%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE129+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 : n013.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 12:58:00 PM UTC 2026
% Result : Theorem 0.15s 10.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 13 |; 2 &)
% ( 0 <=>; 2 =>; 2 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 35 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [X0] :
( divergence(X0) = zero
<= ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [X0] :
( divergence(X0) = zero
<= ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f56,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f60,plain,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f63,plain,
? [X0] :
( ! [X1] :
( domain(X1) = zero
| addition(domain(X1),forward_diamond(X0,domain(X1))) != forward_diamond(X0,domain(X1)) )
& divergence(X0) != zero ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f64,plain,
( ! [X1] :
( domain(X1) = zero
| addition(domain(X1),forward_diamond(sK0_skl,domain(X1))) != forward_diamond(sK0_skl,domain(X1)) )
& divergence(sK0_skl) != zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f63]) ).
fof(f65,plain,
divergence(sK0_skl) != zero,
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0] :
( domain(X0) = zero
| addition(domain(X0),forward_diamond(sK0_skl,domain(X0))) != forward_diamond(sK0_skl,domain(X0)) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f102,plain,
! [X0,X1] :
( domain(multiplication(X0,domain(X1))) = zero
| addition(domain(multiplication(X0,domain(X1))),forward_diamond(sK0_skl,forward_diamond(X0,X1))) != forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1)))) ),
inference(paramodulation,[status(thm)],[f56,f66]) ).
fof(f105,plain,
! [X0,X1] :
( domain(multiplication(X0,domain(X1))) = zero
| addition(forward_diamond(sK0_skl,forward_diamond(X0,X1)),domain(multiplication(X0,domain(X1)))) != forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1)))) ),
inference(forward_demodulation,[status(thm)],[f31,f102]) ).
fof(f106,plain,
! [X0,X1] :
( domain(multiplication(X0,domain(X1))) = zero
| addition(forward_diamond(sK0_skl,forward_diamond(X0,X1)),forward_diamond(X0,X1)) != forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1)))) ),
inference(forward_demodulation,[status(thm)],[f56,f105]) ).
fof(f107,plain,
! [X0,X1] :
( domain(multiplication(X0,domain(X1))) = zero
| addition(forward_diamond(X0,X1),forward_diamond(sK0_skl,forward_diamond(X0,X1))) != forward_diamond(sK0_skl,domain(multiplication(X0,domain(X1)))) ),
inference(forward_demodulation,[status(thm)],[f31,f106]) ).
fof(f108,plain,
! [X0,X1] :
( domain(multiplication(X0,domain(X1))) = zero
| addition(forward_diamond(X0,X1),forward_diamond(sK0_skl,forward_diamond(X0,X1))) != forward_diamond(sK0_skl,forward_diamond(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f56,f107]) ).
fof(f109,plain,
! [X0,X1] :
( forward_diamond(X0,X1) = zero
| addition(forward_diamond(X0,X1),forward_diamond(sK0_skl,forward_diamond(X0,X1))) != forward_diamond(sK0_skl,forward_diamond(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f56,f108]) ).
fof(f312,plain,
! [X0] :
( forward_diamond(X0,divergence(X0)) = zero
| addition(divergence(X0),forward_diamond(sK0_skl,forward_diamond(X0,divergence(X0)))) != forward_diamond(sK0_skl,forward_diamond(X0,divergence(X0))) ),
inference(paramodulation,[status(thm)],[f60,f109]) ).
fof(f314,plain,
! [X0] :
( forward_diamond(X0,divergence(X0)) = zero
| addition(divergence(X0),forward_diamond(sK0_skl,divergence(X0))) != forward_diamond(sK0_skl,forward_diamond(X0,divergence(X0))) ),
inference(forward_demodulation,[status(thm)],[f60,f312]) ).
fof(f315,plain,
! [X0] :
( forward_diamond(X0,divergence(X0)) = zero
| addition(divergence(X0),forward_diamond(sK0_skl,divergence(X0))) != forward_diamond(sK0_skl,divergence(X0)) ),
inference(forward_demodulation,[status(thm)],[f60,f314]) ).
fof(f316,plain,
! [X0] :
( divergence(X0) = zero
| addition(divergence(X0),forward_diamond(sK0_skl,divergence(X0))) != forward_diamond(sK0_skl,divergence(X0)) ),
inference(forward_demodulation,[status(thm)],[f60,f315]) ).
fof(f320,plain,
addition(divergence(sK0_skl),forward_diamond(sK0_skl,divergence(sK0_skl))) != forward_diamond(sK0_skl,divergence(sK0_skl)),
inference(resolution,[status(thm)],[f316,f65]) ).
fof(f321,plain,
addition(divergence(sK0_skl),divergence(sK0_skl)) != forward_diamond(sK0_skl,divergence(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f60,f320]) ).
fof(f322,plain,
divergence(sK0_skl) != forward_diamond(sK0_skl,divergence(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f34,f321]) ).
fof(f323,plain,
divergence(sK0_skl) != divergence(sK0_skl),
inference(forward_demodulation,[status(thm)],[f60,f322]) ).
fof(f324,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f323]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE129+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/10.41 % Computer : n013.cluster.edu
% 0.15/10.41 % Model : x86_64 x86_64
% 0.15/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.41 % Memory : 8046.5625MB
% 0.15/10.41 % OS : Linux 6.8.0-71-generic
% 0.15/10.41 % CPULimit : 300
% 0.15/10.41 % WCLimit : 300
% 0.15/10.41 % DateTime : Sun Sep 20 22:45:02 UTC 2026
% 0.15/10.42 % CPUTime :
% 0.15/10.43 % Drodi V4.1.1
% 0.15/10.45 % Refutation found
% 0.15/10.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/10.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/10.48 % Elapsed time: 0.058618 seconds
% 0.15/10.48 % CPU time: 0.212892 seconds
% 0.15/10.48 % Total memory used: 69.108 MB
% 0.15/10.48 % Net memory used: 68.885 MB
%------------------------------------------------------------------------------