%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE170+1.002 : TPTP v9.3.1. Released v5.2.0.
% 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 12:58:07 PM UTC 2026
% Result : Theorem 4.43s 1.02s
% Output : CNFRefutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 61 unt; 0 def)
% Number of atoms : 79 ( 48 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 8 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 122 ( 122 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
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(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
leq(multiplication(a,a),star(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f30,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f31,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f40,plain,
~ leq(multiplication(a,a),star(a)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f499,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f515,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f535,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f26,f33]) ).
fof(f564,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f861,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f499,f33]) ).
fof(f924,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f20,f861]) ).
fof(f929,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f861]) ).
fof(f932,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(resolution,[status(thm)],[f929,f32]) ).
fof(f938,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f20,f929]) ).
fof(f951,plain,
! [X0,X1,X2] : leq(X0,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f19,f938]) ).
fof(f967,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f20,f951]) ).
fof(f1183,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f1188,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f1183]) ).
fof(f1246,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f19,f932]) ).
fof(f1955,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f19,f924]) ).
fof(f2363,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(resolution,[status(thm)],[f1955,f32]) ).
fof(f2397,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f2363]) ).
fof(f2398,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1246,f2397]) ).
fof(f2399,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f2398]) ).
fof(f2400,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f1246,f2399]) ).
fof(f5452,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f515,f967]) ).
fof(f6352,plain,
! [X0] : addition(addition(multiplication(X0,star(X0)),star(X0)),star(X0)) = addition(one,addition(multiplication(X0,star(X0)),star(X0))),
inference(paramodulation,[status(thm)],[f1188,f932]) ).
fof(f6360,plain,
! [X0] : addition(one,star(X0)) = addition(one,addition(multiplication(X0,star(X0)),star(X0))),
inference(paramodulation,[status(thm)],[f1188,f499]) ).
fof(f6429,plain,
! [X0] : addition(star(X0),addition(star(X0),multiplication(X0,star(X0)))) = addition(one,addition(multiplication(X0,star(X0)),star(X0))),
inference(forward_demodulation,[status(thm)],[f2400,f6352]) ).
fof(f6430,plain,
! [X0] : addition(multiplication(X0,star(X0)),star(X0)) = addition(one,addition(multiplication(X0,star(X0)),star(X0))),
inference(forward_demodulation,[status(thm)],[f1246,f6429]) ).
fof(f6431,plain,
! [X0] : addition(multiplication(X0,star(X0)),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f1188,f6430]) ).
fof(f6437,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f1188,f6360]) ).
fof(f10023,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,star(X2)))),
inference(paramodulation,[status(thm)],[f6437,f5452]) ).
fof(f10066,plain,
! [X0,X1,X2] : leq(X0,addition(multiplication(X0,star(X1)),X2)),
inference(paramodulation,[status(thm)],[f19,f10023]) ).
fof(f10289,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = star(X0),
inference(paramodulation,[status(thm)],[f564,f6431]) ).
fof(f10301,plain,
! [X0] : leq(X0,star(X0)),
inference(paramodulation,[status(thm)],[f6431,f10066]) ).
fof(f10405,plain,
! [X0] : addition(X0,star(X0)) = star(X0),
inference(resolution,[status(thm)],[f10301,f32]) ).
fof(f10478,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,star(X1))
| leq(multiplication(X0,X1),multiplication(X0,star(X1))) ),
inference(paramodulation,[status(thm)],[f10405,f535]) ).
fof(f10502,plain,
! [X0] : addition(X0,star(X0)) = addition(star(X0),X0),
inference(paramodulation,[status(thm)],[f10405,f1246]) ).
fof(f10550,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(X0,star(X1))),
inference(trivial_equality_resolution,[status(thm)],[f10478]) ).
fof(f10553,plain,
! [X0] : star(X0) = addition(star(X0),X0),
inference(forward_demodulation,[status(thm)],[f10405,f10502]) ).
fof(f13728,plain,
! [X0] : leq(multiplication(addition(X0,one),X0),star(X0)),
inference(paramodulation,[status(thm)],[f10289,f10550]) ).
fof(f14752,plain,
! [X0] : leq(addition(multiplication(X0,X0),X0),star(X0)),
inference(paramodulation,[status(thm)],[f564,f13728]) ).
fof(f14806,plain,
! [X0] : leq(addition(X0,multiplication(X0,X0)),star(X0)),
inference(paramodulation,[status(thm)],[f19,f14752]) ).
fof(f14842,plain,
! [X0] : addition(addition(X0,multiplication(X0,X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f14806,f32]) ).
fof(f14862,plain,
! [X0] : addition(multiplication(X0,X0),addition(star(X0),X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f2400,f14842]) ).
fof(f14863,plain,
! [X0] : addition(multiplication(X0,X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f10553,f14862]) ).
fof(f14886,plain,
! [X0] : leq(multiplication(X0,X0),star(X0)),
inference(resolution,[status(thm)],[f14863,f33]) ).
fof(f15074,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f40,f14886]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE170+1.002 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sun Sep 20 22:48:51 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 4.43/1.02 % Refutation found
% 4.43/1.02 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.43/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.14/1.04 % Elapsed time: 0.732560 seconds
% 2.14/1.04 % CPU time: 5.609138 seconds
% 2.14/1.04 % Total memory used: 164.304 MB
% 2.14/1.04 % Net memory used: 161.703 MB
%------------------------------------------------------------------------------