(domain(X0),domain(X1)),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0,X1] : domain(addition(domain(X0),domain(X1))) != addition(domain(X0),domain(X1)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
domain(addition(domain(sK0),domain(sK1))) != addition(domain(sK0),domain(sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_17]) ).
cnf(c_20,negated_conjecture,
domain(addition(domain(sK0),domain(sK1))) != addition(domain(sK0),domain(sK1)),
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_33,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_40,negated_conjecture,
addition(domain(domain(sK0)),domain(domain(sK1))) != addition(domain(sK0),domain(sK1)),
inference(paramod,[status(thm)],[c_21,c_20]) ).
cnf(c_59,plain,
domain(domain(A)) = domain(multiplication(one,A)),
inference(paramod,[status(thm)],[c_33,c_24]) ).
cnf(c_55,plain,
domain(domain(A)) = domain(A),
inference(paramod,[status(thm)],[c_33,c_59]) ).
cnf(c_60,negated_conjecture,
addition(domain(sK0),domain(domain(sK1))) != addition(domain(sK0),domain(sK1)),
inference(paramod,[status(thm)],[c_55,c_40]) ).
cnf(c_61,negated_conjecture,
addition(domain(sK0),domain(sK1)) != addition(domain(sK0),domain(sK1)),
inference(paramod,[status(thm)],[c_55,c_60]) ).
cnf(c_58,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE067+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 19:18:52 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 990917 was started by sandbox on n013,
% 0.09/0.37 % Fri Sep 25 19:18:52 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 11.
% 0.14/0.39 % Level of proof is 3.
% 0.14/0.39 % Maximum clause weight is 13.000.
% 0.14/0.39 % Given clauses 9.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------