%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE035+2 : 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 : n004.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 07:44:09 AM UTC 2026
% Result : Theorem 11.96s 2.14s
% Output : CNFRefutation 11.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 35 unt; 0 def)
% Number of atoms : 61 ( 31 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 31 ( 12 ~; 2 |; 14 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 22 !; 4 ?)
% 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(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('theBenchmark.p',multiplicative_associativity) ).
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(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
fof(goals,conjecture,
! [X0,X1,X2,X3] :
( ( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_19,plain,
? [X0,X1,X2,X3] :
( ~ leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(multiplication(multiplication(sK0,addition(sK1,sK2)),c(sK3)),zero)
& leq(multiplication(multiplication(sK0,sK2),c(sK3)),zero)
& leq(multiplication(multiplication(sK0,sK1),c(sK3)),zero)
& test(sK0)
& test(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK0,sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK0),skolemize(X3,sK3)],[nnf_19]) ).
cnf(c_38,negated_conjecture,
~ leq(multiplication(multiplication(sK0,addition(sK1,sK2)),c(sK3)),zero),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_39,negated_conjecture,
leq(multiplication(multiplication(sK0,sK2),c(sK3)),zero),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_40,negated_conjecture,
leq(multiplication(multiplication(sK0,sK1),c(sK3)),zero),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_46,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_47,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_50,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_51,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_50]) ).
cnf(c_52,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_53,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_56,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_58,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_60,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_65,negated_conjecture,
leq(multiplication(sK0,multiplication(sK1,c(sK3))),zero),
inference(paramod,[status(thm)],[c_56,c_40]) ).
cnf(c_66,negated_conjecture,
leq(multiplication(sK0,multiplication(sK2,c(sK3))),zero),
inference(paramod,[status(thm)],[c_56,c_39]) ).
cnf(c_67,negated_conjecture,
~ leq(multiplication(sK0,multiplication(addition(sK1,sK2),c(sK3))),zero),
inference(paramod,[status(thm)],[c_56,c_38]) ).
cnf(c_143,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_60,c_58]) ).
cnf(c_4585,negated_conjecture,
addition(multiplication(sK0,multiplication(sK1,c(sK3))),zero) = zero,
inference(resolve,[status(thm)],[c_65,c_47]) ).
cnf(c_4586,negated_conjecture,
addition(zero,multiplication(sK0,multiplication(sK1,c(sK3)))) = zero,
inference(paramod,[status(thm)],[c_60,c_4585]) ).
cnf(c_152,negated_conjecture,
multiplication(sK0,multiplication(sK1,c(sK3))) = zero,
inference(paramod,[status(thm)],[c_143,c_4586]) ).
cnf(c_4587,negated_conjecture,
addition(multiplication(sK0,multiplication(sK2,c(sK3))),zero) = zero,
inference(resolve,[status(thm)],[c_66,c_47]) ).
cnf(c_4588,negated_conjecture,
addition(zero,multiplication(sK0,multiplication(sK2,c(sK3)))) = zero,
inference(paramod,[status(thm)],[c_60,c_4587]) ).
cnf(c_153,negated_conjecture,
multiplication(sK0,multiplication(sK2,c(sK3))) = zero,
inference(paramod,[status(thm)],[c_143,c_4588]) ).
cnf(c_4589,negated_conjecture,
addition(multiplication(sK0,multiplication(addition(sK1,sK2),c(sK3))),zero) != zero,
inference(resolve,[status(thm)],[c_46,c_67]) ).
cnf(c_4590,negated_conjecture,
addition(zero,multiplication(sK0,multiplication(addition(sK1,sK2),c(sK3)))) != zero,
inference(paramod,[status(thm)],[c_60,c_4589]) ).
cnf(c_154,negated_conjecture,
multiplication(sK0,multiplication(addition(sK1,sK2),c(sK3))) != zero,
inference(paramod,[status(thm)],[c_143,c_4590]) ).
cnf(c_4591,plain,
addition(zero,multiplication(sK0,A)) = multiplication(sK0,addition(multiplication(sK1,c(sK3)),A)),
inference(paramod,[status(thm)],[c_152,c_53]) ).
cnf(c_4592,plain,
multiplication(sK0,A) = multiplication(sK0,addition(multiplication(sK1,c(sK3)),A)),
inference(paramod,[status(thm)],[c_143,c_4591]) ).
cnf(c_309,plain,
multiplication(sK0,addition(multiplication(sK1,c(sK3)),A)) = multiplication(sK0,A),
inference(copy,[status(thm)],[c_4592]) ).
cnf(c_4568,plain,
multiplication(sK0,multiplication(addition(sK1,A),c(sK3))) = multiplication(sK0,multiplication(A,c(sK3))),
inference(paramod,[status(thm)],[c_51,c_309]) ).
cnf(c_4593,negated_conjecture,
multiplication(sK0,multiplication(sK2,c(sK3))) != zero,
inference(paramod,[status(thm)],[c_4568,c_154]) ).
cnf(c_4594,negated_conjecture,
zero != zero,
inference(paramod,[status(thm)],[c_153,c_4593]) ).
cnf(c_4584,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_4594]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE035+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n004.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 19:15:51 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 3853607 was started by sandbox2 on n004,
% 0.17/0.44 % Fri Sep 25 19:15:51 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 11.96/2.14
% 11.96/2.14 % given #500 (T,wt=7): 3565 leq(multiplication(c3,c4),f1(c(c3))). [back_rewrite(3122),rewrite([3520(5)])].
% 11.96/2.14
% 11.96/2.14 % SZS status Theorem for theBenchmark
% 11.96/2.14
% 11.96/2.14 % Proof 1 at 1.21 (+ 0.44) seconds.
% 11.96/2.14 % Length of proof is 29.
% 11.96/2.14 % Level of proof is 6.
% 11.96/2.14 % Maximum clause weight is 15.000.
% 11.96/2.14 % Given clauses 627.
% 11.96/2.14
% 11.96/2.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------