%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE027+2 : 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 : n013.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 07:44:08 AM UTC 2026
% Result : Theorem 0.14s 10.95s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 66 ( 44 unt; 0 def)
% Number of atoms : 100 ( 50 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 31 ~; 18 |; 10 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 87 ( 7 sgn 31 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_idempotence) ).
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(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(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('theBenchmark.p',test_2) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('theBenchmark.p',test_3) ).
fof(goals,conjecture,
! [X0,X1,X2,X3,X4] :
( ( test(X4)
& test(X3) )
=> ( leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)))
& leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( test(X4)
& test(X3) )
=> ( leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)))
& leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_20,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
fof(nnf_17,plain,
? [X0,X1,X2,X3,X4] :
( ( ~ leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)))
| ~ leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) )
& test(X4)
& test(X3) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ( ~ leq(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)),addition(multiplication(sK0,addition(multiplication(sK0,sK1),multiplication(c(sK0),sK2))),multiplication(c(sK0),sK3)))
| ~ leq(addition(multiplication(sK0,addition(multiplication(sK0,sK1),multiplication(c(sK0),sK2))),multiplication(c(sK0),sK3)),addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3))) )
& test(sK4)
& test(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK4,sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK0),skolemize(X4,sK4)],[nnf_17]) ).
cnf(c_23,negated_conjecture,
test(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_29,negated_conjecture,
( complement(sK0,A)
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_37,negated_conjecture,
( ~ leq(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)),addition(multiplication(sK0,addition(multiplication(sK0,sK1),multiplication(c(sK0),sK2))),multiplication(c(sK0),sK3)))
| ~ leq(addition(multiplication(sK0,addition(multiplication(sK0,sK1),multiplication(c(sK0),sK2))),multiplication(c(sK0),sK3)),addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3))) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_39,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_40,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_41,plain,
( multiplication(B,A) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_42,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_44,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_46,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_47,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_48,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_49,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_50,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_52,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_53,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_54,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_56,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_1796,negated_conjecture,
( ~ leq(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)),addition(multiplication(sK0,addition(multiplication(sK0,sK1),multiplication(c(sK0),sK2))),multiplication(c(sK0),sK3)))
| ~ leq(addition(multiplication(c(sK0),sK3),multiplication(sK0,addition(multiplication(sK0,sK1),multiplication(c(sK0),sK2)))),addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3))) ),
inference(paramod,[status(thm)],[c_56,c_37]) ).
cnf(c_60,negated_conjecture,
( ~ leq(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)),addition(multiplication(c(sK0),sK3),multiplication(sK0,addition(multiplication(sK0,sK1),multiplication(c(sK0),sK2)))))
| ~ leq(addition(multiplication(c(sK0),sK3),multiplication(sK0,addition(multiplication(sK0,sK1),multiplication(c(sK0),sK2)))),addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3))) ),
inference(paramod,[status(thm)],[c_56,c_1796]) ).
cnf(c_62,plain,
complement(sK0,c(sK0)),
inference(xxres,[status(thm)],[c_29]) ).
cnf(c_95,plain,
leq(A,A),
inference(resolve,[status(thm)],[c_53,c_42]) ).
cnf(c_115,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_56,c_54]) ).
cnf(c_128,plain,
multiplication(c(sK0),sK0) = zero,
inference(resolve,[status(thm)],[c_62,c_41]) ).
cnf(c_129,plain,
multiplication(sK0,c(sK0)) = zero,
inference(resolve,[status(thm)],[c_62,c_40]) ).
cnf(c_1797,plain,
addition(c(sK0),sK0) = one,
inference(resolve,[status(thm)],[c_62,c_39]) ).
cnf(c_130,plain,
addition(sK0,c(sK0)) = one,
inference(paramod,[status(thm)],[c_56,c_1797]) ).
cnf(c_1798,plain,
addition(multiplication(A,sK0),zero) = multiplication(addition(A,c(sK0)),sK0),
inference(paramod,[status(thm)],[c_128,c_47]) ).
cnf(c_1799,plain,
addition(zero,multiplication(A,sK0)) = multiplication(addition(A,c(sK0)),sK0),
inference(paramod,[status(thm)],[c_56,c_1798]) ).
cnf(c_1800,plain,
multiplication(A,sK0) = multiplication(addition(A,c(sK0)),sK0),
inference(paramod,[status(thm)],[c_115,c_1799]) ).
cnf(c_204,plain,
multiplication(addition(A,c(sK0)),sK0) = multiplication(A,sK0),
inference(copy,[status(thm)],[c_1800]) ).
cnf(c_1801,plain,
multiplication(zero,A) = multiplication(sK0,multiplication(c(sK0),A)),
inference(paramod,[status(thm)],[c_129,c_52]) ).
cnf(c_1802,plain,
zero = multiplication(sK0,multiplication(c(sK0),A)),
inference(paramod,[status(thm)],[c_44,c_1801]) ).
cnf(c_212,plain,
multiplication(sK0,multiplication(c(sK0),A)) = zero,
inference(copy,[status(thm)],[c_1802]) ).
cnf(c_1803,plain,
addition(multiplication(sK0,A),zero) = multiplication(sK0,addition(A,multiplication(c(sK0),B))),
inference(paramod,[status(thm)],[c_212,c_49]) ).
