%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE069+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 07:44:15 AM UTC 2026
% Result : Theorem 0.06s 0.37s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 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 : 63 ( 5 sgn 18 !; 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(goals,conjecture,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0,X1] : domain(X0) != multiplication(domain(X0),addition(domain(X0),domain(X1))),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
domain(sK0) != multiplication(domain(sK0),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(sK0) != multiplication(domain(sK0),addition(domain(sK0),domain(sK1))),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_21,negated_conjecture,
multiplication(domain(sK0),addition(domain(sK0),domain(sK1))) != domain(sK0),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_24,plain,
addition(domain(A),one) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_25,plain,
domain(multiplication(A,domain(B))) = domain(multiplication(A,B)),
inference(clausify,[status(thm)],[domain2]) ).
cnf(c_26,plain,
multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)),
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_27,plain,
addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A),
inference(copy,[status(thm)],[c_26]) ).
cnf(c_30,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_31,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_32,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_33,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_34,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_35,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_40,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_41,plain,
addition(one,domain(A)) = one,
inference(paramod,[status(thm)],[c_40,c_24]) ).
cnf(c_108,plain,
domain(domain(A)) = domain(multiplication(one,A)),
inference(paramod,[status(thm)],[c_34,c_25]) ).
cnf(c_55,plain,
domain(domain(A)) = domain(A),
inference(paramod,[status(thm)],[c_34,c_108]) ).
cnf(c_109,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_35,c_33]) ).
cnf(c_61,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_109]) ).
cnf(c_110,plain,
addition(multiplication(one,A),multiplication(domain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_41,c_31]) ).
cnf(c_111,plain,
addition(A,multiplication(domain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_34,c_110]) ).
cnf(c_76,plain,
addition(A,multiplication(domain(B),A)) = A,
inference(paramod,[status(thm)],[c_34,c_111]) ).
cnf(c_112,plain,
A = multiplication(domain(A),A),
inference(paramod,[status(thm)],[c_76,c_27]) ).
cnf(c_79,plain,
multiplication(domain(A),A) = A,
inference(copy,[status(thm)],[c_112]) ).
cnf(c_89,plain,
multiplication(domain(A),domain(A)) = domain(A),
inference(paramod,[status(thm)],[c_55,c_79]) ).
cnf(c_113,plain,
addition(domain(A),multiplication(domain(A),B)) = multiplication(domain(A),addition(domain(A),B)),
inference(paramod,[status(thm)],[c_89,c_33]) ).
cnf(c_114,plain,
multiplication(domain(A),addition(one,B)) = multiplication(domain(A),addition(domain(A),B)),
inference(paramod,[status(thm)],[c_61,c_113]) ).
cnf(c_104,plain,
multiplication(domain(A),addition(domain(A),B)) = multiplication(domain(A),addition(one,B)),
inference(copy,[status(thm)],[c_114]) ).
cnf(c_115,negated_conjecture,
multiplication(domain(sK0),addition(one,domain(sK1))) != domain(sK0),
inference(paramod,[status(thm)],[c_104,c_21]) ).
cnf(c_116,negated_conjecture,
multiplication(domain(sK0),one) != domain(sK0),
inference(paramod,[status(thm)],[c_41,c_115]) ).
cnf(c_117,negated_conjecture,
domain(sK0) != domain(sK0),
inference(paramod,[status(thm)],[c_35,c_116]) ).
cnf(c_107,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE069+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.33 % Computer : n011.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Fri Sep 25 19:19:43 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.34 % Process 2667338 was started by sandbox2 on n011,
% 0.06/0.34 % Fri Sep 25 19:19:43 2026
% 0.06/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.06/0.35
% 0.06/0.35 % From the command line: assign(max_seconds, 300).
% 0.06/0.37
% 0.06/0.37 % SZS status Theorem for theBenchmark
% 0.06/0.37
% 0.06/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.06/0.37 % Length of proof is 30.
% 0.06/0.37 % Level of proof is 7.
% 0.06/0.37 % Maximum clause weight is 14.000.
% 0.06/0.37 % Given clauses 26.
% 0.06/0.37
% 0.06/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------