%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE045+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 : n002.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 12:57:51 PM UTC 2026
% Result : Theorem 14.40s 2.33s
% Output : CNFRefutation 15.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 57 unt; 0 def)
% Number of atoms : 87 ( 60 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 9 |; 4 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 107 ( 104 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
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(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1,X2] :
( leq(multiplication(X0,X2),multiplication(X2,X1))
=> leq(multiplication(star(X0),X2),multiplication(X2,star(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(multiplication(X0,X2),multiplication(X2,X1))
=> leq(multiplication(star(X0),X2),multiplication(X2,star(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(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(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,X2] :
( ~ leq(multiplication(star(X0),X2),multiplication(X2,star(X1)))
& leq(multiplication(X0,X2),multiplication(X2,X1)) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
( ~ leq(multiplication(star(sK0_skl),sK2_skl),multiplication(sK2_skl,star(sK1_skl)))
& leq(multiplication(sK0_skl,sK2_skl),multiplication(sK2_skl,sK1_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X2,sK2_skl)],[f40]) ).
fof(f42,plain,
leq(multiplication(sK0_skl,sK2_skl),multiplication(sK2_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
~ leq(multiplication(star(sK0_skl),sK2_skl),multiplication(sK2_skl,star(sK1_skl))),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f44,plain,
addition(multiplication(sK0_skl,sK2_skl),multiplication(sK2_skl,sK1_skl)) = multiplication(sK2_skl,sK1_skl),
inference(resolution,[status(thm)],[f32,f42]) ).
fof(f50,plain,
! [X0,X1,X2] :
( addition(addition(multiplication(X0,X2),X1),X2) != X2
| leq(multiplication(star(X0),X1),X2) ),
inference(resolution,[status(thm)],[f37,f33]) ).
fof(f57,plain,
addition(addition(multiplication(sK0_skl,multiplication(sK2_skl,star(sK1_skl))),sK2_skl),multiplication(sK2_skl,star(sK1_skl))) != multiplication(sK2_skl,star(sK1_skl)),
inference(resolution,[status(thm)],[f50,f43]) ).
fof(f122,plain,
addition(multiplication(sK2_skl,sK1_skl),multiplication(sK0_skl,sK2_skl)) = multiplication(sK2_skl,sK1_skl),
inference(backward_demodulation,[status(thm)],[f19,f44]) ).
fof(f154,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f170,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f179,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f26,f20]) ).
fof(f204,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f27]) ).
fof(f208,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f214,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(f226,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f27,f204]) ).
fof(f485,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f489,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f485]) ).
fof(f490,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f19,f489]) ).
fof(f544,plain,
addition(multiplication(sK0_skl,multiplication(sK2_skl,star(sK1_skl))),addition(sK2_skl,multiplication(sK2_skl,star(sK1_skl)))) != multiplication(sK2_skl,star(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f20,f57]) ).
fof(f549,plain,
! [X0] : addition(one,star(X0)) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(paramodulation,[status(thm)],[f490,f154]) ).
fof(f557,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f490,f549]) ).
fof(f561,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f557,f20]) ).
fof(f564,plain,
! [X0] : addition(star(X0),multiplication(X0,star(X0))) = star(X0),
inference(backward_demodulation,[status(thm)],[f561,f490]) ).
fof(f743,plain,
addition(multiplication(sK0_skl,multiplication(sK2_skl,star(sK1_skl))),multiplication(sK2_skl,addition(one,star(sK1_skl)))) != multiplication(sK2_skl,star(sK1_skl)),
inference(backward_demodulation,[status(thm)],[f170,f544]) ).
fof(f770,plain,
addition(multiplication(sK2_skl,addition(one,star(sK1_skl))),multiplication(sK0_skl,multiplication(sK2_skl,star(sK1_skl)))) != multiplication(sK2_skl,star(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f19,f743]) ).
fof(f771,plain,
addition(multiplication(sK2_skl,star(sK1_skl)),multiplication(sK0_skl,multiplication(sK2_skl,star(sK1_skl)))) != multiplication(sK2_skl,star(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f557,f770]) ).
