%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE021+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:57:46 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 14 unt; 2 def)
% Number of atoms : 126 ( 48 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 122 ( 50 ~; 46 |; 17 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 51 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
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(f14,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(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1] :
( test(X1)
=> ( leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0)
& leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> ( leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0)
& leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),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(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
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(f33,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f39,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(f40,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)],[f39]) ).
fof(f43,plain,
! [X0,X1] :
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f46,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0] :
( ( ! [X1] :
( ~ complement(X0,X1)
| c(X0) = X1 )
& ! [X1] :
( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,plain,
? [X0,X1] :
( ( ~ leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0)
| ~ leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) )
& test(X1) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
? [X1] :
( ( ? [X0] : ~ leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0)
| ? [X0] : ~ leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) )
& test(X1) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f54,plain,
( ( ~ leq(addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK3_skl)),sK3_skl)
| ~ leq(sK2_skl,addition(multiplication(sK1_skl,sK2_skl),multiplication(c(sK1_skl),sK2_skl))) )
& test(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(X1,sK1_skl),skolemize(X0,sK2_skl),skolemize(X0,sK3_skl)],[f53]) ).
fof(f55,plain,
test(sK1_skl),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
( ~ leq(addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK3_skl)),sK3_skl)
| ~ leq(sK2_skl,addition(multiplication(sK1_skl,sK2_skl),multiplication(c(sK1_skl),sK2_skl))) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f57,definition,
( sQ0_spl
<=> leq(sK2_skl,addition(multiplication(sK1_skl,sK2_skl),multiplication(c(sK1_skl),sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( sQ0_spl
| ~ leq(sK2_skl,addition(multiplication(sK1_skl,sK2_skl),multiplication(c(sK1_skl),sK2_skl))) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,definition,
( sQ1_spl
<=> leq(addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK3_skl)),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( sQ1_spl
| ~ leq(addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK3_skl)),sK3_skl) ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f56,f57,f60]) ).
fof(f64,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f225,plain,
( sQ0_spl
| ~ leq(sK2_skl,multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl)) ),
inference(backward_demodulation,[status(thm)],[f27,f59]) ).
fof(f266,plain,
! [X0] :
( ~ test(X0)
| addition(c(X0),X0) = one ),
inference(resolution,[status(thm)],[f43,f64]) ).
fof(f271,plain,
( sQ0_spl
| addition(sK2_skl,multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl)) != multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f225,f33]) ).
fof(f409,plain,
addition(c(sK1_skl),sK1_skl) = one,
inference(resolution,[status(thm)],[f266,f55]) ).
fof(f412,plain,
addition(sK1_skl,c(sK1_skl)) = one,
inference(paramodulation,[status(thm)],[f19,f409]) ).
fof(f422,plain,
( sQ0_spl
| addition(sK2_skl,multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl)) != multiplication(one,sK2_skl) ),
inference(backward_demodulation,[status(thm)],[f412,f271]) ).
fof(f429,plain,
( sQ0_spl
| addition(sK2_skl,multiplication(one,sK2_skl)) != multiplication(one,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f412,f422]) ).
fof(f430,plain,
( sQ0_spl
| addition(sK2_skl,sK2_skl) != multiplication(one,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f25,f429]) ).
fof(f431,plain,
( sQ0_spl
| sK2_skl != multiplication(one,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f22,f430]) ).
fof(f432,plain,
( sQ0_spl
| sK2_skl != sK2_skl ),
inference(forward_demodulation,[status(thm)],[f25,f431]) ).
fof(f433,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f432]) ).
fof(f434,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f433]) ).
fof(f437,plain,
( sQ1_spl
| ~ leq(multiplication(addition(sK1_skl,c(sK1_skl)),sK3_skl),sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f27,f62]) ).
fof(f438,plain,
( sQ1_spl
| ~ leq(multiplication(one,sK3_skl),sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f412,f437]) ).
fof(f439,plain,
( sQ1_spl
| ~ leq(sK3_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f25,f438]) ).
fof(f443,plain,
( sQ1_spl
| addition(sK3_skl,sK3_skl) != sK3_skl ),
inference(resolution,[status(thm)],[f439,f33]) ).
fof(f444,plain,
( sQ1_spl
| sK3_skl != sK3_skl ),
inference(forward_demodulation,[status(thm)],[f22,f443]) ).
fof(f445,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f444]) ).
fof(f446,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f445]) ).
fof(f447,plain,
$false,
inference(sat_refutation,[status(thm)],[f63,f434,f446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE021+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.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 22:42:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.052350 seconds
% 0.13/0.41 % CPU time: 0.174934 seconds
% 0.13/0.41 % Total memory used: 93.637 MB
% 0.13/0.41 % Net memory used: 93.330 MB
%------------------------------------------------------------------------------