%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE009+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 0.13s 0.41s
% Output : CNFRefutation 0.13s
% 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/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(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
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(f19,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/sandbox/benchmark/theBenchmark.p') ).
fof(f20,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)],[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(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
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] :
( 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)],[f20]) ).
fof(f59,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)],[f58]) ).
fof(f60,plain,
test(sK2_skl),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
test(sK1_skl),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,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)],[f59]) ).
fof(f63,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f50]) ).
fof(f74,plain,
one != addition(addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),multiplication(c(sK1_skl),sK2_skl))),multiplication(c(sK1_skl),c(sK2_skl))),
inference(backward_demodulation,[status(thm)],[f22,f62]) ).
fof(f75,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f85,plain,
one != addition(multiplication(sK1_skl,sK2_skl),addition(addition(multiplication(sK1_skl,c(sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))),
inference(forward_demodulation,[status(thm)],[f22,f74]) ).
fof(f86,plain,
one != addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),addition(multiplication(c(sK1_skl),sK2_skl),multiplication(c(sK1_skl),c(sK2_skl))))),
inference(forward_demodulation,[status(thm)],[f22,f85]) ).
fof(f277,plain,
one != addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl))))),
inference(forward_demodulation,[status(thm)],[f28,f86]) ).
fof(f308,plain,
! [X0] :
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f63,f45]) ).
fof(f594,plain,
addition(c(sK1_skl),sK1_skl) = one,
inference(resolution,[status(thm)],[f308,f61]) ).
fof(f595,plain,
addition(c(sK2_skl),sK2_skl) = one,
inference(resolution,[status(thm)],[f308,f60]) ).
fof(f609,plain,
addition(sK2_skl,c(sK2_skl)) = one,
inference(paramodulation,[status(thm)],[f21,f595]) ).
fof(f795,plain,
one != addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),multiplication(c(sK1_skl),one))),
inference(backward_demodulation,[status(thm)],[f609,f277]) ).
fof(f803,plain,
one != addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),c(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f26,f795]) ).
fof(f828,plain,
one != addition(c(sK1_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl)))),
inference(paramodulation,[status(thm)],[f75,f803]) ).
fof(f831,plain,
one != addition(c(sK1_skl),multiplication(sK1_skl,addition(sK2_skl,c(sK2_skl)))),
inference(forward_demodulation,[status(thm)],[f28,f828]) ).
fof(f832,plain,
one != addition(c(sK1_skl),multiplication(sK1_skl,one)),
inference(forward_demodulation,[status(thm)],[f609,f831]) ).
fof(f833,plain,
one != addition(c(sK1_skl),sK1_skl),
inference(forward_demodulation,[status(thm)],[f26,f832]) ).
fof(f834,plain,
one != one,
inference(forward_demodulation,[status(thm)],[f594,f833]) ).
fof(f835,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f834]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.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 22:38:03 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.058697 seconds
% 0.13/0.43 % CPU time: 0.233487 seconds
% 0.13/0.43 % Total memory used: 79.716 MB
% 0.13/0.43 % Net memory used: 79.454 MB
%------------------------------------------------------------------------------