%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE089+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 : n012.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 12:57:57 PM UTC 2026
% Result : Theorem 0.08s 0.34s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 13 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 2 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] : addition(A,zero) = 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(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [X0,X1] :
( multiplication(domain(X0),X1) = zero
<= addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [X0,X1] :
( multiplication(domain(X0),X1) = zero
<= addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f25,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f31,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f46,plain,
? [X0,X1] :
( addition(domain(X0),antidomain(X1)) = antidomain(X1)
& multiplication(domain(X0),X1) != zero ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f47,plain,
( addition(domain(sK0_skl),antidomain(sK1_skl)) = antidomain(sK1_skl)
& multiplication(domain(sK0_skl),sK1_skl) != zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f46]) ).
fof(f48,plain,
multiplication(domain(sK0_skl),sK1_skl) != zero,
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
addition(domain(sK0_skl),antidomain(sK1_skl)) = antidomain(sK1_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f226,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f38,f31]) ).
fof(f247,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f25,f226]) ).
fof(f886,plain,
multiplication(antidomain(sK1_skl),sK1_skl) = multiplication(domain(sK0_skl),sK1_skl),
inference(paramodulation,[status(thm)],[f49,f247]) ).
fof(f905,plain,
zero = multiplication(domain(sK0_skl),sK1_skl),
inference(forward_demodulation,[status(thm)],[f38,f886]) ).
fof(f906,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f905,f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE089+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 20 22:42:22 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 0.08/0.34 % Refutation found
% 0.08/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.35 % Elapsed time: 0.048658 seconds
% 0.08/0.35 % CPU time: 0.217387 seconds
% 0.08/0.35 % Total memory used: 71.993 MB
% 0.08/0.35 % Net memory used: 71.654 MB
%------------------------------------------------------------------------------