%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE043+2 : TPTP v9.3.1. Released v4.0.0.
% 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 12:57:50 PM UTC 2026
% Result : Theorem 0.03s 0.47s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 42 unt; 0 def)
% Number of atoms : 90 ( 48 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 45 ~; 20 |; 4 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 98 ( 92 !; 6 ?)
% 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(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
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(f15,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1] :
( leq(addition(X1,multiplication(multiplication(X0,star(X0)),X1)),multiplication(star(X0),X1))
& leq(multiplication(star(X0),X1),addition(X1,multiplication(multiplication(X0,star(X0)),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( leq(addition(X1,multiplication(multiplication(X0,star(X0)),X1)),multiplication(star(X0),X1))
& leq(multiplication(star(X0),X1),addition(X1,multiplication(multiplication(X0,star(X0)),X1))) ),
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(f23,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
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(f36,plain,
! [A,B,C] :
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f37,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,plain,
? [X0,X1] :
( ~ leq(addition(X1,multiplication(multiplication(X0,star(X0)),X1)),multiplication(star(X0),X1))
| ~ leq(multiplication(star(X0),X1),addition(X1,multiplication(multiplication(X0,star(X0)),X1))) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
( ? [X0,X1] : ~ leq(addition(X1,multiplication(multiplication(X0,star(X0)),X1)),multiplication(star(X0),X1))
| ? [X0,X1] : ~ leq(multiplication(star(X0),X1),addition(X1,multiplication(multiplication(X0,star(X0)),X1))) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
( ~ leq(addition(sK3_skl,multiplication(multiplication(sK2_skl,star(sK2_skl)),sK3_skl)),multiplication(star(sK2_skl),sK3_skl))
| ~ leq(multiplication(star(sK0_skl),sK1_skl),addition(sK1_skl,multiplication(multiplication(sK0_skl,star(sK0_skl)),sK1_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X0,sK2_skl),skolemize(X1,sK3_skl)],[f41]) ).
fof(f43,plain,
( ~ leq(addition(sK3_skl,multiplication(multiplication(sK2_skl,star(sK2_skl)),sK3_skl)),multiplication(star(sK2_skl),sK3_skl))
| ~ leq(multiplication(star(sK0_skl),sK1_skl),addition(sK1_skl,multiplication(multiplication(sK0_skl,star(sK0_skl)),sK1_skl))) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
( ~ leq(addition(sK3_skl,multiplication(multiplication(sK2_skl,star(sK2_skl)),sK3_skl)),multiplication(star(sK2_skl),sK3_skl))
| ~ leq(multiplication(star(sK0_skl),sK1_skl),addition(sK1_skl,multiplication(sK0_skl,multiplication(star(sK0_skl),sK1_skl)))) ),
inference(forward_demodulation,[status(thm)],[f23,f43]) ).
fof(f45,plain,
( ~ leq(addition(sK3_skl,multiplication(sK2_skl,multiplication(star(sK2_skl),sK3_skl))),multiplication(star(sK2_skl),sK3_skl))
| ~ leq(multiplication(star(sK0_skl),sK1_skl),addition(sK1_skl,multiplication(sK0_skl,multiplication(star(sK0_skl),sK1_skl)))) ),
inference(forward_demodulation,[status(thm)],[f23,f44]) ).
fof(f50,plain,
( ~ leq(multiplication(star(sK0_skl),sK1_skl),addition(sK1_skl,multiplication(sK0_skl,multiplication(star(sK0_skl),sK1_skl))))
| addition(addition(sK3_skl,multiplication(sK2_skl,multiplication(star(sK2_skl),sK3_skl))),multiplication(star(sK2_skl),sK3_skl)) != multiplication(star(sK2_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f33,f45]) ).
fof(f52,plain,
( ~ leq(multiplication(star(sK0_skl),sK1_skl),addition(sK1_skl,multiplication(sK0_skl,multiplication(star(sK0_skl),sK1_skl))))
| addition(sK3_skl,addition(multiplication(sK2_skl,multiplication(star(sK2_skl),sK3_skl)),multiplication(star(sK2_skl),sK3_skl))) != multiplication(star(sK2_skl),sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f20,f50]) ).
fof(f60,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f62,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f68,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f60]) ).
fof(f622,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(X2,multiplication(X0,addition(X1,X3))),
inference(paramodulation,[status(thm)],[f26,f68]) ).
fof(f723,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f23,f27]) ).
fof(f726,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f23,f27]) ).
fof(f750,plain,
( ~ leq(multiplication(star(sK0_skl),sK1_skl),addition(sK1_skl,multiplication(sK0_skl,multiplication(star(sK0_skl),sK1_skl))))
| addition(sK3_skl,multiplication(addition(multiplication(sK2_skl,star(sK2_skl)),star(sK2_skl)),sK3_skl)) != multiplication(star(sK2_skl),sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f723,f52]) ).
