%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE167+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:58:06 PM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 27 unt; 0 def)
% Number of atoms : 86 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 37 ~; 23 |; 7 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 70 ( 64 !; 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(f3,axiom,
! [A] : addition(A,zero) = A,
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(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(f12,axiom,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C] :
( leq(addition(multiplication(C,A),B),C)
=> leq(multiplication(B,star(A)),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1] :
( leq(X0,multiplication(X0,star(X1)))
& ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,star(X1)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,multiplication(X0,star(X1)))
& ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,star(X1)),X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [X0] : addition(one,multiplication(star(X0),X0)) = star(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f35,plain,
! [A,B,C] :
( leq(multiplication(B,star(A)),C)
| ~ leq(addition(multiplication(C,A),B),C) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f36,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f41,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f42,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f44,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
? [X0,X1] :
( ~ leq(X0,multiplication(X0,star(X1)))
| ( ~ leq(multiplication(X0,star(X1)),X0)
& multiplication(X0,X1) = zero ) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
( ? [X0,X1] : ~ leq(X0,multiplication(X0,star(X1)))
| ? [X0,X1] :
( ~ leq(multiplication(X0,star(X1)),X0)
& multiplication(X0,X1) = zero ) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( ~ leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))
| ( ~ leq(multiplication(sK0_skl,star(sK1_skl)),sK0_skl)
& multiplication(sK0_skl,sK1_skl) = zero ) ),
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)],[f46]) ).
fof(f48,plain,
( ~ leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))
| multiplication(sK0_skl,sK1_skl) = zero ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
( ~ leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))
| ~ leq(multiplication(sK0_skl,star(sK1_skl)),sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
( multiplication(sK0_skl,sK1_skl) = zero
| addition(sK2_skl,multiplication(sK2_skl,star(sK3_skl))) != multiplication(sK2_skl,star(sK3_skl)) ),
inference(resolution,[status(thm)],[f44,f48]) ).
fof(f60,plain,
! [X0,X1,X2] :
( addition(addition(multiplication(X2,X1),X0),X2) != X2
| leq(multiplication(X0,star(X1)),X2) ),
inference(resolution,[status(thm)],[f36,f44]) ).
fof(f64,plain,
! [X0,X1,X2] :
( addition(multiplication(X2,X1),addition(X0,X2)) != X2
| leq(multiplication(X0,star(X1)),X2) ),
inference(forward_demodulation,[status(thm)],[f22,f60]) ).
fof(f91,plain,
( ~ leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))
| addition(multiplication(sK0_skl,sK1_skl),addition(sK0_skl,sK0_skl)) != sK0_skl ),
inference(resolution,[status(thm)],[f64,f49]) ).
fof(f96,plain,
( ~ leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))
| addition(multiplication(sK0_skl,sK1_skl),sK0_skl) != sK0_skl ),
inference(forward_demodulation,[status(thm)],[f24,f91]) ).
fof(f124,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f242,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f257,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f261,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f276,plain,
( multiplication(sK0_skl,sK1_skl) = zero
| multiplication(sK2_skl,addition(one,star(sK3_skl))) != multiplication(sK2_skl,star(sK3_skl)) ),
inference(backward_demodulation,[status(thm)],[f257,f51]) ).
fof(f286,plain,
( ~ leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))
| multiplication(sK0_skl,addition(sK1_skl,one)) != sK0_skl ),
inference(backward_demodulation,[status(thm)],[f261,f96]) ).
fof(f321,plain,
( addition(sK2_skl,multiplication(sK2_skl,star(sK3_skl))) != multiplication(sK2_skl,star(sK3_skl))
| multiplication(sK0_skl,addition(sK1_skl,one)) != sK0_skl ),
inference(resolution,[status(thm)],[f286,f44]) ).
fof(f322,plain,
( multiplication(sK2_skl,addition(one,star(sK3_skl))) != multiplication(sK2_skl,star(sK3_skl))
| multiplication(sK0_skl,addition(sK1_skl,one)) != sK0_skl ),
inference(forward_demodulation,[status(thm)],[f257,f321]) ).
fof(f485,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(star(X0),X0)),
inference(paramodulation,[status(thm)],[f32,f242]) ).
fof(f512,plain,
( multiplication(sK2_skl,star(sK3_skl)) != multiplication(sK2_skl,star(sK3_skl))
| multiplication(sK0_skl,addition(sK1_skl,one)) != sK0_skl ),
inference(backward_demodulation,[status(thm)],[f519,f322]) ).
fof(f513,plain,
( multiplication(sK0_skl,sK1_skl) = zero
| multiplication(sK2_skl,star(sK3_skl)) != multiplication(sK2_skl,star(sK3_skl)) ),
inference(backward_demodulation,[status(thm)],[f519,f276]) ).
fof(f519,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f32,f485]) ).
fof(f532,plain,
multiplication(sK0_skl,addition(sK1_skl,one)) != sK0_skl,
inference(trivial_equality_resolution,[status(thm)],[f512]) ).
fof(f534,plain,
multiplication(sK0_skl,sK1_skl) = zero,
inference(trivial_equality_resolution,[status(thm)],[f513]) ).
fof(f550,plain,
! [X0] : multiplication(sK0_skl,addition(sK1_skl,X0)) = addition(zero,multiplication(sK0_skl,X0)),
inference(paramodulation,[status(thm)],[f534,f28]) ).
fof(f558,plain,
multiplication(sK0_skl,one) != sK0_skl,
inference(backward_demodulation,[status(thm)],[f559,f532]) ).
fof(f559,plain,
! [X0] : multiplication(sK0_skl,addition(sK1_skl,X0)) = multiplication(sK0_skl,X0),
inference(forward_demodulation,[status(thm)],[f124,f550]) ).
fof(f564,plain,
sK0_skl != sK0_skl,
inference(forward_demodulation,[status(thm)],[f26,f558]) ).
fof(f565,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f564]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE167+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 22:53:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.42 % Refutation found
% 0.11/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.46 % Elapsed time: 0.076249 seconds
% 0.11/0.46 % CPU time: 0.255765 seconds
% 0.11/0.46 % Total memory used: 69.085 MB
% 0.11/0.46 % Net memory used: 68.699 MB
%------------------------------------------------------------------------------