%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE027+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 : Thu Sep 24 12:57:48 PM UTC 2026
% Result : Theorem 39.41s 5.36s
% Output : CNFRefutation 39.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 96 ( 48 unt; 0 def)
% Number of atoms : 195 ( 90 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 179 ( 80 ~; 66 |; 25 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 145 ( 129 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,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('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,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(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X0] : X0 = addition(X0,zero),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f25,plain,
! [X0] : X0 = multiplication(one,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f29,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f30,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f31,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ~ leq(X1,X0)
| X0 = addition(X1,X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( leq(X1,X0)
| X0 != addition(X1,X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f35,plain,
( ! [X0] :
( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ! [X0] :
( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
( ! [X0] :
( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ! [X0] :
( complement(sK0_skl(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X1,sK0_skl(X0))],[f35]) ).
fof(f37,plain,
! [X0] :
( ~ test(X0)
| complement(sK0_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( ( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
( ! [X0,X1] :
( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ! [X0,X1] :
( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| multiplication(X0,X1) = zero ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| one = addition(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,plain,
! [X0,X1] :
( complement(X0,X1)
| zero != multiplication(X1,X0)
| one != addition(X1,X0)
| zero != multiplication(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f46,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0] :
( ( ! [X1] :
( ~ complement(X0,X1)
| c(X0) = X1 )
& ! [X1] :
( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) = X1
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,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(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
? [X3] :
( ( ? [X0,X1,X2] : ~ leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)))
| ? [X0,X1,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))) )
& ? [X4] : test(X4)
& test(X3) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f54,plain,
( ( ~ leq(addition(multiplication(sK1_skl,sK6_skl),multiplication(c(sK1_skl),sK8_skl)),addition(multiplication(sK1_skl,addition(multiplication(sK1_skl,sK6_skl),multiplication(c(sK1_skl),sK7_skl))),multiplication(c(sK1_skl),sK8_skl)))
| ~ leq(addition(multiplication(sK1_skl,addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK4_skl))),multiplication(c(sK1_skl),sK5_skl)),addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl))) )
& test(sK2_skl)
& test(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl,sK8_skl]),skolemize(X3,sK1_skl),skolemize(X4,sK2_skl),skolemize(X0,sK3_skl),skolemize(X1,sK4_skl),skolemize(X2,sK5_skl),skolemize(X0,sK6_skl),skolemize(X1,sK7_skl),skolemize(X2,sK8_skl)],[f53]) ).
fof(f55,plain,
test(sK1_skl),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f57,plain,
( ~ leq(addition(multiplication(sK1_skl,addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK4_skl))),multiplication(c(sK1_skl),sK5_skl)),addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl)))
| ~ leq(addition(multiplication(sK1_skl,sK6_skl),multiplication(c(sK1_skl),sK8_skl)),addition(multiplication(sK1_skl,addition(multiplication(sK1_skl,sK6_skl),multiplication(c(sK1_skl),sK7_skl))),multiplication(c(sK1_skl),sK8_skl))) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f58,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f67,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f20,f22]) ).
fof(f71,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f105,plain,
complement(sK1_skl,c(sK1_skl)),
inference(resolution,[status(thm)],[f58,f55]) ).
fof(f160,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(multiplication(X0,X2),X3)) = multiplication(X0,addition(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f23,f26]) ).
fof(f190,plain,
multiplication(sK1_skl,c(sK1_skl)) = zero,
inference(resolution,[status(thm)],[f105,f42]) ).
fof(f285,plain,
! [X0] :
( leq(X0,X0)
| X0 != X0 ),
inference(paramodulation,[status(thm)],[f22,f33]) ).
fof(f287,plain,
! [X0] : leq(X0,X0),
inference(trivial_equality_resolution,[status(thm)],[f285]) ).
fof(f300,plain,
complement(sK0_skl(sK1_skl),sK1_skl),
inference(resolution,[status(thm)],[f37,f55]) ).
