%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE026+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 1.07s 0.60s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 28 unt; 0 def)
% Number of atoms : 100 ( 53 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 82 ( 29 ~; 22 |; 24 &)
% ( 3 <=>; 4 =>; 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 : 76 ( 67 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f17,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/sandbox/benchmark/theBenchmark.p') ).
fof(f18,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)],[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(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] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
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(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(f33,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
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] :
( complement(sK0_skl(X0),X0)
| ~ test(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(f43,plain,
! [X0,X1] :
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f52,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)],[f18]) ).
fof(f53,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)],[f52]) ).
fof(f54,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)],[f53]) ).
fof(f55,plain,
test(sK1_skl),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f57,plain,
multiplication(sK1_skl,sK3_skl) = multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f58,plain,
~ leq(multiplication(sK1_skl,sK3_skl),multiplication(sK3_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f60,plain,
multiplication(sK1_skl,sK3_skl) = multiplication(sK1_skl,multiplication(sK3_skl,sK2_skl)),
inference(backward_demodulation,[status(thm)],[f23,f57]) ).
fof(f64,plain,
addition(multiplication(sK1_skl,sK3_skl),multiplication(sK3_skl,sK2_skl)) != multiplication(sK3_skl,sK2_skl),
inference(resolution,[status(thm)],[f33,f58]) ).
fof(f82,plain,
addition(multiplication(sK3_skl,sK2_skl),multiplication(sK1_skl,sK3_skl)) != multiplication(sK3_skl,sK2_skl),
inference(paramodulation,[status(thm)],[f19,f64]) ).
fof(f127,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f184,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f601,plain,
! [X0] :
( ~ test(X0)
| addition(X0,sK0_skl(X0)) = one ),
inference(resolution,[status(thm)],[f43,f37]) ).
fof(f1569,plain,
addition(sK1_skl,sK0_skl(sK1_skl)) = one,
inference(resolution,[status(thm)],[f601,f55]) ).
fof(f1592,plain,
addition(sK1_skl,one) = addition(sK1_skl,sK0_skl(sK1_skl)),
inference(paramodulation,[status(thm)],[f1569,f127]) ).
fof(f1594,plain,
addition(sK1_skl,one) = one,
inference(forward_demodulation,[status(thm)],[f1569,f1592]) ).
fof(f1595,plain,
addition(one,sK1_skl) = one,
inference(paramodulation,[status(thm)],[f19,f1594]) ).
fof(f5384,plain,
multiplication(addition(one,sK1_skl),multiplication(sK3_skl,sK2_skl)) = addition(multiplication(sK3_skl,sK2_skl),multiplication(sK1_skl,sK3_skl)),
inference(paramodulation,[status(thm)],[f60,f184]) ).
fof(f5499,plain,
multiplication(one,multiplication(sK3_skl,sK2_skl)) = addition(multiplication(sK3_skl,sK2_skl),multiplication(sK1_skl,sK3_skl)),
inference(forward_demodulation,[status(thm)],[f1595,f5384]) ).
fof(f5500,plain,
multiplication(sK3_skl,sK2_skl) = addition(multiplication(sK3_skl,sK2_skl),multiplication(sK1_skl,sK3_skl)),
inference(forward_demodulation,[status(thm)],[f25,f5499]) ).
fof(f5501,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5500,f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE026+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 22:39:25 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 1.07/0.60 % Refutation found
% 1.07/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.07/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.07/0.63 % Elapsed time: 0.243911 seconds
% 1.07/0.63 % CPU time: 1.672739 seconds
% 1.07/0.63 % Total memory used: 135.949 MB
% 1.07/0.63 % Net memory used: 135.018 MB
%------------------------------------------------------------------------------