%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE048+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 : n008.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 0.13s 0.87s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 77 ( 45 unt; 0 def)
% Number of atoms : 133 ( 59 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 95 ( 39 ~; 35 |; 15 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 97 ( 93 !; 4 ?)
% 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(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(f14,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [X0] :
( test(X0)
=> star(X0) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [X0] :
( test(X0)
=> star(X0) = one ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f34,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f35,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f39,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f42,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(f43,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f45,plain,
( ! [X0] :
( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ! [X0] :
( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
( ! [X0] :
( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ! [X0] :
( complement(sK0_skl(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X1,sK0_skl(X0))],[f45]) ).
fof(f47,plain,
! [X0] :
( complement(sK0_skl(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
! [X0,X1] :
( ( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f50,plain,
( ! [X0,X1] :
( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ! [X0,X1] :
( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f53,plain,
! [X0,X1] :
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f62,plain,
? [X0] :
( star(X0) != one
& test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f63,plain,
( star(sK1_skl) != one
& test(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X0,sK1_skl)],[f62]) ).
fof(f64,plain,
test(sK1_skl),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
star(sK1_skl) != one,
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f69,plain,
leq(addition(one,star(one)),star(one)),
inference(paramodulation,[status(thm)],[f29,f38]) ).
fof(f73,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f29,f43]) ).
fof(f74,plain,
! [X0,X1] :
( leq(multiplication(X1,star(one)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f28,f43]) ).
fof(f80,plain,
! [X0] :
( leq(multiplication(X0,star(one)),X0)
| ~ leq(X0,X0) ),
inference(paramodulation,[status(thm)],[f26,f74]) ).
fof(f170,plain,
addition(addition(one,star(one)),star(one)) = star(one),
inference(resolution,[status(thm)],[f36,f69]) ).
fof(f171,plain,
! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f36,f39]) ).
fof(f180,plain,
! [X0] :
( leq(multiplication(X0,star(one)),X0)
| addition(X0,X0) != X0 ),
inference(resolution,[status(thm)],[f37,f80]) ).
fof(f181,plain,
! [X0] :
( leq(multiplication(X0,star(one)),X0)
| X0 != X0 ),
inference(forward_demodulation,[status(thm)],[f26,f180]) ).
fof(f182,plain,
! [X0] : leq(multiplication(X0,star(one)),X0),
inference(trivial_equality_resolution,[status(thm)],[f181]) ).
fof(f183,plain,
! [X0] :
( addition(X0,sK0_skl(X0)) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f47,f53]) ).
fof(f196,plain,
leq(star(one),one),
inference(paramodulation,[status(thm)],[f29,f182]) ).
fof(f198,plain,
addition(star(one),one) = one,
inference(resolution,[status(thm)],[f196,f36]) ).
fof(f211,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),X1),
inference(paramodulation,[status(thm)],[f26,f24]) ).
fof(f240,plain,
addition(one,star(one)) = star(one),
inference(backward_demodulation,[status(thm)],[f211,f170]) ).
fof(f330,plain,
addition(one,star(one)) = one,
inference(paramodulation,[status(thm)],[f23,f198]) ).
fof(f341,plain,
! [X0] : leq(multiplication(X0,one),X0),
inference(backward_demodulation,[status(thm)],[f358,f182]) ).
fof(f342,plain,
! [X0,X1] :
( leq(multiplication(X1,one),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(backward_demodulation,[status(thm)],[f358,f74]) ).
fof(f358,plain,
star(one) = one,
inference(forward_demodulation,[status(thm)],[f240,f330]) ).
fof(f374,plain,
! [X0] : leq(X0,X0),
inference(forward_demodulation,[status(thm)],[f28,f341]) ).
fof(f375,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f28,f342]) ).
fof(f418,plain,
addition(sK1_skl,sK0_skl(sK1_skl)) = one,
inference(resolution,[status(thm)],[f183,f64]) ).
fof(f421,plain,
! [X0] : addition(sK1_skl,addition(sK0_skl(sK1_skl),X0)) = addition(one,X0),
inference(paramodulation,[status(thm)],[f418,f24]) ).
fof(f430,plain,
addition(sK1_skl,sK0_skl(sK1_skl)) = addition(one,sK0_skl(sK1_skl)),
inference(paramodulation,[status(thm)],[f26,f421]) ).
fof(f436,plain,
one = addition(one,sK0_skl(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f418,f430]) ).
fof(f437,plain,
one = addition(sK0_skl(sK1_skl),one),
inference(paramodulation,[status(thm)],[f23,f436]) ).
fof(f450,plain,
addition(sK1_skl,one) = addition(one,one),
inference(paramodulation,[status(thm)],[f437,f421]) ).
fof(f455,plain,
addition(sK1_skl,one) = one,
inference(forward_demodulation,[status(thm)],[f26,f450]) ).
fof(f461,plain,
( leq(multiplication(one,star(sK1_skl)),one)
| ~ leq(one,one) ),
inference(paramodulation,[status(thm)],[f455,f73]) ).
fof(f463,plain,
( leq(star(sK1_skl),one)
| ~ leq(one,one) ),
inference(forward_demodulation,[status(thm)],[f29,f461]) ).
fof(f464,plain,
leq(star(sK1_skl),one),
inference(forward_subsumption_resolution,[status(thm)],[f463,f374]) ).
fof(f466,plain,
addition(star(sK1_skl),one) = one,
inference(resolution,[status(thm)],[f464,f36]) ).
fof(f468,plain,
addition(one,star(sK1_skl)) = one,
inference(paramodulation,[status(thm)],[f23,f466]) ).
fof(f803,plain,
! [X0,X1] :
( leq(X1,addition(X0,X1))
| ~ leq(addition(X0,X1),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f211,f375]) ).
fof(f813,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f803,f374]) ).
fof(f1045,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f23,f813]) ).
fof(f1073,plain,
! [X0,X1,X2] : leq(X0,addition(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f24,f1045]) ).
fof(f1893,plain,
! [X0] : leq(one,star(X0)),
inference(paramodulation,[status(thm)],[f171,f1073]) ).
fof(f2039,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(resolution,[status(thm)],[f1893,f36]) ).
fof(f2045,plain,
star(sK1_skl) = one,
inference(backward_demodulation,[status(thm)],[f2039,f468]) ).
fof(f2081,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2045,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 22:41:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.87 % Refutation found
% 0.13/0.87 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.28/0.89 % Elapsed time: 0.513937 seconds
% 0.28/0.89 % CPU time: 3.757230 seconds
% 0.28/0.89 % Total memory used: 140.457 MB
% 0.28/0.89 % Net memory used: 138.049 MB
%------------------------------------------------------------------------------