%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE038+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 : n011.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 1.45s 0.65s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 64 unt; 0 def)
% Number of atoms : 78 ( 63 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 6 |; 2 &)
% ( 1 <=>; 0 =>; 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 : 118 ( 117 !; 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(f17,conjecture,
! [X0] : leq(X0,star(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] : leq(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(f40,plain,
? [X0] : ~ leq(X0,star(X0)),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
~ leq(sK0_skl,star(sK0_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f40]) ).
fof(f42,plain,
~ leq(sK0_skl,star(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f70,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f76,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f78,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f85,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f76]) ).
fof(f87,plain,
addition(sK0_skl,star(sK0_skl)) != star(sK0_skl),
inference(resolution,[status(thm)],[f33,f42]) ).
fof(f95,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f78]) ).
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(f204,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f70,f78]) ).
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,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f26]) ).
fof(f718,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f733,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f26,f706]) ).
fof(f749,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f718]) ).
fof(f845,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f849,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f845]) ).
fof(f850,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f253,f849]) ).
fof(f869,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f27]) ).
fof(f874,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f881,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f904,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f27,f869]) ).
fof(f907,plain,
! [X0] : addition(one,multiplication(addition(one,X0),star(X0))) = star(X0),
inference(backward_demodulation,[status(thm)],[f874,f850]) ).
fof(f912,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f881]) ).
fof(f1541,plain,
! [X0,X1] : addition(one,addition(X0,multiplication(addition(one,X1),star(X1)))) = addition(X0,star(X1)),
inference(paramodulation,[status(thm)],[f907,f85]) ).
fof(f1545,plain,
! [X0] : addition(multiplication(addition(one,X0),star(X0)),star(X0)) = addition(multiplication(addition(one,X0),star(X0)),one),
inference(paramodulation,[status(thm)],[f907,f95]) ).
fof(f1546,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(addition(one,X0),star(X0))),
inference(paramodulation,[status(thm)],[f907,f78]) ).
fof(f1558,plain,
! [X0] : addition(star(X0),multiplication(addition(one,X0),star(X0))) = addition(multiplication(addition(one,X0),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f19,f1545]) ).
fof(f1559,plain,
! [X0] : multiplication(addition(addition(one,X0),one),star(X0)) = addition(multiplication(addition(one,X0),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f912,f1558]) ).
fof(f1560,plain,
! [X0] : multiplication(addition(one,addition(one,X0)),star(X0)) = addition(multiplication(addition(one,X0),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f904,f1559]) ).
fof(f1561,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(multiplication(addition(one,X0),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f78,f1560]) ).
fof(f1562,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(one,multiplication(addition(one,X0),star(X0))),
inference(forward_demodulation,[status(thm)],[f19,f1561]) ).
fof(f1564,plain,
! [X0,X1] : addition(one,addition(X0,star(X1))) = addition(X0,star(X1)),
inference(backward_demodulation,[status(thm)],[f1569,f1541]) ).
fof(f1569,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f907,f1562]) ).
fof(f1572,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f907,f1546]) ).
fof(f1636,plain,
! [X0] : multiplication(addition(one,X0),addition(star(X0),one)) = addition(addition(one,X0),star(X0)),
inference(paramodulation,[status(thm)],[f1569,f749]) ).
fof(f1658,plain,
! [X0] : multiplication(addition(one,X0),addition(one,star(X0))) = addition(addition(one,X0),star(X0)),
inference(forward_demodulation,[status(thm)],[f733,f1636]) ).
fof(f1659,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(addition(one,X0),star(X0)),
inference(forward_demodulation,[status(thm)],[f1572,f1658]) ).
fof(f1660,plain,
! [X0] : star(X0) = addition(addition(one,X0),star(X0)),
inference(forward_demodulation,[status(thm)],[f1569,f1659]) ).
fof(f1661,plain,
! [X0] : star(X0) = addition(one,addition(X0,star(X0))),
inference(forward_demodulation,[status(thm)],[f20,f1660]) ).
fof(f1662,plain,
star(sK0_skl) != star(sK0_skl),
inference(backward_demodulation,[status(thm)],[f1663,f87]) ).
fof(f1663,plain,
! [X0] : star(X0) = addition(X0,star(X0)),
inference(forward_demodulation,[status(thm)],[f1564,f1661]) ).
fof(f1674,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1662]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE038+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n011.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 22:39:40 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 1.45/0.65 % Refutation found
% 1.45/0.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.45/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.79/0.67 % Elapsed time: 0.300217 seconds
% 0.79/0.67 % CPU time: 2.096040 seconds
% 0.79/0.67 % Total memory used: 94.035 MB
% 0.79/0.67 % Net memory used: 92.837 MB
%------------------------------------------------------------------------------