%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE061+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 : n026.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 12:57:53 PM UTC 2026
% Result : Theorem 0.14s 0.59s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 5 ( 5 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/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [X0] : multiplication(domain(X0),domain(X0)) = domain(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0] : multiplication(domain(X0),domain(X0)) = domain(X0),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f35,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f36,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f37,plain,
! [X0] : addition(domain(X0),one) = one,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f40,plain,
? [X0] : multiplication(domain(X0),domain(X0)) != domain(X0),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
multiplication(domain(sK0_skl),domain(sK0_skl)) != domain(sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f40]) ).
fof(f42,plain,
multiplication(domain(sK0_skl),domain(sK0_skl)) != domain(sK0_skl),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f20,f37]) ).
fof(f107,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f117,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f107]) ).
fof(f195,plain,
! [X0] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f26,f36]) ).
fof(f200,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f195]) ).
fof(f262,plain,
! [X0] : addition(domain(X0),multiplication(domain(X0),domain(X0))) = multiplication(domain(domain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f200,f35]) ).
fof(f266,plain,
! [X0] : multiplication(addition(domain(X0),one),domain(X0)) = multiplication(domain(domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f117,f262]) ).
fof(f267,plain,
! [X0] : multiplication(addition(one,domain(X0)),domain(X0)) = multiplication(domain(domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f20,f266]) ).
fof(f268,plain,
! [X0] : multiplication(one,domain(X0)) = multiplication(domain(domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f43,f267]) ).
fof(f269,plain,
! [X0] : domain(X0) = multiplication(domain(domain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f268]) ).
fof(f270,plain,
domain(sK0_skl) != domain(sK0_skl),
inference(backward_demodulation,[status(thm)],[f271,f42]) ).
fof(f271,plain,
! [X0] : domain(X0) = multiplication(domain(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f200,f269]) ).
fof(f272,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f270]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE061+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n026.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Sun Sep 20 22:44:23 UTC 2026
% 0.08/0.56 % CPUTime :
% 0.14/0.57 % Drodi V4.1.1
% 0.14/0.59 % Refutation found
% 0.14/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.62 % Elapsed time: 0.054421 seconds
% 0.14/0.62 % CPU time: 0.174782 seconds
% 0.14/0.62 % Total memory used: 68.344 MB
% 0.14/0.62 % Net memory used: 67.983 MB
%------------------------------------------------------------------------------