%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE039+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 : n005.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 5.41s 1.25s
% Output : CNFRefutation 5.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 103 ( 85 unt; 0 def)
% Number of atoms : 125 ( 81 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 31 ~; 16 |; 4 &)
% ( 1 <=>; 1 =>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 169 ( 166 !; 3 ?)
% 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(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(f14,axiom,
! [A] : leq(addition(one,multiplication(star(A),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] :
( leq(star(X0),star(star(X0)))
& leq(star(star(X0)),star(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] :
( leq(star(X0),star(star(X0)))
& leq(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(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(f35,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
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),star(star(X0)))
| ~ leq(star(star(X0)),star(X0)) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
( ? [X0] : ~ leq(star(X0),star(star(X0)))
| ? [X0] : ~ leq(star(star(X0)),star(X0)) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
( ~ leq(star(sK1_skl),star(star(sK1_skl)))
| ~ leq(star(star(sK0_skl)),star(sK0_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X0,sK1_skl)],[f41]) ).
fof(f43,plain,
( ~ leq(star(sK1_skl),star(star(sK1_skl)))
| ~ leq(star(star(sK0_skl)),star(sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f72,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f78,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f80,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f87,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f78]) ).
fof(f95,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f80]) ).
fof(f126,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f95,f20]) ).
fof(f142,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f20,f126]) ).
fof(f144,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f142]) ).
fof(f174,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f95,f72]) ).
fof(f204,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f72,f80]) ).
fof(f230,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f20,f174]) ).
fof(f231,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f95,f230]) ).
fof(f253,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f144,f204]) ).
fof(f706,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f710,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f706]) ).
fof(f711,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f253,f710]) ).
fof(f714,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f26]) ).
fof(f726,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f741,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f26,f714]) ).
fof(f757,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f726]) ).
fof(f888,plain,
! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f35,f32]) ).
fof(f893,plain,
! [X0] : addition(one,addition(multiplication(star(X0),X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f888]) ).
fof(f894,plain,
! [X0] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f253,f893]) ).
fof(f895,plain,
! [X0] : addition(one,multiplication(star(X0),addition(X0,one))) = star(X0),
inference(forward_demodulation,[status(thm)],[f757,f894]) ).
fof(f899,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f27]) ).
fof(f904,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f911,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f934,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f27,f899]) ).
fof(f937,plain,
! [X0] : addition(one,multiplication(addition(one,X0),star(X0))) = star(X0),
inference(backward_demodulation,[status(thm)],[f904,f711]) ).
fof(f942,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f911]) ).
fof(f1540,plain,
! [X0,X1] :
( leq(star(X0),X1)
| ~ leq(addition(multiplication(X0,X1),one),X1) ),
inference(paramodulation,[status(thm)],[f24,f37]) ).
fof(f1542,plain,
! [X0,X1] :
( leq(star(X0),X1)
| ~ leq(addition(one,multiplication(X0,X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f19,f1540]) ).
fof(f1999,plain,
! [X0,X1] : addition(one,addition(X0,star(X1))) = addition(one,addition(X0,multiplication(star(X1),addition(X1,one)))),
inference(paramodulation,[status(thm)],[f895,f144]) ).
fof(f2003,plain,
! [X0,X1] : addition(one,addition(X0,multiplication(star(X1),addition(X1,one)))) = addition(X0,star(X1)),
inference(paramodulation,[status(thm)],[f895,f87]) ).
fof(f2007,plain,
! [X0] : addition(multiplication(star(X0),addition(X0,one)),star(X0)) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(paramodulation,[status(thm)],[f895,f95]) ).
fof(f2008,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(star(X0),addition(X0,one))),
inference(paramodulation,[status(thm)],[f895,f80]) ).
fof(f2028,plain,
! [X0,X1] : addition(one,addition(X0,star(X1))) = addition(X0,star(X1)),
inference(forward_demodulation,[status(thm)],[f1999,f2003]) ).
fof(f2032,plain,
! [X0] : addition(star(X0),multiplication(star(X0),addition(X0,one))) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f19,f2007]) ).
fof(f2033,plain,
! [X0] : multiplication(star(X0),addition(addition(X0,one),one)) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f757,f2032]) ).
fof(f2034,plain,
! [X0] : multiplication(star(X0),addition(one,addition(X0,one))) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f741,f2033]) ).
fof(f2035,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f95,f2034]) ).
fof(f2036,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = addition(one,multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f19,f2035]) ).
fof(f2038,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f895,f2036]) ).
fof(f2041,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f895,f2008]) ).
fof(f2048,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(star(X0),X1)),
inference(paramodulation,[status(thm)],[f2041,f904]) ).
fof(f2052,plain,
! [X0,X1] : addition(star(X0),addition(one,X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f2041,f231]) ).
fof(f2071,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(X1,star(X0)),
inference(forward_demodulation,[status(thm)],[f87,f2052]) ).
