%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE009+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 27 unt; 0 def)
% Number of atoms : 84 ( 52 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 77 ( 35 ~; 20 |; 16 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 48 !; 2 ?)
% 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(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(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] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
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(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(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,X1] :
( one != addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))
& test(X0)
& test(X1) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( one != addition(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))
& test(sK1_skl)
& test(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(X0,sK1_skl),skolemize(X1,sK2_skl)],[f52]) ).
fof(f54,plain,
test(sK2_skl),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
test(sK1_skl),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,plain,
one != addition(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f57,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f62,plain,
one != addition(addition(multiplication(c(sK1_skl),sK2_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl)))),multiplication(c(sK1_skl),c(sK2_skl))),
inference(paramodulation,[status(thm)],[f19,f56]) ).
fof(f68,plain,
! [X0] :
( ~ test(X0)
| addition(c(X0),X0) = one ),
inference(resolution,[status(thm)],[f43,f57]) ).
fof(f70,plain,
addition(c(sK1_skl),sK1_skl) = one,
inference(resolution,[status(thm)],[f68,f55]) ).
fof(f71,plain,
addition(c(sK2_skl),sK2_skl) = one,
inference(resolution,[status(thm)],[f68,f54]) ).
fof(f75,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f208,plain,
addition(sK1_skl,c(sK1_skl)) = one,
inference(paramodulation,[status(thm)],[f19,f70]) ).
fof(f266,plain,
one != addition(multiplication(c(sK1_skl),sK2_skl),addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))),multiplication(c(sK1_skl),c(sK2_skl)))),
inference(forward_demodulation,[status(thm)],[f20,f62]) ).
fof(f267,plain,
one != addition(multiplication(c(sK1_skl),sK2_skl),addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))))),
inference(forward_demodulation,[status(thm)],[f20,f266]) ).
fof(f268,plain,
one != addition(multiplication(c(sK1_skl),sK2_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(addition(sK1_skl,c(sK1_skl)),c(sK2_skl)))),
inference(forward_demodulation,[status(thm)],[f27,f267]) ).
fof(f269,plain,
one != addition(multiplication(c(sK1_skl),sK2_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(one,c(sK2_skl)))),
inference(forward_demodulation,[status(thm)],[f208,f268]) ).
fof(f270,plain,
one != addition(multiplication(c(sK1_skl),sK2_skl),addition(multiplication(sK1_skl,sK2_skl),c(sK2_skl))),
inference(forward_demodulation,[status(thm)],[f25,f269]) ).
fof(f400,plain,
one != addition(c(sK2_skl),addition(multiplication(c(sK1_skl),sK2_skl),multiplication(sK1_skl,sK2_skl))),
inference(paramodulation,[status(thm)],[f75,f270]) ).
fof(f439,plain,
one != addition(c(sK2_skl),multiplication(addition(c(sK1_skl),sK1_skl),sK2_skl)),
inference(forward_demodulation,[status(thm)],[f27,f400]) ).
fof(f440,plain,
one != addition(c(sK2_skl),multiplication(one,sK2_skl)),
inference(forward_demodulation,[status(thm)],[f70,f439]) ).
fof(f441,plain,
one != addition(c(sK2_skl),sK2_skl),
inference(forward_demodulation,[status(thm)],[f25,f440]) ).
fof(f442,plain,
one != one,
inference(forward_demodulation,[status(thm)],[f71,f441]) ).
fof(f443,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n020.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 22:39:02 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.057863 seconds
% 0.09/0.43 % CPU time: 0.176826 seconds
% 0.09/0.43 % Total memory used: 102.989 MB
% 0.09/0.43 % Net memory used: 102.674 MB
%------------------------------------------------------------------------------