%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE039+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 : n026.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 16.01s 2.46s
% Output : CNFRefutation 16.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 79 ( 63 unt; 0 def)
% Number of atoms : 99 ( 54 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 15 |; 2 &)
% ( 1 <=>; 2 =>; 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 : 140 ( 139 !; 1 ?)
% 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(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(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(f16,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0] : star(star(X0)) = star(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] : star(star(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(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(f38,plain,
! [A,B,C] :
( leq(multiplication(C,star(B)),A)
| ~ leq(addition(multiplication(A,B),C),A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f39,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
? [X0] : star(star(X0)) != star(X0),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
star(star(sK0_skl)) != star(sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f40]) ).
fof(f42,plain,
star(star(sK0_skl)) != star(sK0_skl),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f47,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f53,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f61,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f33,f22]) ).
fof(f129,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f53,f33]) ).
fof(f136,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f53]) ).
fof(f206,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f129]) ).
fof(f211,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f20,f206]) ).
fof(f225,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f230,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f274,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f308,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f312,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f308]) ).
fof(f319,plain,
! [X0,X1,X2] : leq(X0,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f19,f211]) ).
fof(f331,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f20,f319]) ).
fof(f561,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f27,f37]) ).
fof(f584,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f22,f39]) ).
fof(f593,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f584]) ).
fof(f1794,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f225,f331]) ).
fof(f4940,plain,
! [X0] : addition(one,multiplication(addition(X0,one),star(X0))) = star(X0),
inference(paramodulation,[status(thm)],[f274,f312]) ).
fof(f5004,plain,
! [X0] : addition(one,star(X0)) = addition(one,addition(multiplication(X0,star(X0)),star(X0))),
inference(paramodulation,[status(thm)],[f312,f53]) ).
fof(f5056,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f312,f5004]) ).
fof(f5214,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(star(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f5056,f47]) ).
fof(f5224,plain,
! [X0] : addition(star(X0),star(X0)) = addition(star(X0),one),
inference(paramodulation,[status(thm)],[f5056,f136]) ).
fof(f5259,plain,
! [X0] : star(X0) = addition(star(X0),one),
inference(forward_demodulation,[status(thm)],[f22,f5224]) ).
fof(f6237,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,star(X2)))),
inference(paramodulation,[status(thm)],[f5056,f1794]) ).
fof(f6261,plain,
! [X0,X1,X2] : leq(X0,multiplication(addition(X1,X0),star(X2))),
inference(paramodulation,[status(thm)],[f27,f6237]) ).
fof(f6284,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(X1,X0),star(X2))) = multiplication(addition(X1,X0),star(X2)),
inference(resolution,[status(thm)],[f6261,f32]) ).
fof(f6317,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = star(X0),
inference(backward_demodulation,[status(thm)],[f6284,f4940]) ).
fof(f6418,plain,
! [X0] : multiplication(star(X0),star(star(X0))) = star(star(X0)),
inference(paramodulation,[status(thm)],[f5259,f6317]) ).
fof(f6431,plain,
! [X0] :
( leq(multiplication(star(X0),multiplication(one,star(X0))),star(X0))
| ~ leq(star(X0),star(X0)) ),
inference(paramodulation,[status(thm)],[f6317,f561]) ).
fof(f6455,plain,
! [X0] : multiplication(addition(X0,one),addition(star(X0),one)) = addition(star(X0),addition(X0,one)),
inference(paramodulation,[status(thm)],[f6317,f230]) ).
fof(f6474,plain,
! [X0] :
( leq(multiplication(star(X0),star(X0)),star(X0))
| ~ leq(star(X0),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f25,f6431]) ).
fof(f6475,plain,
! [X0] : leq(multiplication(star(X0),star(X0)),star(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f6474,f61]) ).
fof(f6497,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = addition(star(X0),addition(X0,one)),
inference(forward_demodulation,[status(thm)],[f5259,f6455]) ).
fof(f6498,plain,
! [X0] : star(X0) = addition(star(X0),addition(X0,one)),
inference(forward_demodulation,[status(thm)],[f6317,f6497]) ).
fof(f6499,plain,
! [X0] : star(X0) = addition(X0,star(X0)),
inference(forward_demodulation,[status(thm)],[f5214,f6498]) ).
fof(f6592,plain,
! [X0] : addition(star(X0),star(X0)) = addition(star(X0),X0),
inference(paramodulation,[status(thm)],[f6499,f136]) ).
fof(f6640,plain,
! [X0] : star(X0) = addition(star(X0),X0),
inference(forward_demodulation,[status(thm)],[f22,f6592]) ).
fof(f9986,plain,
! [X0] : leq(multiplication(star(X0),multiplication(star(X0),star(star(X0)))),star(X0)),
inference(resolution,[status(thm)],[f6475,f593]) ).
fof(f9995,plain,
! [X0] : leq(multiplication(star(X0),star(star(X0))),star(X0)),
inference(forward_demodulation,[status(thm)],[f6418,f9986]) ).
fof(f9996,plain,
! [X0] : leq(star(star(X0)),star(X0)),
inference(forward_demodulation,[status(thm)],[f6418,f9995]) ).
fof(f10018,plain,
! [X0] : addition(star(star(X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f9996,f32]) ).
fof(f10026,plain,
star(sK0_skl) != star(sK0_skl),
inference(backward_demodulation,[status(thm)],[f10109,f42]) ).
fof(f10109,plain,
! [X0] : star(star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f6640,f10018]) ).
fof(f10119,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f10026]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE039+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 22:43:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 16.01/2.46 % Refutation found
% 16.01/2.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 16.01/2.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.25/2.50 % Elapsed time: 2.114701 seconds
% 2.25/2.50 % CPU time: 16.474304 seconds
% 2.25/2.50 % Total memory used: 178.118 MB
% 2.25/2.50 % Net memory used: 174.779 MB
%------------------------------------------------------------------------------