fof(f2123,plain,
! [X0] : multiplication(addition(star(X0),one),addition(one,X0)) = addition(addition(one,X0),star(X0)),
inference(paramodulation,[status(thm)],[f2038,f942]) ).
fof(f2137,plain,
! [X0] : multiplication(addition(one,star(X0)),addition(one,X0)) = addition(addition(one,X0),star(X0)),
inference(forward_demodulation,[status(thm)],[f934,f2123]) ).
fof(f2138,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = addition(addition(one,X0),star(X0)),
inference(forward_demodulation,[status(thm)],[f2041,f2137]) ).
fof(f2139,plain,
! [X0] : star(X0) = addition(addition(one,X0),star(X0)),
inference(forward_demodulation,[status(thm)],[f2038,f2138]) ).
fof(f2140,plain,
! [X0] : star(X0) = addition(one,addition(X0,star(X0))),
inference(forward_demodulation,[status(thm)],[f20,f2139]) ).
fof(f2141,plain,
! [X0] : star(X0) = addition(X0,star(X0)),
inference(forward_demodulation,[status(thm)],[f2028,f2140]) ).
fof(f2437,plain,
( addition(star(sK1_skl),star(star(sK1_skl))) != star(star(sK1_skl))
| ~ leq(star(star(sK0_skl)),star(sK0_skl)) ),
inference(resolution,[status(thm)],[f43,f33]) ).
fof(f2438,plain,
( star(star(sK1_skl)) != star(star(sK1_skl))
| ~ leq(star(star(sK0_skl)),star(sK0_skl)) ),
inference(forward_demodulation,[status(thm)],[f2141,f2437]) ).
fof(f2439,plain,
~ leq(star(star(sK0_skl)),star(sK0_skl)),
inference(trivial_equality_resolution,[status(thm)],[f2438]) ).
fof(f2982,plain,
! [X0,X1] : addition(one,multiplication(star(X0),star(X1))) = addition(multiplication(star(X0),star(X1)),star(X1)),
inference(paramodulation,[status(thm)],[f2048,f2071]) ).
fof(f2985,plain,
! [X0,X1] : addition(one,multiplication(addition(one,X0),star(X1))) = addition(multiplication(X0,star(X1)),star(X1)),
inference(paramodulation,[status(thm)],[f904,f2071]) ).
fof(f3044,plain,
! [X0,X1] : addition(one,multiplication(star(X0),star(X1))) = addition(star(X1),multiplication(star(X0),star(X1))),
inference(forward_demodulation,[status(thm)],[f19,f2982]) ).
fof(f3045,plain,
! [X0,X1] : addition(one,multiplication(star(X0),star(X1))) = multiplication(star(X0),star(X1)),
inference(forward_demodulation,[status(thm)],[f2048,f3044]) ).
fof(f3050,plain,
! [X0,X1] : addition(one,multiplication(addition(one,X0),star(X1))) = addition(star(X1),multiplication(X0,star(X1))),
inference(forward_demodulation,[status(thm)],[f19,f2985]) ).
fof(f3051,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = star(X0),
inference(backward_demodulation,[status(thm)],[f3052,f937]) ).
fof(f3052,plain,
! [X0,X1] : addition(one,multiplication(addition(one,X0),star(X1))) = multiplication(addition(X0,one),star(X1)),
inference(forward_demodulation,[status(thm)],[f942,f3050]) ).
fof(f3688,plain,
~ leq(addition(one,multiplication(star(sK0_skl),star(sK0_skl))),star(sK0_skl)),
inference(resolution,[status(thm)],[f1542,f2439]) ).
fof(f3690,plain,
~ leq(multiplication(star(sK0_skl),star(sK0_skl)),star(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f3045,f3688]) ).
fof(f3691,plain,
~ leq(addition(multiplication(sK0_skl,star(sK0_skl)),star(sK0_skl)),star(sK0_skl)),
inference(resolution,[status(thm)],[f3690,f37]) ).
fof(f3694,plain,
~ leq(addition(star(sK0_skl),multiplication(sK0_skl,star(sK0_skl))),star(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f19,f3691]) ).
fof(f3695,plain,
~ leq(multiplication(addition(sK0_skl,one),star(sK0_skl)),star(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f942,f3694]) ).
fof(f3696,plain,
~ leq(star(sK0_skl),star(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f3051,f3695]) ).
fof(f3702,plain,
~ leq(addition(one,multiplication(sK0_skl,star(sK0_skl))),star(sK0_skl)),
inference(resolution,[status(thm)],[f3696,f1542]) ).
fof(f3704,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3702,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE039+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 22:40:19 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 5.41/1.25 % Refutation found
% 5.41/1.25 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.41/1.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.41/1.28 % Elapsed time: 0.896048 seconds
% 5.41/1.28 % CPU time: 6.747935 seconds
% 5.41/1.28 % Total memory used: 138.240 MB
% 5.41/1.28 % Net memory used: 135.690 MB
%------------------------------------------------------------------------------