%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE063+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 : 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 0.02s 0.40s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 52 unt; 0 def)
% Number of atoms : 60 ( 59 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 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 : 62 ( 6 sgn 20 !; 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(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_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(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(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(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0)
=> addition(domain(X0),domain(X1)) = domain(X1) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0)
=> addition(domain(X0),domain(X1)) = domain(X1) ),
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_24,plain,
domain(addition(A,B)) = addition(domain(A),domain(B)),
inference(clausify,[status(thm)],[domain5]) ).
cnf(c_26,plain,
addition(domain(A),one) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_27,plain,
domain(multiplication(A,domain(B))) = domain(multiplication(A,B)),
inference(clausify,[status(thm)],[domain2]) ).
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_34,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_35,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_36,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_37,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_42,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_149,plain,
addition(multiplication(domain(A),B),multiplication(one,B)) = multiplication(one,B),
inference(paramod,[status(thm)],[c_26,c_33]) ).
cnf(c_150,plain,
addition(multiplication(domain(A),B),B) = multiplication(one,B),
inference(paramod,[status(thm)],[c_36,c_149]) ).
cnf(c_151,plain,
addition(B,multiplication(domain(A),B)) = multiplication(one,B),
inference(paramod,[status(thm)],[c_42,c_150]) ).
cnf(c_55,plain,
addition(A,multiplication(domain(B),A)) = A,
inference(paramod,[status(thm)],[c_36,c_151]) ).
cnf(c_152,plain,
A = multiplication(domain(A),A),
inference(paramod,[status(thm)],[c_55,c_29]) ).
cnf(c_61,plain,
multiplication(domain(A),A) = A,
inference(copy,[status(thm)],[c_152]) ).
cnf(c_153,negated_conjecture,
sK1 = multiplication(domain(sK0),sK1),
inference(paramod,[status(thm)],[c_55,c_23]) ).
cnf(c_62,negated_conjecture,
multiplication(domain(sK0),sK1) = sK1,
inference(copy,[status(thm)],[c_153]) ).
cnf(c_154,plain,
domain(domain(A)) = domain(multiplication(one,A)),
inference(paramod,[status(thm)],[c_36,c_27]) ).
cnf(c_67,plain,
domain(domain(A)) = domain(A),
inference(paramod,[status(thm)],[c_36,c_154]) ).
cnf(c_155,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_37,c_35]) ).
cnf(c_71,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_155]) ).
cnf(c_84,plain,
addition(one,domain(A)) = one,
inference(paramod,[status(thm)],[c_42,c_26]) ).
cnf(c_156,plain,
one = domain(one),
inference(paramod,[status(thm)],[c_61,c_37]) ).
cnf(c_96,plain,
domain(one) = one,
inference(copy,[status(thm)],[c_156]) ).
cnf(c_157,plain,
multiplication(domain(sK0),addition(one,sK1)) = addition(domain(sK0),sK1),
inference(paramod,[status(thm)],[c_62,c_71]) ).
cnf(c_129,plain,
multiplication(domain(sK0),addition(one,sK1)) = addition(sK1,domain(sK0)),
inference(paramod,[status(thm)],[c_42,c_157]) ).
cnf(c_158,plain,
domain(multiplication(domain(sK0),domain(addition(one,sK1)))) = domain(addition(sK1,domain(sK0))),
inference(paramod,[status(thm)],[c_129,c_27]) ).
cnf(c_159,plain,
domain(multiplication(domain(sK0),addition(domain(one),domain(sK1)))) = domain(addition(sK1,domain(sK0))),
inference(paramod,[status(thm)],[c_24,c_158]) ).
cnf(c_160,plain,
domain(multiplication(domain(sK0),addition(one,domain(sK1)))) = domain(addition(sK1,domain(sK0))),
inference(paramod,[status(thm)],[c_96,c_159]) ).
cnf(c_161,plain,
domain(multiplication(domain(sK0),one)) = domain(addition(sK1,domain(sK0))),
inference(paramod,[status(thm)],[c_84,c_160]) ).
cnf(c_162,plain,
domain(domain(sK0)) = domain(addition(sK1,domain(sK0))),
inference(paramod,[status(thm)],[c_37,c_161]) ).
cnf(c_163,plain,
domain(sK0) = domain(addition(sK1,domain(sK0))),
inference(paramod,[status(thm)],[c_67,c_162]) ).
cnf(c_164,plain,
domain(sK0) = addition(domain(sK1),domain(domain(sK0))),
inference(paramod,[status(thm)],[c_24,c_163]) ).
cnf(c_165,plain,
domain(sK0) = addition(domain(sK1),domain(sK0)),
inference(paramod,[status(thm)],[c_67,c_164]) ).
cnf(c_166,plain,
addition(domain(sK1),domain(sK0)) = domain(sK0),
inference(copy,[status(thm)],[c_165]) ).
cnf(c_148,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_21,c_166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE063+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.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 19:19:14 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.37 % Process 2665537 was started by sandbox2 on n011,
% 0.02/0.37 % Fri Sep 25 19:19:14 2026
% 0.02/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.37
% 0.02/0.37 % From the command line: assign(max_seconds, 300).
% 0.02/0.40
% 0.02/0.40 % Assigning unary symbol domain kb_weight 0 and highest precedence (8).
% 0.02/0.40
% 0.02/0.40 % SZS status Theorem for theBenchmark
% 0.02/0.40
% 0.02/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.02/0.40 % Length of proof is 35.
% 0.02/0.40 % Level of proof is 6.
% 0.02/0.40 % Maximum clause weight is 31.000.
% 0.02/0.40 % Given clauses 31.
% 0.02/0.40
% 0.02/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------