%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE114+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 : n010.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 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 52 unt; 0 def)
% Number of atoms : 52 ( 51 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 : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 34 !; 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(f21,axiom,
! [X0] : c(X0) = antidomain(domain(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(f25,axiom,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [X0] : forward_box(X0,one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [X0] : forward_box(X0,one) = one,
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(f52,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f54,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f56,plain,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f58,plain,
? [X0] : forward_box(X0,one) != one,
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f59,plain,
forward_box(sK0_skl,one) != one,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f58]) ).
fof(f60,plain,
forward_box(sK0_skl,one) != one,
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f88,plain,
antidomain(one) = zero,
inference(paramodulation,[status(thm)],[f34,f44]) ).
fof(f109,plain,
domain(one) = antidomain(zero),
inference(paramodulation,[status(thm)],[f88,f47]) ).
fof(f110,plain,
! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f47,f44]) ).
fof(f141,plain,
! [X0] : domain(domain(X0)) = antidomain(c(X0)),
inference(paramodulation,[status(thm)],[f52,f47]) ).
fof(f142,plain,
! [X0] : multiplication(c(X0),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f52,f44]) ).
fof(f143,plain,
c(one) = antidomain(antidomain(zero)),
inference(paramodulation,[status(thm)],[f109,f52]) ).
fof(f144,plain,
c(one) = domain(zero),
inference(forward_demodulation,[status(thm)],[f47,f143]) ).
fof(f397,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f47,f46]) ).
fof(f402,plain,
addition(antidomain(zero),antidomain(one)) = one,
inference(paramodulation,[status(thm)],[f109,f397]) ).
fof(f405,plain,
addition(domain(one),zero) = one,
inference(paramodulation,[status(thm)],[f88,f397]) ).
fof(f415,plain,
addition(antidomain(zero),zero) = one,
inference(forward_demodulation,[status(thm)],[f88,f402]) ).
fof(f416,plain,
antidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f31,f415]) ).
fof(f419,plain,
domain(one) = one,
inference(forward_demodulation,[status(thm)],[f31,f405]) ).
fof(f422,plain,
multiplication(domain(zero),one) = zero,
inference(paramodulation,[status(thm)],[f416,f110]) ).
fof(f426,plain,
domain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f34,f422]) ).
fof(f429,plain,
multiplication(c(one),one) = zero,
inference(paramodulation,[status(thm)],[f419,f142]) ).
fof(f430,plain,
domain(one) = antidomain(c(one)),
inference(paramodulation,[status(thm)],[f419,f141]) ).
fof(f435,plain,
c(one) = zero,
inference(forward_demodulation,[status(thm)],[f34,f429]) ).
fof(f436,plain,
one = antidomain(c(one)),
inference(forward_demodulation,[status(thm)],[f419,f430]) ).
fof(f437,plain,
one = antidomain(domain(zero)),
inference(forward_demodulation,[status(thm)],[f144,f436]) ).
fof(f438,plain,
one = c(zero),
inference(forward_demodulation,[status(thm)],[f52,f437]) ).
fof(f620,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f426,f54]) ).
fof(f636,plain,
! [X0] : forward_diamond(X0,zero) = domain(zero),
inference(forward_demodulation,[status(thm)],[f38,f620]) ).
fof(f637,plain,
! [X0] : forward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f426,f636]) ).
fof(f681,plain,
! [X0] : forward_box(X0,one) = c(forward_diamond(X0,zero)),
inference(paramodulation,[status(thm)],[f435,f56]) ).
fof(f688,plain,
! [X0] : forward_box(X0,one) = c(zero),
inference(forward_demodulation,[status(thm)],[f637,f681]) ).
fof(f689,plain,
! [X0] : forward_box(X0,one) = one,
inference(forward_demodulation,[status(thm)],[f438,f688]) ).
fof(f690,plain,
one != one,
inference(backward_demodulation,[status(thm)],[f689,f60]) ).
fof(f693,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE114+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n010.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 22:44:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.051775 seconds
% 0.12/0.40 % CPU time: 0.172303 seconds
% 0.12/0.40 % Total memory used: 58.185 MB
% 0.12/0.40 % Net memory used: 58.042 MB
%------------------------------------------------------------------------------