fof(f384,plain,
addition(sK1_skl,sK0_skl(sK1_skl)) = one,
inference(resolution,[status(thm)],[f300,f43]) ).
fof(f385,plain,
zero = multiplication(sK1_skl,sK0_skl(sK1_skl)),
inference(resolution,[status(thm)],[f300,f41]) ).
fof(f387,plain,
zero = multiplication(sK0_skl(sK1_skl),sK1_skl),
inference(resolution,[status(thm)],[f300,f42]) ).
fof(f1168,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X1,X0))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f67]) ).
fof(f1204,plain,
! [X0,X1] :
( leq(X1,addition(X0,addition(X1,X0)))
| addition(X0,addition(X1,X0)) != addition(X1,X0) ),
inference(paramodulation,[status(thm)],[f67,f33]) ).
fof(f1246,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(forward_demodulation,[status(thm)],[f71,f1168]) ).
fof(f1247,plain,
! [X0,X1] :
( leq(X1,addition(X0,addition(X1,X0)))
| addition(X0,X1) != addition(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f1246,f1204]) ).
fof(f1248,plain,
! [X0,X1] :
( leq(X1,addition(X0,X1))
| addition(X0,X1) != addition(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f1246,f1247]) ).
fof(f1249,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f1248,f19]) ).
fof(f1336,plain,
! [X0] : multiplication(addition(X0,sK0_skl(sK1_skl)),sK1_skl) = addition(multiplication(X0,sK1_skl),zero),
inference(paramodulation,[status(thm)],[f387,f27]) ).
fof(f1344,plain,
! [X0] : multiplication(addition(X0,sK0_skl(sK1_skl)),sK1_skl) = multiplication(X0,sK1_skl),
inference(forward_demodulation,[status(thm)],[f21,f1336]) ).
fof(f1378,plain,
leq(sK0_skl(sK1_skl),one),
inference(paramodulation,[status(thm)],[f384,f1249]) ).
fof(f2434,plain,
addition(sK0_skl(sK1_skl),one) = one,
inference(resolution,[status(thm)],[f1378,f32]) ).
fof(f2595,plain,
( complement(sK1_skl,sK0_skl(sK1_skl))
| zero != multiplication(sK0_skl(sK1_skl),sK1_skl)
| one != addition(sK0_skl(sK1_skl),sK1_skl)
| zero != zero ),
inference(paramodulation,[status(thm)],[f385,f44]) ).
fof(f2603,plain,
( complement(sK1_skl,sK0_skl(sK1_skl))
| zero != zero
| one != addition(sK0_skl(sK1_skl),sK1_skl)
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f387,f2595]) ).
fof(f2604,plain,
( complement(sK1_skl,sK0_skl(sK1_skl))
| one != addition(sK0_skl(sK1_skl),sK1_skl)
| zero != zero ),
inference(duplicate_literals_removal,[status(thm)],[f2603]) ).
fof(f2605,plain,
( addition(sK0_skl(sK1_skl),sK1_skl) != one
| complement(sK1_skl,sK0_skl(sK1_skl)) ),
inference(trivial_equality_resolution,[status(thm)],[f2604]) ).
fof(f5184,plain,
addition(sK0_skl(sK1_skl),one) = addition(sK0_skl(sK1_skl),sK1_skl),
inference(paramodulation,[status(thm)],[f384,f1246]) ).
fof(f5414,plain,
( one != one
| complement(sK1_skl,sK0_skl(sK1_skl)) ),
inference(backward_demodulation,[status(thm)],[f5415,f2605]) ).
fof(f5415,plain,
one = addition(sK0_skl(sK1_skl),sK1_skl),
inference(forward_demodulation,[status(thm)],[f2434,f5184]) ).
fof(f5416,plain,
complement(sK1_skl,sK0_skl(sK1_skl)),
inference(trivial_equality_resolution,[status(thm)],[f5414]) ).
