%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE006+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 : n018.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 12:57:43 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 60 ( 33 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 62 ( 24 ~; 20 |; 12 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 29 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
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(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0] :
( test(X0)
=> one = addition(X0,c(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] :
( test(X0)
=> one = addition(X0,c(X0)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
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(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(f52,plain,
? [X0] :
( one != addition(X0,c(X0))
& test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( one != addition(sK1_skl,c(sK1_skl))
& test(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X0,sK1_skl)],[f52]) ).
fof(f54,plain,
test(sK1_skl),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
one != addition(sK1_skl,c(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f63,plain,
! [X0] :
( ~ test(X0)
| addition(c(X0),X0) = one ),
inference(resolution,[status(thm)],[f43,f56]) ).
fof(f65,plain,
addition(c(sK1_skl),sK1_skl) = one,
inference(resolution,[status(thm)],[f63,f54]) ).
fof(f68,plain,
addition(sK1_skl,c(sK1_skl)) = one,
inference(paramodulation,[status(thm)],[f19,f65]) ).
fof(f72,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f68,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE006+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 22:39:43 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.055821 seconds
% 0.10/0.43 % CPU time: 0.159857 seconds
% 0.10/0.43 % Total memory used: 101.768 MB
% 0.10/0.43 % Net memory used: 101.479 MB
%------------------------------------------------------------------------------