%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE064+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 : n011.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 0.13s 0.60s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 28 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 40 ( 6 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
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(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(goals,conjecture,
! [X0,X1] :
( addition(domain(X0),domain(X1)) = domain(X1)
=> addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( addition(domain(X0),domain(X1)) = domain(X1)
=> addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0,X1] :
( domain(X1) = addition(domain(X0),domain(X1))
& multiplication(domain(X1),X0) != addition(X0,multiplication(domain(X1),X0)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( domain(sK0) = addition(domain(sK1),domain(sK0))
& multiplication(domain(sK0),sK1) != addition(sK1,multiplication(domain(sK0),sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK1),skolemize(X1,sK0)],[nnf_17]) ).
cnf(c_20,negated_conjecture,
domain(sK0) = addition(domain(sK1),domain(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_21,negated_conjecture,
addition(domain(sK1),domain(sK0)) = domain(sK0),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_22,negated_conjecture,
multiplication(domain(sK0),sK1) != addition(sK1,multiplication(domain(sK0),sK1)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_23,negated_conjecture,
addition(sK1,multiplication(domain(sK0),sK1)) != multiplication(domain(sK0),sK1),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_26,plain,
addition(domain(A),one) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_28,plain,
multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)),
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_29,plain,
addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_32,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_33,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_36,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_42,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_183,plain,
addition(multiplication(domain(A),B),multiplication(one,B)) = multiplication(one,B),
inference(paramod,[status(thm)],[c_26,c_33]) ).
cnf(c_184,plain,
addition(multiplication(domain(A),B),B) = multiplication(one,B),
inference(paramod,[status(thm)],[c_36,c_183]) ).
cnf(c_185,plain,
addition(B,multiplication(domain(A),B)) = multiplication(one,B),
inference(paramod,[status(thm)],[c_42,c_184]) ).
cnf(c_54,plain,
addition(A,multiplication(domain(B),A)) = A,
inference(paramod,[status(thm)],[c_36,c_185]) ).
cnf(c_186,plain,
A = multiplication(domain(A),A),
inference(paramod,[status(thm)],[c_54,c_29]) ).
cnf(c_59,plain,
multiplication(domain(A),A) = A,
inference(copy,[status(thm)],[c_186]) ).
cnf(c_187,negated_conjecture,
sK1 != multiplication(domain(sK0),sK1),
inference(paramod,[status(thm)],[c_54,c_23]) ).
cnf(c_60,negated_conjecture,
multiplication(domain(sK0),sK1) != sK1,
inference(copy,[status(thm)],[c_187]) ).
cnf(c_95,plain,
addition(A,multiplication(B,A)) = multiplication(addition(domain(A),B),A),
inference(paramod,[status(thm)],[c_59,c_33]) ).
cnf(c_101,plain,
multiplication(addition(domain(A),domain(B)),A) = A,
inference(paramod,[status(thm)],[c_95,c_54]) ).
cnf(c_188,plain,
multiplication(domain(sK0),sK1) = sK1,
inference(paramod,[status(thm)],[c_21,c_101]) ).
cnf(c_182,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_60,c_188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE064+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.55 % Computer : n011.cluster.edu
% 0.08/0.55 % Model : x86_64 x86_64
% 0.08/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.55 % Memory : 8046.5625MB
% 0.08/0.55 % OS : Linux 6.8.0-71-generic
% 0.08/0.55 % CPULimit : 300
% 0.08/0.55 % WCLimit : 300
% 0.08/0.55 % DateTime : Fri Sep 25 19:19:14 UTC 2026
% 0.08/0.56 % CPUTime :
% 0.08/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.56 % Process 2665481 was started by sandbox on n011,
% 0.08/0.56 % Fri Sep 25 19:19:14 2026
% 0.08/0.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.56
% 0.08/0.56 % From the command line: assign(max_seconds, 300).
% 0.13/0.60
% 0.13/0.60 % Assigning unary symbol domain kb_weight 0 and highest precedence (8).
% 0.13/0.60
% 0.13/0.60 % SZS status Theorem for theBenchmark
% 0.13/0.60
% 0.13/0.60 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.13/0.60 % Length of proof is 23.
% 0.13/0.60 % Level of proof is 7.
% 0.13/0.60 % Maximum clause weight is 32.000.
% 0.13/0.60 % Given clauses 39.
% 0.13/0.60
% 0.13/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------