fof(f5628,plain,
! [X0,X1] : addition(multiplication(sK1_skl,X0),multiplication(zero,X1)) = multiplication(sK1_skl,addition(X0,multiplication(c(sK1_skl),X1))),
inference(paramodulation,[status(thm)],[f190,f160]) ).
fof(f5690,plain,
! [X0,X1] : addition(multiplication(sK1_skl,X0),zero) = multiplication(sK1_skl,addition(X0,multiplication(c(sK1_skl),X1))),
inference(forward_demodulation,[status(thm)],[f29,f5628]) ).
fof(f5691,plain,
( ~ leq(addition(multiplication(sK1_skl,multiplication(sK1_skl,sK3_skl)),multiplication(c(sK1_skl),sK5_skl)),addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl)))
| ~ leq(addition(multiplication(sK1_skl,sK6_skl),multiplication(c(sK1_skl),sK8_skl)),addition(multiplication(sK1_skl,addition(multiplication(sK1_skl,sK6_skl),multiplication(c(sK1_skl),sK7_skl))),multiplication(c(sK1_skl),sK8_skl))) ),
inference(backward_demodulation,[status(thm)],[f5692,f57]) ).
fof(f5692,plain,
! [X0,X1] : multiplication(sK1_skl,X0) = multiplication(sK1_skl,addition(X0,multiplication(c(sK1_skl),X1))),
inference(forward_demodulation,[status(thm)],[f21,f5690]) ).
fof(f5755,plain,
( ~ leq(addition(multiplication(sK1_skl,multiplication(sK1_skl,sK3_skl)),multiplication(c(sK1_skl),sK5_skl)),addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl)))
| ~ leq(addition(multiplication(sK1_skl,sK6_skl),multiplication(c(sK1_skl),sK8_skl)),addition(multiplication(sK1_skl,multiplication(sK1_skl,sK6_skl)),multiplication(c(sK1_skl),sK8_skl))) ),
inference(forward_demodulation,[status(thm)],[f5692,f5691]) ).
fof(f5799,plain,
( ~ test(sK1_skl)
| c(sK1_skl) = sK0_skl(sK1_skl) ),
inference(resolution,[status(thm)],[f5416,f49]) ).
fof(f5817,plain,
( ~ leq(addition(multiplication(sK1_skl,multiplication(sK1_skl,sK3_skl)),multiplication(c(sK1_skl),sK5_skl)),addition(multiplication(sK1_skl,sK3_skl),multiplication(sK0_skl(sK1_skl),sK5_skl)))
| ~ leq(addition(multiplication(sK1_skl,sK6_skl),multiplication(c(sK1_skl),sK8_skl)),addition(multiplication(sK1_skl,multiplication(sK1_skl,sK6_skl)),multiplication(c(sK1_skl),sK8_skl))) ),
inference(backward_demodulation,[status(thm)],[f5875,f5755]) ).
fof(f5875,plain,
sK0_skl(sK1_skl) = c(sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f5799,f55]) ).
fof(f5893,plain,
( ~ leq(addition(multiplication(sK1_skl,multiplication(sK1_skl,sK3_skl)),multiplication(c(sK1_skl),sK5_skl)),addition(multiplication(sK1_skl,sK3_skl),multiplication(sK0_skl(sK1_skl),sK5_skl)))
| ~ leq(addition(multiplication(sK1_skl,sK6_skl),multiplication(sK0_skl(sK1_skl),sK8_skl)),addition(multiplication(sK1_skl,multiplication(sK1_skl,sK6_skl)),multiplication(c(sK1_skl),sK8_skl))) ),
inference(forward_demodulation,[status(thm)],[f5875,f5817]) ).
