%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE026+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 : n007.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 12:57:47 PM UTC 2026
% Result : Theorem 8.27s 1.60s
% Output : CNFRefutation 8.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 26 unt; 0 def)
% Number of atoms : 113 ( 57 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 97 ( 35 ~; 30 |; 23 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 86 ( 80 !; 6 ?)
% 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(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(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(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
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(f19,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f29,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f32,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f33,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f41,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(f42,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)],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f47,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f48,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0] :
( ( ! [X1] :
( ~ complement(X0,X1)
| c(X0) = X1 )
& ! [X1] :
( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f58,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
& multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
& test(X2)
& test(X1) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f59,plain,
? [X1,X2] :
( ? [X0] :
( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
& multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) )
& test(X2)
& test(X1) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f60,plain,
( ~ leq(multiplication(sK1_skl,sK3_skl),multiplication(sK3_skl,sK2_skl))
& multiplication(sK1_skl,sK3_skl) = multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl)
& test(sK2_skl)
& test(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(X1,sK1_skl),skolemize(X2,sK2_skl),skolemize(X0,sK3_skl)],[f59]) ).
fof(f61,plain,
test(sK1_skl),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f63,plain,
multiplication(sK1_skl,sK3_skl) = multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f64,plain,
~ leq(multiplication(sK1_skl,sK3_skl),multiplication(sK3_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f65,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f50]) ).
fof(f66,plain,
multiplication(sK1_skl,sK3_skl) = multiplication(sK1_skl,multiplication(sK3_skl,sK2_skl)),
inference(backward_demodulation,[status(thm)],[f25,f63]) ).
fof(f160,plain,
complement(sK1_skl,c(sK1_skl)),
inference(resolution,[status(thm)],[f65,f61]) ).
fof(f171,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f245,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f29,f35]) ).
fof(f432,plain,
addition(c(sK1_skl),sK1_skl) = one,
inference(resolution,[status(thm)],[f45,f160]) ).
fof(f5963,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f171,f35]) ).
fof(f6229,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f21,f5963]) ).
fof(f8766,plain,
leq(sK1_skl,one),
inference(paramodulation,[status(thm)],[f432,f6229]) ).
fof(f8789,plain,
addition(sK1_skl,one) = one,
inference(resolution,[status(thm)],[f8766,f34]) ).
fof(f8800,plain,
! [X0] :
( multiplication(one,X0) != multiplication(one,X0)
| leq(multiplication(sK1_skl,X0),multiplication(one,X0)) ),
inference(paramodulation,[status(thm)],[f8789,f245]) ).
fof(f8821,plain,
! [X0] :
( multiplication(one,X0) != multiplication(one,X0)
| leq(multiplication(sK1_skl,X0),X0) ),
inference(forward_demodulation,[status(thm)],[f27,f8800]) ).
fof(f8822,plain,
! [X0] :
( X0 != multiplication(one,X0)
| leq(multiplication(sK1_skl,X0),X0) ),
inference(forward_demodulation,[status(thm)],[f27,f8821]) ).
fof(f8823,plain,
! [X0] :
( X0 != X0
| leq(multiplication(sK1_skl,X0),X0) ),
inference(forward_demodulation,[status(thm)],[f27,f8822]) ).
fof(f8824,plain,
! [X0] : leq(multiplication(sK1_skl,X0),X0),
inference(trivial_equality_resolution,[status(thm)],[f8823]) ).
fof(f8853,plain,
leq(multiplication(sK1_skl,sK3_skl),multiplication(sK3_skl,sK2_skl)),
inference(paramodulation,[status(thm)],[f66,f8824]) ).
fof(f8856,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f8853,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE026+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 20 22:37:20 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 8.27/1.60 % Refutation found
% 8.27/1.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.27/1.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.35/1.64 % Elapsed time: 1.191817 seconds
% 1.35/1.64 % CPU time: 8.888368 seconds
% 1.35/1.64 % Total memory used: 192.300 MB
% 1.35/1.64 % Net memory used: 189.861 MB
%------------------------------------------------------------------------------