cnf(c_1804,plain,
addition(zero,multiplication(sK0,A)) = multiplication(sK0,addition(A,multiplication(c(sK0),B))),
inference(paramod,[status(thm)],[c_56,c_1803]) ).
cnf(c_1805,plain,
multiplication(sK0,A) = multiplication(sK0,addition(A,multiplication(c(sK0),B))),
inference(paramod,[status(thm)],[c_115,c_1804]) ).
cnf(c_350,plain,
multiplication(sK0,addition(A,multiplication(c(sK0),B))) = multiplication(sK0,A),
inference(copy,[status(thm)],[c_1805]) ).
cnf(c_1806,negated_conjecture,
( ~ leq(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)),addition(multiplication(c(sK0),sK3),multiplication(sK0,addition(multiplication(sK0,sK1),multiplication(c(sK0),sK2)))))
| ~ leq(addition(multiplication(c(sK0),sK3),multiplication(sK0,multiplication(sK0,sK1))),addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3))) ),
inference(paramod,[status(thm)],[c_350,c_60]) ).
cnf(c_1807,negated_conjecture,
( ~ leq(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)),addition(multiplication(c(sK0),sK3),multiplication(sK0,addition(multiplication(sK0,sK1),multiplication(c(sK0),sK2)))))
| ~ leq(addition(multiplication(sK0,multiplication(sK0,sK1)),multiplication(c(sK0),sK3)),addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3))) ),
inference(paramod,[status(thm)],[c_56,c_1806]) ).
cnf(c_1808,negated_conjecture,
( ~ leq(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)),addition(multiplication(c(sK0),sK3),multiplication(sK0,multiplication(sK0,sK1))))
| ~ leq(addition(multiplication(sK0,multiplication(sK0,sK1)),multiplication(c(sK0),sK3)),addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3))) ),
inference(paramod,[status(thm)],[c_350,c_1807]) ).
cnf(c_351,negated_conjecture,
( ~ leq(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)),addition(multiplication(sK0,multiplication(sK0,sK1)),multiplication(c(sK0),sK3)))
| ~ leq(addition(multiplication(sK0,multiplication(sK0,sK1)),multiplication(c(sK0),sK3)),addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3))) ),
inference(paramod,[status(thm)],[c_56,c_1808]) ).
cnf(c_1809,plain,
multiplication(one,sK0) = multiplication(sK0,sK0),
inference(paramod,[status(thm)],[c_130,c_204]) ).
cnf(c_1810,plain,
sK0 = multiplication(sK0,sK0),
inference(paramod,[status(thm)],[c_50,c_1809]) ).
cnf(c_1770,plain,
multiplication(sK0,sK0) = sK0,
inference(copy,[status(thm)],[c_1810]) ).
cnf(c_1811,plain,
multiplication(sK0,A) = multiplication(sK0,multiplication(sK0,A)),
inference(paramod,[status(thm)],[c_1770,c_52]) ).
cnf(c_1785,plain,
multiplication(sK0,multiplication(sK0,A)) = multiplication(sK0,A),
inference(copy,[status(thm)],[c_1811]) ).
cnf(c_1812,negated_conjecture,
( ~ leq(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)),addition(multiplication(sK0,multiplication(sK0,sK1)),multiplication(c(sK0),sK3)))
| ~ leq(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)),addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3))) ),
inference(paramod,[status(thm)],[c_1785,c_351]) ).
cnf(c_1813,negated_conjecture,
( ~ leq(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)),addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)))
| ~ leq(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)),addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3))) ),
inference(paramod,[status(thm)],[c_1785,c_1812]) ).
cnf(c_1814,negated_conjecture,
~ leq(addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3)),addition(multiplication(sK0,sK1),multiplication(c(sK0),sK3))),
inference(copy,[status(thm)],[c_1813]) ).
cnf(c_1795,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_95,c_1814]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE027+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.54 % Computer : n013.cluster.edu
% 0.09/10.54 % Model : x86_64 x86_64
% 0.09/10.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.54 % Memory : 8046.5625MB
% 0.09/10.54 % OS : Linux 6.8.0-71-generic
% 0.09/10.54 % CPULimit : 300
% 0.09/10.54 % WCLimit : 300
% 0.09/10.54 % DateTime : Fri Sep 25 19:14:34 UTC 2026
% 0.09/10.55 % CPUTime :
% 0.09/10.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.55 % Process 980592 was started by sandbox on n013,
% 0.09/10.55 % Fri Sep 25 19:14:34 2026
% 0.09/10.55 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/10.55
% 0.09/10.55 % From the command line: assign(max_seconds, 300).
% 0.14/10.95
% 0.14/10.95 % SZS status Theorem for theBenchmark
% 0.14/10.95
% 0.14/10.95 % Proof 1 at 0.27 (+ 0.11) seconds.
% 0.14/10.95 % Length of proof is 44.
% 0.14/10.95 % Level of proof is 8.
% 0.14/10.95 % Maximum clause weight is 48.000.
% 0.14/10.95 % Given clauses 281.
% 0.14/10.95
% 0.14/10.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------