%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE066+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 : n012.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 0.03s 0.32s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 34 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 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 : 27 ( 4 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('theBenchmark.p',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(domain1,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('theBenchmark.p',domain1) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('theBenchmark.p',domain2) ).
fof(goals,conjecture,
! [X0,X1] :
( multiplication(X0,domain(X1)) = zero
=> multiplication(X0,X1) = zero ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( multiplication(X0,domain(X1)) = zero
=> multiplication(X0,X1) = zero ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0,X1] :
( multiplication(X0,domain(X1)) = zero
& multiplication(X0,X1) != zero ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( multiplication(sK0,domain(sK1)) = zero
& multiplication(sK0,sK1) != zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_17]) ).
cnf(c_20,negated_conjecture,
multiplication(sK0,domain(sK1)) = zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_21,negated_conjecture,
zero = multiplication(sK0,domain(sK1)),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_22,negated_conjecture,
multiplication(sK0,sK1) != zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_83,negated_conjecture,
multiplication(sK0,sK1) != multiplication(sK0,domain(sK1)),
inference(paramod,[status(thm)],[c_21,c_22]) ).
cnf(c_23,negated_conjecture,
multiplication(sK0,domain(sK1)) != multiplication(sK0,sK1),
inference(copy,[status(thm)],[c_83]) ).
fof(domain4,axiom,
domain(zero) = zero,
file('theBenchmark.p',domain4) ).
cnf(c_25,plain,
domain(zero) = zero,
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_84,plain,
domain(multiplication(sK0,domain(sK1))) = zero,
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_26,plain,
domain(multiplication(sK0,domain(sK1))) = multiplication(sK0,domain(sK1)),
inference(paramod,[status(thm)],[c_21,c_84]) ).
cnf(c_28,plain,
domain(multiplication(A,domain(B))) = domain(multiplication(A,B)),
inference(clausify,[status(thm)],[domain2]) ).
cnf(c_29,plain,
multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)),
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_30,plain,
addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_31,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_85,plain,
multiplication(multiplication(sK0,domain(sK1)),A) = zero,
inference(paramod,[status(thm)],[c_21,c_31]) ).
cnf(c_32,plain,
multiplication(multiplication(sK0,domain(sK1)),A) = multiplication(sK0,domain(sK1)),
inference(paramod,[status(thm)],[c_21,c_85]) ).
cnf(c_41,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_43,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_44,plain,
addition(A,multiplication(sK0,domain(sK1))) = A,
inference(paramod,[status(thm)],[c_21,c_43]) ).
cnf(c_47,plain,
domain(multiplication(sK0,sK1)) = multiplication(sK0,domain(sK1)),
inference(paramod,[status(thm)],[c_28,c_26]) ).
cnf(c_48,plain,
multiplication(sK0,multiplication(domain(sK1),A)) = multiplication(sK0,domain(sK1)),
inference(paramod,[status(thm)],[c_41,c_32]) ).
cnf(c_86,plain,
addition(multiplication(sK0,sK1),multiplication(multiplication(sK0,domain(sK1)),multiplication(sK0,sK1))) = multiplication(domain(multiplication(sK0,sK1)),multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_47,c_30]) ).
cnf(c_87,plain,
addition(multiplication(sK0,sK1),multiplication(sK0,multiplication(domain(sK1),multiplication(sK0,sK1)))) = multiplication(domain(multiplication(sK0,sK1)),multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_41,c_86]) ).
cnf(c_88,plain,
addition(multiplication(sK0,sK1),multiplication(sK0,domain(sK1))) = multiplication(domain(multiplication(sK0,sK1)),multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_48,c_87]) ).
cnf(c_89,plain,
multiplication(sK0,sK1) = multiplication(domain(multiplication(sK0,sK1)),multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_44,c_88]) ).
cnf(c_90,plain,
multiplication(sK0,sK1) = multiplication(multiplication(sK0,domain(sK1)),multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_47,c_89]) ).
cnf(c_91,plain,
multiplication(sK0,sK1) = multiplication(sK0,multiplication(domain(sK1),multiplication(sK0,sK1))),
inference(paramod,[status(thm)],[c_41,c_90]) ).
cnf(c_92,plain,
multiplication(sK0,sK1) = multiplication(sK0,domain(sK1)),
inference(paramod,[status(thm)],[c_48,c_91]) ).
cnf(c_81,plain,
multiplication(sK0,domain(sK1)) = multiplication(sK0,sK1),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_82,plain,
$false,
inference(resolve,[status(thm)],[c_81,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE066+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Fri Sep 25 19:19:05 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 2756977 was started by sandbox on n012,
% 0.03/0.31 % Fri Sep 25 19:19:05 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 0.03/0.32
% 0.03/0.32 % SZS status Theorem for theBenchmark
% 0.03/0.32
% 0.03/0.32 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.32 % Length of proof is 24.
% 0.03/0.32 % Level of proof is 6.
% 0.03/0.32 % Maximum clause weight is 11.000.
% 0.03/0.32 % Given clauses 16.
% 0.03/0.32
% 0.03/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------