fof(f5894,plain,
( ~ leq(addition(multiplication(sK1_skl,multiplication(sK1_skl,sK3_skl)),multiplication(c(sK1_skl),sK5_skl)),addition(multiplication(sK1_skl,sK3_skl),multiplication(sK0_skl(sK1_skl),sK5_skl)))
| ~ leq(addition(multiplication(sK1_skl,sK6_skl),multiplication(sK0_skl(sK1_skl),sK8_skl)),addition(multiplication(sK1_skl,multiplication(sK1_skl,sK6_skl)),multiplication(sK0_skl(sK1_skl),sK8_skl))) ),
inference(forward_demodulation,[status(thm)],[f5875,f5893]) ).
fof(f5895,plain,
( ~ leq(addition(multiplication(sK1_skl,multiplication(sK1_skl,sK3_skl)),multiplication(sK0_skl(sK1_skl),sK5_skl)),addition(multiplication(sK1_skl,sK3_skl),multiplication(sK0_skl(sK1_skl),sK5_skl)))
| ~ leq(addition(multiplication(sK1_skl,sK6_skl),multiplication(sK0_skl(sK1_skl),sK8_skl)),addition(multiplication(sK1_skl,multiplication(sK1_skl,sK6_skl)),multiplication(sK0_skl(sK1_skl),sK8_skl))) ),
inference(forward_demodulation,[status(thm)],[f5875,f5894]) ).
fof(f9624,plain,
multiplication(one,sK1_skl) = multiplication(sK1_skl,sK1_skl),
inference(paramodulation,[status(thm)],[f384,f1344]) ).
fof(f9714,plain,
multiplication(sK1_skl,sK1_skl) = sK1_skl,
inference(forward_demodulation,[status(thm)],[f25,f9624]) ).
fof(f9746,plain,
! [X0] : multiplication(sK1_skl,multiplication(sK1_skl,X0)) = multiplication(sK1_skl,X0),
inference(paramodulation,[status(thm)],[f9714,f23]) ).
fof(f9750,plain,
( ~ leq(addition(multiplication(sK1_skl,sK3_skl),multiplication(sK0_skl(sK1_skl),sK5_skl)),addition(multiplication(sK1_skl,sK3_skl),multiplication(sK0_skl(sK1_skl),sK5_skl)))
| ~ leq(addition(multiplication(sK1_skl,sK6_skl),multiplication(sK0_skl(sK1_skl),sK8_skl)),addition(multiplication(sK1_skl,multiplication(sK1_skl,sK6_skl)),multiplication(sK0_skl(sK1_skl),sK8_skl))) ),
inference(backward_demodulation,[status(thm)],[f9746,f5895]) ).
fof(f9752,plain,
( ~ leq(addition(multiplication(sK1_skl,sK3_skl),multiplication(sK0_skl(sK1_skl),sK5_skl)),addition(multiplication(sK1_skl,sK3_skl),multiplication(sK0_skl(sK1_skl),sK5_skl)))
| ~ leq(addition(multiplication(sK1_skl,sK6_skl),multiplication(sK0_skl(sK1_skl),sK8_skl)),addition(multiplication(sK1_skl,sK6_skl),multiplication(sK0_skl(sK1_skl),sK8_skl))) ),
inference(forward_demodulation,[status(thm)],[f9746,f9750]) ).
fof(f9753,plain,
~ leq(addition(multiplication(sK1_skl,sK3_skl),multiplication(sK0_skl(sK1_skl),sK5_skl)),addition(multiplication(sK1_skl,sK3_skl),multiplication(sK0_skl(sK1_skl),sK5_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f9752,f287]) ).
fof(f9967,plain,
$false,
inference(resolution,[status(thm)],[f9753,f287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE027+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sun Sep 20 22:39:07 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 39.41/5.36 % Refutation found
% 39.41/5.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 39.41/5.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.42/6.26 % Elapsed time: 5.953614 seconds
% 3.42/6.26 % CPU time: 41.138353 seconds
% 3.42/6.26 % Total memory used: 476.077 MB
% 3.42/6.26 % Net memory used: 455.568 MB
%------------------------------------------------------------------------------