%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE119+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 : n011.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 0.16s 0.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 27 !; 2 ?)
% 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(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f31,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f38,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f48,plain,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f50,plain,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f51,plain,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f58,plain,
? [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) != domain(X1),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f59,plain,
addition(backward_diamond(zero,domain(sK0_skl)),domain(sK1_skl)) != domain(sK1_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f58]) ).
fof(f60,plain,
addition(backward_diamond(zero,domain(sK0_skl)),domain(sK1_skl)) != domain(sK1_skl),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f63,plain,
! [X0] : addition(codomain(X0),coantidomain(X0)) = one,
inference(backward_demodulation,[status(thm)],[f51,f50]) ).
fof(f77,plain,
addition(domain(sK1_skl),backward_diamond(zero,domain(sK0_skl))) != domain(sK1_skl),
inference(paramodulation,[status(thm)],[f29,f60]) ).
fof(f186,plain,
zero = coantidomain(one),
inference(paramodulation,[status(thm)],[f48,f35]) ).
fof(f247,plain,
codomain(one) = coantidomain(zero),
inference(paramodulation,[status(thm)],[f186,f51]) ).
fof(f276,plain,
addition(coantidomain(zero),coantidomain(one)) = one,
inference(paramodulation,[status(thm)],[f247,f63]) ).
fof(f282,plain,
addition(coantidomain(zero),zero) = one,
inference(forward_demodulation,[status(thm)],[f186,f276]) ).
fof(f284,plain,
coantidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f31,f282]) ).
fof(f290,plain,
codomain(zero) = coantidomain(one),
inference(paramodulation,[status(thm)],[f284,f51]) ).
fof(f293,plain,
codomain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f186,f290]) ).
fof(f435,plain,
! [X0] : backward_diamond(zero,X0) = codomain(zero),
inference(paramodulation,[status(thm)],[f38,f55]) ).
fof(f443,plain,
addition(domain(sK1_skl),zero) != domain(sK1_skl),
inference(backward_demodulation,[status(thm)],[f445,f77]) ).
fof(f445,plain,
! [X0] : backward_diamond(zero,X0) = zero,
inference(forward_demodulation,[status(thm)],[f293,f435]) ).
fof(f449,plain,
domain(sK1_skl) != domain(sK1_skl),
inference(forward_demodulation,[status(thm)],[f31,f443]) ).
fof(f450,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE119+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n011.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 20 22:44:55 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Drodi V4.1.1
% 0.16/0.45 % Refutation found
% 0.16/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.49 % Elapsed time: 0.070105 seconds
% 0.16/0.49 % CPU time: 0.205636 seconds
% 0.16/0.49 % Total memory used: 39.312 MB
% 0.16/0.49 % Net memory used: 39.227 MB
%------------------------------------------------------------------------------