fof(f818,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = star(X0),
inference(backward_demodulation,[status(thm)],[f208,f564]) ).
fof(f945,plain,
multiplication(addition(one,sK0_skl),multiplication(sK2_skl,star(sK1_skl))) != multiplication(sK2_skl,star(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f208,f771]) ).
fof(f946,plain,
multiplication(addition(sK0_skl,one),multiplication(sK2_skl,star(sK1_skl))) != multiplication(sK2_skl,star(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f226,f945]) ).
fof(f5028,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,addition(one,X2))),star(X2)) = addition(multiplication(X0,star(X2)),multiplication(X1,star(X2))),
inference(paramodulation,[status(thm)],[f818,f214]) ).
fof(f5112,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,addition(one,X2))),star(X2)) = multiplication(addition(X0,X1),star(X2)),
inference(forward_demodulation,[status(thm)],[f27,f5028]) ).
fof(f5843,plain,
! [X0] : addition(multiplication(sK2_skl,X0),multiplication(sK2_skl,sK1_skl)) = addition(multiplication(sK2_skl,addition(X0,sK1_skl)),multiplication(sK0_skl,sK2_skl)),
inference(paramodulation,[status(thm)],[f122,f179]) ).
fof(f5964,plain,
! [X0] : multiplication(sK2_skl,addition(X0,sK1_skl)) = addition(multiplication(sK2_skl,addition(X0,sK1_skl)),multiplication(sK0_skl,sK2_skl)),
inference(forward_demodulation,[status(thm)],[f26,f5843]) ).
fof(f5965,plain,
! [X0] : multiplication(sK2_skl,addition(X0,sK1_skl)) = addition(multiplication(sK0_skl,sK2_skl),multiplication(sK2_skl,addition(X0,sK1_skl))),
inference(forward_demodulation,[status(thm)],[f19,f5964]) ).
fof(f6383,plain,
multiplication(multiplication(sK2_skl,addition(one,sK1_skl)),star(sK1_skl)) = multiplication(addition(multiplication(sK0_skl,sK2_skl),sK2_skl),star(sK1_skl)),
inference(paramodulation,[status(thm)],[f5965,f5112]) ).
fof(f6420,plain,
multiplication(sK2_skl,multiplication(addition(one,sK1_skl),star(sK1_skl))) = multiplication(addition(multiplication(sK0_skl,sK2_skl),sK2_skl),star(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f23,f6383]) ).
fof(f6421,plain,
multiplication(sK2_skl,star(sK1_skl)) = multiplication(addition(multiplication(sK0_skl,sK2_skl),sK2_skl),star(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f818,f6420]) ).
fof(f6422,plain,
multiplication(sK2_skl,star(sK1_skl)) = multiplication(addition(sK2_skl,multiplication(sK0_skl,sK2_skl)),star(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f226,f6421]) ).
fof(f6423,plain,
multiplication(sK2_skl,star(sK1_skl)) = multiplication(multiplication(addition(one,sK0_skl),sK2_skl),star(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f208,f6422]) ).
fof(f6424,plain,
multiplication(sK2_skl,star(sK1_skl)) = multiplication(addition(one,sK0_skl),multiplication(sK2_skl,star(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f23,f6423]) ).
fof(f6425,plain,
multiplication(sK2_skl,star(sK1_skl)) = multiplication(addition(sK0_skl,one),multiplication(sK2_skl,star(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f226,f6424]) ).
fof(f6426,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6425,f946]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE045+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n002.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 22:43:16 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 14.40/2.33 % Refutation found
% 14.40/2.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 14.40/2.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.20/2.39 % Elapsed time: 2.028770 seconds
% 15.20/2.39 % CPU time: 15.681037 seconds
% 15.20/2.39 % Total memory used: 164.444 MB
% 15.20/2.39 % Net memory used: 161.924 MB
%------------------------------------------------------------------------------