fof(f915,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f916,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f924,plain,
( ~ leq(multiplication(star(sK0_skl),sK1_skl),addition(sK1_skl,multiplication(sK0_skl,multiplication(star(sK0_skl),sK1_skl))))
| addition(sK3_skl,multiplication(multiplication(addition(sK2_skl,one),star(sK2_skl)),sK3_skl)) != multiplication(star(sK2_skl),sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f915,f750]) ).
fof(f929,plain,
( ~ leq(multiplication(star(sK0_skl),sK1_skl),addition(sK1_skl,multiplication(sK0_skl,multiplication(star(sK0_skl),sK1_skl))))
| multiplication(addition(one,multiplication(addition(sK2_skl,one),star(sK2_skl))),sK3_skl) != multiplication(star(sK2_skl),sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f916,f924]) ).
fof(f1041,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f1047,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f1041]) ).
fof(f1049,plain,
( ~ leq(multiplication(star(sK0_skl),sK1_skl),addition(sK1_skl,multiplication(sK0_skl,multiplication(star(sK0_skl),sK1_skl))))
| multiplication(star(sK2_skl),sK3_skl) != multiplication(star(sK2_skl),sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f1050,f929]) ).
fof(f1050,plain,
! [X0] : addition(one,multiplication(addition(X0,one),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f915,f1047]) ).
fof(f1053,plain,
~ leq(multiplication(star(sK0_skl),sK1_skl),addition(sK1_skl,multiplication(sK0_skl,multiplication(star(sK0_skl),sK1_skl)))),
inference(trivial_equality_resolution,[status(thm)],[f1049]) ).
fof(f1506,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),one),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f25,f723]) ).
fof(f1604,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f25,f726]) ).
fof(f1662,plain,
~ leq(multiplication(star(sK0_skl),sK1_skl),multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl)),
inference(backward_demodulation,[status(thm)],[f1604,f1053]) ).
fof(f1726,plain,
~ leq(addition(multiplication(sK0_skl,multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl)),sK1_skl),multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl)),
inference(resolution,[status(thm)],[f1662,f37]) ).
fof(f1728,plain,
~ leq(multiplication(addition(multiplication(sK0_skl,addition(one,multiplication(sK0_skl,star(sK0_skl)))),one),sK1_skl),multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl)),
inference(forward_demodulation,[status(thm)],[f1506,f1726]) ).
fof(f1745,plain,
addition(multiplication(addition(multiplication(sK0_skl,addition(one,multiplication(sK0_skl,star(sK0_skl)))),one),sK1_skl),multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl)) != multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl),
inference(resolution,[status(thm)],[f1728,f33]) ).
fof(f1751,plain,
multiplication(addition(addition(multiplication(sK0_skl,addition(one,multiplication(sK0_skl,star(sK0_skl)))),one),addition(one,multiplication(sK0_skl,star(sK0_skl)))),sK1_skl) != multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl),
inference(forward_demodulation,[status(thm)],[f27,f1745]) ).
fof(f1752,plain,
multiplication(addition(multiplication(sK0_skl,addition(one,multiplication(sK0_skl,star(sK0_skl)))),addition(one,addition(one,multiplication(sK0_skl,star(sK0_skl))))),sK1_skl) != multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl),
inference(forward_demodulation,[status(thm)],[f20,f1751]) ).
fof(f1753,plain,
multiplication(addition(multiplication(sK0_skl,addition(one,multiplication(sK0_skl,star(sK0_skl)))),addition(one,multiplication(sK0_skl,star(sK0_skl)))),sK1_skl) != multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl),
inference(forward_demodulation,[status(thm)],[f62,f1752]) ).
fof(f1754,plain,
multiplication(addition(one,multiplication(sK0_skl,addition(addition(one,multiplication(sK0_skl,star(sK0_skl))),star(sK0_skl)))),sK1_skl) != multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl),
inference(forward_demodulation,[status(thm)],[f622,f1753]) ).
fof(f1755,plain,
multiplication(addition(one,multiplication(sK0_skl,addition(one,addition(multiplication(sK0_skl,star(sK0_skl)),star(sK0_skl))))),sK1_skl) != multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl),
inference(forward_demodulation,[status(thm)],[f20,f1754]) ).
fof(f1756,plain,
multiplication(addition(one,multiplication(sK0_skl,addition(one,multiplication(addition(sK0_skl,one),star(sK0_skl))))),sK1_skl) != multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl),
inference(forward_demodulation,[status(thm)],[f915,f1755]) ).
fof(f1757,plain,
multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl) != multiplication(addition(one,multiplication(sK0_skl,star(sK0_skl))),sK1_skl),
inference(forward_demodulation,[status(thm)],[f1050,f1756]) ).
fof(f1758,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1757]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE043+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sun Sep 20 22:40:22 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.03/0.47 % Refutation found
% 0.03/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.49 % Elapsed time: 0.184885 seconds
% 0.12/0.49 % CPU time: 1.285418 seconds
% 0.12/0.49 % Total memory used: 84.147 MB
% 0.12/0.49 % Net memory used: 83.426 MB
%------------------------------------------------------------------------------