%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE065+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 : n006.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 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 43 unt; 0 def)
% Number of atoms : 51 ( 50 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 6 sgn 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('theBenchmark.p',multiplicative_associativity) ).
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(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(domain3,axiom,
! [X0] : addition(domain(X0),one) = one,
file('theBenchmark.p',domain3) ).
fof(goals,conjecture,
! [X0,X1] :
( multiplication(X0,X1) = zero
=> multiplication(X0,domain(X1)) = zero ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( multiplication(X0,X1) = zero
=> multiplication(X0,domain(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,
multiplication(sK0,sK1) = zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_22,negated_conjecture,
zero = multiplication(sK0,sK1),
inference(copy,[status(thm)],[c_21]) ).
fof(domain4,axiom,
domain(zero) = zero,
file('theBenchmark.p',domain4) ).
cnf(c_24,plain,
domain(zero) = zero,
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_203,plain,
domain(multiplication(sK0,sK1)) = zero,
inference(paramod,[status(thm)],[c_22,c_24]) ).
cnf(c_25,plain,
domain(multiplication(sK0,sK1)) = multiplication(sK0,sK1),
inference(paramod,[status(thm)],[c_22,c_203]) ).
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_30,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_204,plain,
multiplication(multiplication(sK0,sK1),A) = zero,
inference(paramod,[status(thm)],[c_22,c_30]) ).
cnf(c_31,plain,
multiplication(multiplication(sK0,sK1),A) = multiplication(sK0,sK1),
inference(paramod,[status(thm)],[c_22,c_204]) ).
cnf(c_34,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_35,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_38,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_40,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_45,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_46,negated_conjecture,
multiplication(sK0,domain(sK1)) != multiplication(sK0,sK1),
inference(paramod,[status(thm)],[c_22,c_20]) ).
cnf(c_47,plain,
multiplication(sK0,multiplication(sK1,A)) = multiplication(sK0,sK1),
inference(paramod,[status(thm)],[c_40,c_31]) ).
cnf(c_48,plain,
addition(one,domain(A)) = one,
inference(paramod,[status(thm)],[c_45,c_26]) ).
cnf(c_205,plain,
addition(multiplication(A,domain(B)),multiplication(domain(multiplication(A,B)),multiplication(A,domain(B)))) = multiplication(domain(multiplication(A,domain(B))),multiplication(A,domain(B))),
inference(paramod,[status(thm)],[c_27,c_29]) ).
cnf(c_54,plain,
addition(multiplication(A,domain(B)),multiplication(domain(multiplication(A,B)),multiplication(A,domain(B)))) = multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))),
inference(paramod,[status(thm)],[c_27,c_205]) ).
cnf(c_206,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_38,c_35]) ).
cnf(c_60,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_206]) ).
cnf(c_207,plain,
multiplication(addition(one,domain(multiplication(A,B))),multiplication(A,domain(B))) = multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))),
inference(paramod,[status(thm)],[c_60,c_54]) ).
cnf(c_208,plain,
multiplication(one,multiplication(A,domain(B))) = multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))),
inference(paramod,[status(thm)],[c_48,c_207]) ).
cnf(c_209,plain,
multiplication(A,domain(B)) = multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))),
inference(paramod,[status(thm)],[c_38,c_208]) ).
cnf(c_63,plain,
multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))) = multiplication(A,domain(B)),
inference(copy,[status(thm)],[c_209]) ).
cnf(c_210,plain,
multiplication(multiplication(sK0,sK1),multiplication(sK0,domain(sK1))) = multiplication(sK0,domain(sK1)),
inference(paramod,[status(thm)],[c_25,c_63]) ).
cnf(c_211,plain,
multiplication(sK0,multiplication(sK1,multiplication(sK0,domain(sK1)))) = multiplication(sK0,domain(sK1)),
inference(paramod,[status(thm)],[c_40,c_210]) ).
cnf(c_212,plain,
multiplication(sK0,sK1) = multiplication(sK0,domain(sK1)),
inference(paramod,[status(thm)],[c_47,c_211]) ).
cnf(c_201,plain,
multiplication(sK0,domain(sK1)) = multiplication(sK0,sK1),
inference(copy,[status(thm)],[c_212]) ).
cnf(c_202,plain,
$false,
inference(resolve,[status(thm)],[c_201,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE065+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 19:19:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 3541069 was started by sandbox2 on n006,
% 0.10/0.38 % Fri Sep 25 19:19:11 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.45
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45
% 0.10/0.45 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.10/0.45 % Length of proof is 33.
% 0.10/0.45 % Level of proof is 6.
% 0.10/0.45 % Maximum clause weight is 59.000.
% 0.10/0.45 % Given clauses 38.
% 0.10/0.45
% 0.10/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------