%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE044+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 : n006.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 12:57:51 PM UTC 2026
% Result : Theorem 16.71s 2.55s
% Output : CNFRefutation 16.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of formulae : 100 ( 59 unt; 0 def)
% Number of atoms : 145 ( 99 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 90 ( 45 ~; 40 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 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 : 172 ( 171 !; 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(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(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(addition(one,X0)) = star(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] : star(addition(one,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(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(addition(one,X0)) != star(X0),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
star(addition(one,sK0_skl)) != star(sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f40]) ).
fof(f42,plain,
star(addition(one,sK0_skl)) != star(sK0_skl),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f49,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,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f55,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f61,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f53]) ).
fof(f66,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f55]) ).
fof(f91,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f66,f20]) ).
fof(f104,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f20,f91]) ).
fof(f106,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f104]) ).
fof(f118,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f66,f49]) ).
fof(f143,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f49,f55]) ).
fof(f166,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f20,f118]) ).
fof(f167,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f66,f166]) ).
fof(f186,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f106,f143]) ).
fof(f605,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f736,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f926,plain,
! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f32,f35]) ).
fof(f928,plain,
! [X0] : addition(one,addition(multiplication(star(X0),X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f926]) ).
fof(f929,plain,
! [X0] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f186,f928]) ).
fof(f930,plain,
! [X0] : addition(one,multiplication(star(X0),addition(one,X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f605,f929]) ).
fof(f1395,plain,
! [X0,X1] : addition(multiplication(star(X0),addition(one,X0)),addition(one,X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f930,f167]) ).
fof(f1401,plain,
! [X0] : addition(multiplication(star(X0),addition(one,X0)),star(X0)) = addition(multiplication(star(X0),addition(one,X0)),one),
inference(paramodulation,[status(thm)],[f930,f66]) ).
fof(f1402,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(star(X0),addition(one,X0))),
inference(paramodulation,[status(thm)],[f930,f55]) ).
fof(f1422,plain,
! [X0,X1] : addition(one,addition(multiplication(star(X0),addition(one,X0)),X1)) = addition(X1,star(X0)),
inference(forward_demodulation,[status(thm)],[f61,f1395]) ).
fof(f1430,plain,
! [X0] : addition(star(X0),multiplication(star(X0),addition(one,X0))) = addition(multiplication(star(X0),addition(one,X0)),one),
inference(forward_demodulation,[status(thm)],[f19,f1401]) ).
fof(f1431,plain,
! [X0] : multiplication(star(X0),addition(one,addition(one,X0))) = addition(multiplication(star(X0),addition(one,X0)),one),
inference(forward_demodulation,[status(thm)],[f605,f1430]) ).
fof(f1432,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = addition(multiplication(star(X0),addition(one,X0)),one),
inference(forward_demodulation,[status(thm)],[f55,f1431]) ).
fof(f1433,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = addition(one,multiplication(star(X0),addition(one,X0))),
inference(forward_demodulation,[status(thm)],[f19,f1432]) ).
fof(f1435,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(X1,star(X0)),
inference(backward_demodulation,[status(thm)],[f1437,f1422]) ).
fof(f1437,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f930,f1433]) ).
fof(f1440,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f930,f1402]) ).
fof(f1644,plain,
! [X0,X1] :
( leq(star(X0),X1)
| ~ leq(addition(multiplication(X0,X1),one),X1) ),
inference(paramodulation,[status(thm)],[f24,f37]) ).
fof(f1647,plain,
! [X0,X1] :
( leq(star(X0),X1)
| ~ leq(addition(one,multiplication(X0,X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f19,f1644]) ).
fof(f1651,plain,
! [X0,X1] :
( leq(star(X1),X0)
| ~ leq(addition(multiplication(X0,X1),one),X0) ),
inference(paramodulation,[status(thm)],[f25,f39]) ).
fof(f1653,plain,
! [X0,X1] :
( leq(star(X1),X0)
| ~ leq(addition(one,multiplication(X0,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f19,f1651]) ).
fof(f2457,plain,
! [X0,X1] :
( addition(star(X0),X1) = X1
| ~ leq(addition(one,multiplication(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f1647,f32]) ).
fof(f2458,plain,
! [X0,X1] :
( addition(star(X1),X0) = X0
| ~ leq(addition(one,multiplication(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f1653,f32]) ).
fof(f2462,plain,
! [X0] :
( addition(star(one),X0) = X0
| ~ leq(multiplication(one,addition(one,X0)),X0) ),
inference(paramodulation,[status(thm)],[f605,f2457]) ).
fof(f2481,plain,
! [X0] :
( addition(star(one),X0) = X0
| ~ leq(addition(one,X0),X0) ),
inference(forward_demodulation,[status(thm)],[f25,f2462]) ).
fof(f2496,plain,
! [X0] :
( addition(addition(one,X0),X0) != X0
| addition(star(one),X0) = X0 ),
inference(resolution,[status(thm)],[f2481,f33]) ).
fof(f2520,plain,
! [X0] :
( addition(one,addition(X0,X0)) != X0
| addition(star(one),X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f20,f2496]) ).
fof(f2521,plain,
! [X0] :
( addition(one,X0) != X0
| addition(star(one),X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f22,f2520]) ).
