%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE009+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12:57:44 PM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 19 unt; 2 def)
% Number of atoms : 158 ( 48 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 148 ( 61 ~; 58 |; 20 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 60 !; 2 ?)
% 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(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(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f33,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f35,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f41,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)],[f14]) ).
fof(f42,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)],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f47,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f48,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0] :
( ( ! [X1] :
( ~ complement(X0,X1)
| c(X0) = X1 )
& ! [X1] :
( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f58,plain,
? [X0,X1] :
( ( ~ leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f59,plain,
( ( ~ leq(addition(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) )
& test(sK1_skl)
& test(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(X0,sK1_skl),skolemize(X1,sK2_skl)],[f58]) ).
fof(f60,plain,
test(sK2_skl),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
test(sK1_skl),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
( ~ leq(addition(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f63,definition,
( sQ0_spl
<=> leq(one,addition(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( sQ0_spl
| ~ leq(one,addition(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,definition,
( sQ1_spl
<=> leq(addition(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( sQ1_spl
| ~ leq(addition(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f63,f66]) ).
fof(f70,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f50]) ).
fof(f83,plain,
( sQ0_spl
| ~ leq(one,addition(addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),multiplication(c(sK1_skl),sK2_skl))),multiplication(c(sK1_skl),c(sK2_skl)))) ),
inference(backward_demodulation,[status(thm)],[f22,f65]) ).
fof(f84,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f94,plain,
( sQ0_spl
| ~ leq(one,addition(multiplication(sK1_skl,sK2_skl),addition(addition(multiplication(sK1_skl,c(sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))))) ),
inference(forward_demodulation,[status(thm)],[f22,f83]) ).
fof(f95,plain,
( sQ0_spl
| ~ leq(one,addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),addition(multiplication(c(sK1_skl),sK2_skl),multiplication(c(sK1_skl),c(sK2_skl)))))) ),
inference(forward_demodulation,[status(thm)],[f22,f94]) ).
fof(f233,plain,
! [X0] :
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f70,f45]) ).
fof(f290,plain,
( sQ0_spl
| ~ leq(one,addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl)))))) ),
inference(forward_demodulation,[status(thm)],[f28,f95]) ).
fof(f339,plain,
addition(c(sK1_skl),sK1_skl) = one,
inference(resolution,[status(thm)],[f233,f61]) ).
fof(f340,plain,
addition(c(sK2_skl),sK2_skl) = one,
inference(resolution,[status(thm)],[f233,f60]) ).
fof(f352,plain,
addition(sK2_skl,c(sK2_skl)) = one,
inference(paramodulation,[status(thm)],[f21,f340]) ).
fof(f516,plain,
( sQ0_spl
| ~ leq(one,addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),multiplication(c(sK1_skl),one)))) ),
inference(backward_demodulation,[status(thm)],[f352,f290]) ).
fof(f525,plain,
( sQ0_spl
| ~ leq(one,addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),c(sK1_skl)))) ),
inference(forward_demodulation,[status(thm)],[f26,f516]) ).
fof(f539,plain,
( sQ0_spl
| ~ leq(one,addition(c(sK1_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))))) ),
inference(paramodulation,[status(thm)],[f84,f525]) ).
fof(f542,plain,
( sQ0_spl
| ~ leq(one,addition(c(sK1_skl),multiplication(sK1_skl,addition(sK2_skl,c(sK2_skl))))) ),
inference(forward_demodulation,[status(thm)],[f28,f539]) ).
fof(f543,plain,
( sQ0_spl
| ~ leq(one,addition(c(sK1_skl),multiplication(sK1_skl,one))) ),
inference(forward_demodulation,[status(thm)],[f352,f542]) ).
fof(f544,plain,
( sQ0_spl
| ~ leq(one,addition(c(sK1_skl),sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f26,f543]) ).
fof(f545,plain,
( sQ0_spl
| ~ leq(one,one) ),
inference(forward_demodulation,[status(thm)],[f339,f544]) ).
fof(f547,plain,
( sQ0_spl
| addition(one,one) != one ),
inference(resolution,[status(thm)],[f545,f35]) ).
fof(f548,plain,
( sQ0_spl
| one != one ),
inference(forward_demodulation,[status(thm)],[f24,f547]) ).
fof(f549,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f548]) ).
fof(f550,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f551,plain,
( sQ1_spl
| ~ leq(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))),addition(multiplication(c(sK1_skl),sK2_skl),multiplication(c(sK1_skl),c(sK2_skl)))),one) ),
inference(forward_demodulation,[status(thm)],[f22,f68]) ).
fof(f552,plain,
( sQ1_spl
| ~ leq(addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),addition(multiplication(c(sK1_skl),sK2_skl),multiplication(c(sK1_skl),c(sK2_skl))))),one) ),
inference(forward_demodulation,[status(thm)],[f22,f551]) ).
fof(f553,plain,
( sQ1_spl
| ~ leq(addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl))))),one) ),
inference(forward_demodulation,[status(thm)],[f28,f552]) ).
fof(f554,plain,
( sQ1_spl
| ~ leq(addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),multiplication(c(sK1_skl),one))),one) ),
inference(forward_demodulation,[status(thm)],[f352,f553]) ).
fof(f555,plain,
( sQ1_spl
| ~ leq(addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),c(sK1_skl))),one) ),
inference(forward_demodulation,[status(thm)],[f26,f554]) ).
fof(f574,plain,
( sQ1_spl
| ~ leq(addition(c(sK1_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl)))),one) ),
inference(paramodulation,[status(thm)],[f84,f555]) ).
fof(f580,plain,
( sQ1_spl
| ~ leq(addition(c(sK1_skl),multiplication(sK1_skl,addition(sK2_skl,c(sK2_skl)))),one) ),
inference(forward_demodulation,[status(thm)],[f28,f574]) ).
fof(f581,plain,
( sQ1_spl
| ~ leq(addition(c(sK1_skl),multiplication(sK1_skl,one)),one) ),
inference(forward_demodulation,[status(thm)],[f352,f580]) ).
fof(f582,plain,
( sQ1_spl
| ~ leq(addition(c(sK1_skl),sK1_skl),one) ),
inference(forward_demodulation,[status(thm)],[f26,f581]) ).
fof(f583,plain,
( sQ1_spl
| ~ leq(one,one) ),
inference(forward_demodulation,[status(thm)],[f339,f582]) ).
fof(f738,plain,
( sQ1_spl
| addition(one,one) != one ),
inference(resolution,[status(thm)],[f583,f35]) ).
fof(f739,plain,
( sQ1_spl
| one != one ),
inference(forward_demodulation,[status(thm)],[f24,f738]) ).
fof(f740,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f739]) ).
fof(f741,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f740]) ).
fof(f742,plain,
$false,
inference(sat_refutation,[status(thm)],[f69,f550,f741]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 22:33:12 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.44 % Refutation found
% 0.09/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.46 % Elapsed time: 0.084007 seconds
% 0.09/0.46 % CPU time: 0.385217 seconds
% 0.09/0.46 % Total memory used: 108.716 MB
% 0.09/0.46 % Net memory used: 108.267 MB
%------------------------------------------------------------------------------