%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE113+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 : n017.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 12:57:59 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 32 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
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,conjecture,
! [X0] : forward_diamond(X0,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [X0] : forward_diamond(X0,zero) = zero,
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f31,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f34,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f38,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f44,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f46,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f47,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f54,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
? [X0] : forward_diamond(X0,zero) != zero,
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f59,plain,
forward_diamond(sK0_skl,zero) != zero,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f58]) ).
fof(f60,plain,
forward_diamond(sK0_skl,zero) != zero,
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = one,
inference(backward_demodulation,[status(thm)],[f47,f46]) ).
fof(f304,plain,
zero = antidomain(one),
inference(paramodulation,[status(thm)],[f44,f34]) ).
fof(f350,plain,
domain(one) = antidomain(zero),
inference(paramodulation,[status(thm)],[f304,f47]) ).
fof(f425,plain,
addition(antidomain(zero),antidomain(one)) = one,
inference(paramodulation,[status(thm)],[f350,f61]) ).
fof(f433,plain,
addition(antidomain(zero),zero) = one,
inference(forward_demodulation,[status(thm)],[f304,f425]) ).
fof(f437,plain,
antidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f31,f433]) ).
fof(f537,plain,
domain(zero) = antidomain(one),
inference(paramodulation,[status(thm)],[f437,f47]) ).
fof(f544,plain,
domain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f304,f537]) ).
fof(f552,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f544,f54]) ).
fof(f558,plain,
! [X0] : forward_diamond(X0,zero) = domain(zero),
inference(forward_demodulation,[status(thm)],[f38,f552]) ).
fof(f559,plain,
zero != zero,
inference(backward_demodulation,[status(thm)],[f561,f60]) ).
fof(f561,plain,
! [X0] : forward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f544,f558]) ).
fof(f563,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f559]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE113+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n017.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 20 22:38:57 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.55 % Elapsed time: 0.106442 seconds
% 0.18/0.55 % CPU time: 0.139327 seconds
% 0.18/0.55 % Total memory used: 11.740 MB
% 0.18/0.55 % Net memory used: 11.537 MB
%------------------------------------------------------------------------------