fof(f2561,plain,
! [X0] :
( addition(one,X0) != X0
| addition(X0,star(one)) = X0 ),
inference(paramodulation,[status(thm)],[f19,f2521]) ).
fof(f2567,plain,
( addition(one,one) != one
| star(one) = one ),
inference(paramodulation,[status(thm)],[f1440,f2561]) ).
fof(f2575,plain,
( one != one
| star(one) = one ),
inference(forward_demodulation,[status(thm)],[f22,f2567]) ).
fof(f2604,plain,
star(one) = one,
inference(trivial_equality_resolution,[status(thm)],[f2575]) ).
fof(f2633,plain,
! [X0,X1] :
( leq(multiplication(X1,one),X0)
| ~ leq(addition(multiplication(X0,one),X1),X0) ),
inference(paramodulation,[status(thm)],[f2604,f39]) ).
fof(f2656,plain,
! [X0,X1] :
( leq(multiplication(X1,one),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f2633]) ).
fof(f2657,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f2656]) ).
fof(f2681,plain,
! [X0,X1] :
( addition(star(X1),X0) = X0
| ~ leq(addition(X0,addition(one,multiplication(X1,X0))),X0) ),
inference(resolution,[status(thm)],[f2657,f2457]) ).
fof(f3387,plain,
! [X0,X1] :
( ~ leq(addition(X1,addition(one,multiplication(X1,X0))),X1)
| addition(star(X0),X1) = X1 ),
inference(resolution,[status(thm)],[f2458,f2657]) ).
fof(f5486,plain,
! [X0,X1] :
( addition(star(X1),X0) = X0
| ~ leq(addition(one,addition(X0,multiplication(X1,X0))),X0) ),
inference(paramodulation,[status(thm)],[f61,f2681]) ).
fof(f5515,plain,
! [X0,X1] :
( addition(star(X0),X1) = X1
| ~ leq(addition(one,multiplication(addition(one,X0),X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f736,f5486]) ).
fof(f5699,plain,
! [X0,X1] :
( addition(addition(X1,addition(one,multiplication(X1,X0))),X1) != X1
| addition(star(X0),X1) = X1 ),
inference(resolution,[status(thm)],[f3387,f33]) ).
fof(f5725,plain,
! [X0,X1] :
( addition(X1,addition(addition(one,multiplication(X1,X0)),X1)) != X1
| addition(star(X0),X1) = X1 ),
inference(forward_demodulation,[status(thm)],[f20,f5699]) ).
fof(f5726,plain,
! [X0,X1] :
( addition(X1,addition(X1,addition(one,multiplication(X1,X0)))) != X1
| addition(star(X0),X1) = X1 ),
inference(forward_demodulation,[status(thm)],[f186,f5725]) ).
fof(f5727,plain,
! [X0,X1] :
( addition(X1,addition(one,multiplication(X1,X0))) != X1
| addition(star(X0),X1) = X1 ),
inference(forward_demodulation,[status(thm)],[f55,f5726]) ).
fof(f5800,plain,
! [X0] :
( addition(star(X0),addition(one,star(X0))) != star(X0)
| addition(star(addition(one,X0)),star(X0)) = star(X0) ),
inference(paramodulation,[status(thm)],[f1437,f5727]) ).
fof(f5852,plain,
! [X0] :
( addition(star(X0),addition(one,star(X0))) != star(X0)
| addition(star(X0),star(addition(one,X0))) = star(X0) ),
inference(forward_demodulation,[status(thm)],[f19,f5800]) ).
fof(f5853,plain,
! [X0] :
( addition(one,addition(star(X0),star(X0))) != star(X0)
| addition(star(X0),star(addition(one,X0))) = star(X0) ),
inference(forward_demodulation,[status(thm)],[f61,f5852]) ).
fof(f5854,plain,
! [X0] :
( addition(star(X0),star(X0)) != star(X0)
| addition(star(X0),star(addition(one,X0))) = star(X0) ),
inference(forward_demodulation,[status(thm)],[f1435,f5853]) ).
fof(f5855,plain,
! [X0] :
( star(X0) != star(X0)
| addition(star(X0),star(addition(one,X0))) = star(X0) ),
inference(forward_demodulation,[status(thm)],[f22,f5854]) ).
fof(f5857,plain,
! [X0] : addition(star(X0),star(addition(one,X0))) = star(X0),
inference(trivial_equality_resolution,[status(thm)],[f5855]) ).
fof(f5872,plain,
! [X0] : addition(star(X0),star(addition(one,X0))) = star(addition(one,X0)),
inference(resolution,[status(thm)],[f5515,f34]) ).
fof(f5913,plain,
star(sK0_skl) != star(sK0_skl),
inference(backward_demodulation,[status(thm)],[f5924,f42]) ).
fof(f5924,plain,
! [X0] : star(X0) = star(addition(one,X0)),
inference(forward_demodulation,[status(thm)],[f5857,f5872]) ).
fof(f5983,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f5913]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE044+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 22:40:27 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 16.71/2.55 % Refutation found
% 16.71/2.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 16.71/2.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 16.71/2.60 % Elapsed time: 2.225782 seconds
% 16.71/2.60 % CPU time: 17.301388 seconds
% 16.71/2.60 % Total memory used: 146.845 MB
% 16.71/2.60 % Net memory used: 144.698 MB
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