%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE005+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 : n003.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 12:57:42 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 89 ( 66 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 97 ( 42 ~; 40 |; 10 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = 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(f16,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
c(one) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
c(one) != zero,
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
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(f44,plain,
! [X0,X1] :
( addition(X1,X0) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| 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(f49,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| c(X0) = X1
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X0] :
( c(X0) = zero
| test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
! [X0] :
( c(X0) = zero
| test(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
c(one) != zero,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f63,plain,
! [X0,X1] :
( c(X0) = zero
| ~ complement(X0,X1)
| c(X0) = X1 ),
inference(resolution,[status(thm)],[f49,f51]) ).
fof(f76,plain,
! [X0,X1] :
( c(X1) = zero
| c(X1) = X0
| addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero ),
inference(resolution,[status(thm)],[f44,f63]) ).
fof(f78,plain,
! [X0] :
( c(one) = X0
| addition(X0,one) != one
| multiplication(one,X0) != zero
| multiplication(X0,one) != zero ),
inference(resolution,[status(thm)],[f76,f52]) ).
fof(f81,plain,
! [X0] :
( c(one) = X0
| addition(X0,one) != one
| multiplication(one,X0) != zero
| X0 != zero ),
inference(forward_demodulation,[status(thm)],[f24,f78]) ).
fof(f82,plain,
! [X0] :
( c(one) = X0
| addition(X0,one) != one
| X0 != zero
| X0 != zero ),
inference(forward_demodulation,[status(thm)],[f25,f81]) ).
fof(f83,plain,
! [X0] :
( c(one) = X0
| addition(X0,one) != one
| X0 != zero ),
inference(duplicate_literals_removal,[status(thm)],[f82]) ).
fof(f84,plain,
( c(one) = zero
| addition(zero,one) != one ),
inference(destructive_equality_resolution,[status(thm)],[f83]) ).
fof(f85,plain,
addition(zero,one) != one,
inference(forward_subsumption_resolution,[status(thm)],[f84,f52]) ).
fof(f160,plain,
addition(one,zero) != one,
inference(paramodulation,[status(thm)],[f19,f85]) ).
fof(f164,plain,
one != one,
inference(forward_demodulation,[status(thm)],[f21,f160]) ).
fof(f165,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE005+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 22:39:15 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.047074 seconds
% 0.13/0.41 % CPU time: 0.157449 seconds
% 0.13/0.41 % Total memory used: 102.156 MB
% 0.13/0.41 % Net memory used: 101.832 MB
%------------------------------------------------------------------------------