%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE036+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 : n018.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 12:57:49 PM UTC 2026
% Result : Theorem 2.72s 0.79s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 47 unt; 0 def)
% Number of atoms : 69 ( 45 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 22 ~; 9 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 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 : 90 ( 89 !; 1 ?)
% 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(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] : leq(star(X0),addition(one,multiplication(X0,star(X0)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] : leq(star(X0),addition(one,multiplication(X0,star(X0)))),
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(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] : ~ leq(star(X0),addition(one,multiplication(X0,star(X0)))),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
~ leq(star(sK0_skl),addition(one,multiplication(sK0_skl,star(sK0_skl)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f40]) ).
fof(f42,plain,
~ leq(star(sK0_skl),addition(one,multiplication(sK0_skl,star(sK0_skl)))),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f48,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f51,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f52,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f59,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f52]) ).
fof(f97,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(f120,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f225,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f228,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f225]) ).
fof(f229,plain,
! [X0] : addition(one,multiplication(addition(X0,one),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f120,f228]) ).
fof(f261,plain,
! [X0,X1] :
( leq(star(X0),X1)
| ~ leq(addition(multiplication(X0,X1),one),X1) ),
inference(paramodulation,[status(thm)],[f24,f37]) ).
fof(f865,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(X3,multiplication(X0,X4)))) = addition(multiplication(X0,addition(X1,X4)),addition(X2,X3)),
inference(paramodulation,[status(thm)],[f48,f97]) ).
fof(f2093,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(paramodulation,[status(thm)],[f229,f51]) ).
fof(f2114,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f229,f2093]) ).
fof(f2118,plain,
! [X0,X1] : addition(one,addition(X0,star(X1))) = addition(X0,star(X1)),
inference(paramodulation,[status(thm)],[f2114,f59]) ).
fof(f2600,plain,
! [X0,X1] : addition(one,multiplication(addition(X0,one),star(X1))) = addition(multiplication(X0,star(X1)),star(X1)),
inference(paramodulation,[status(thm)],[f120,f2118]) ).
fof(f2624,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = star(X0),
inference(backward_demodulation,[status(thm)],[f2625,f229]) ).
fof(f2625,plain,
! [X0,X1] : addition(one,multiplication(addition(X0,one),star(X1))) = multiplication(addition(X0,one),star(X1)),
inference(forward_demodulation,[status(thm)],[f120,f2600]) ).
fof(f2714,plain,
~ leq(addition(multiplication(sK0_skl,addition(one,multiplication(sK0_skl,star(sK0_skl)))),one),addition(one,multiplication(sK0_skl,star(sK0_skl)))),
inference(resolution,[status(thm)],[f261,f42]) ).
fof(f2773,plain,
addition(addition(multiplication(sK0_skl,addition(one,multiplication(sK0_skl,star(sK0_skl)))),one),addition(one,multiplication(sK0_skl,star(sK0_skl)))) != addition(one,multiplication(sK0_skl,star(sK0_skl))),
inference(resolution,[status(thm)],[f2714,f33]) ).
fof(f2776,plain,
addition(multiplication(sK0_skl,addition(one,multiplication(sK0_skl,star(sK0_skl)))),addition(one,addition(one,multiplication(sK0_skl,star(sK0_skl))))) != addition(one,multiplication(sK0_skl,star(sK0_skl))),
inference(forward_demodulation,[status(thm)],[f20,f2773]) ).
fof(f2777,plain,
addition(multiplication(sK0_skl,addition(addition(one,multiplication(sK0_skl,star(sK0_skl))),star(sK0_skl))),addition(one,one)) != addition(one,multiplication(sK0_skl,star(sK0_skl))),
inference(forward_demodulation,[status(thm)],[f865,f2776]) ).
fof(f2778,plain,
addition(multiplication(sK0_skl,addition(one,addition(multiplication(sK0_skl,star(sK0_skl)),star(sK0_skl)))),addition(one,one)) != addition(one,multiplication(sK0_skl,star(sK0_skl))),
inference(forward_demodulation,[status(thm)],[f20,f2777]) ).
fof(f2779,plain,
addition(multiplication(sK0_skl,addition(multiplication(sK0_skl,star(sK0_skl)),star(sK0_skl))),addition(one,one)) != addition(one,multiplication(sK0_skl,star(sK0_skl))),
inference(forward_demodulation,[status(thm)],[f2118,f2778]) ).
fof(f2780,plain,
addition(multiplication(sK0_skl,multiplication(addition(sK0_skl,one),star(sK0_skl))),addition(one,one)) != addition(one,multiplication(sK0_skl,star(sK0_skl))),
inference(forward_demodulation,[status(thm)],[f120,f2779]) ).
fof(f2781,plain,
addition(multiplication(sK0_skl,star(sK0_skl)),addition(one,one)) != addition(one,multiplication(sK0_skl,star(sK0_skl))),
inference(forward_demodulation,[status(thm)],[f2624,f2780]) ).
fof(f2782,plain,
addition(multiplication(sK0_skl,star(sK0_skl)),one) != addition(one,multiplication(sK0_skl,star(sK0_skl))),
inference(forward_demodulation,[status(thm)],[f22,f2781]) ).
fof(f2783,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2782,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE036+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 22:41:42 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 2.72/0.79 % Refutation found
% 2.72/0.79 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.72/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.72/0.83 % Elapsed time: 0.459198 seconds
% 2.72/0.83 % CPU time: 3.250755 seconds
% 2.72/0.83 % Total memory used: 98.997 MB
% 2.72/0.83 % Net memory used: 97.985 MB
%------------------------------------------------------------------------------