%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE009+3 : 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 12:57:44 PM UTC 2026
% Result : Theorem 0.08s 0.42s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 76 ( 24 unt; 2 def)
% Number of atoms : 163 ( 53 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 : 70 ( 68 !; 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(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(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(f17,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(f18,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)],[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(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(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)],[f18]) ).
fof(f53,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)],[f52]) ).
fof(f54,plain,
test(sK2_skl),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
test(sK1_skl),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,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)],[f53]) ).
fof(f57,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(f59,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)],[f57]) ).
fof(f60,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(f62,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)],[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(f69,plain,
( sQ0_spl
| ~ leq(one,addition(addition(multiplication(c(sK1_skl),sK2_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl)))),multiplication(c(sK1_skl),c(sK2_skl)))) ),
inference(paramodulation,[status(thm)],[f19,f59]) ).
fof(f77,plain,
! [X0] :
( ~ test(X0)
| addition(c(X0),X0) = one ),
inference(resolution,[status(thm)],[f43,f64]) ).
fof(f79,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f140,plain,
addition(c(sK1_skl),sK1_skl) = one,
inference(resolution,[status(thm)],[f77,f55]) ).
fof(f141,plain,
addition(c(sK2_skl),sK2_skl) = one,
inference(resolution,[status(thm)],[f77,f54]) ).
fof(f216,plain,
addition(sK1_skl,c(sK1_skl)) = one,
inference(paramodulation,[status(thm)],[f19,f140]) ).
fof(f221,plain,
addition(sK2_skl,c(sK2_skl)) = one,
inference(paramodulation,[status(thm)],[f19,f141]) ).
fof(f276,plain,
( sQ0_spl
| ~ leq(one,addition(multiplication(c(sK1_skl),sK2_skl),addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(sK1_skl,c(sK2_skl))),multiplication(c(sK1_skl),c(sK2_skl))))) ),
inference(forward_demodulation,[status(thm)],[f20,f69]) ).
fof(f277,plain,
( sQ0_spl
| ~ leq(one,addition(multiplication(c(sK1_skl),sK2_skl),addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK1_skl,c(sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))))) ),
inference(forward_demodulation,[status(thm)],[f20,f276]) ).
fof(f278,plain,
( sQ0_spl
| ~ leq(one,addition(multiplication(c(sK1_skl),sK2_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(addition(sK1_skl,c(sK1_skl)),c(sK2_skl))))) ),
inference(forward_demodulation,[status(thm)],[f27,f277]) ).
fof(f279,plain,
( sQ0_spl
| ~ leq(one,addition(multiplication(c(sK1_skl),sK2_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(one,c(sK2_skl))))) ),
inference(forward_demodulation,[status(thm)],[f216,f278]) ).
fof(f280,plain,
( sQ0_spl
| ~ leq(one,addition(multiplication(c(sK1_skl),sK2_skl),addition(multiplication(sK1_skl,sK2_skl),c(sK2_skl)))) ),
inference(forward_demodulation,[status(thm)],[f25,f279]) ).
fof(f424,plain,
( sQ0_spl
| ~ leq(one,addition(c(sK2_skl),addition(multiplication(c(sK1_skl),sK2_skl),multiplication(sK1_skl,sK2_skl)))) ),
inference(paramodulation,[status(thm)],[f79,f280]) ).
fof(f463,plain,
( sQ0_spl
| ~ leq(one,addition(c(sK2_skl),multiplication(addition(c(sK1_skl),sK1_skl),sK2_skl))) ),
inference(forward_demodulation,[status(thm)],[f27,f424]) ).
fof(f464,plain,
( sQ0_spl
| ~ leq(one,addition(c(sK2_skl),multiplication(one,sK2_skl))) ),
inference(forward_demodulation,[status(thm)],[f140,f463]) ).
fof(f465,plain,
( sQ0_spl
| ~ leq(one,addition(c(sK2_skl),sK2_skl)) ),
inference(forward_demodulation,[status(thm)],[f25,f464]) ).
fof(f466,plain,
( sQ0_spl
| ~ leq(one,one) ),
inference(forward_demodulation,[status(thm)],[f141,f465]) ).
fof(f492,plain,
( sQ0_spl
| addition(one,one) != one ),
inference(resolution,[status(thm)],[f466,f33]) ).
fof(f493,plain,
( sQ0_spl
| one != one ),
inference(forward_demodulation,[status(thm)],[f22,f492]) ).
fof(f494,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f493]) ).
fof(f495,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f494]) ).
fof(f496,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)],[f20,f62]) ).
fof(f497,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)],[f20,f496]) ).
fof(f498,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)],[f26,f497]) ).
fof(f499,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)],[f221,f498]) ).
fof(f500,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)],[f24,f499]) ).
fof(f667,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)],[f79,f500]) ).
fof(f673,plain,
( sQ1_spl
| ~ leq(addition(c(sK1_skl),multiplication(sK1_skl,addition(sK2_skl,c(sK2_skl)))),one) ),
inference(forward_demodulation,[status(thm)],[f26,f667]) ).
fof(f674,plain,
( sQ1_spl
| ~ leq(addition(c(sK1_skl),multiplication(sK1_skl,one)),one) ),
inference(forward_demodulation,[status(thm)],[f221,f673]) ).
fof(f675,plain,
( sQ1_spl
| ~ leq(addition(c(sK1_skl),sK1_skl),one) ),
inference(forward_demodulation,[status(thm)],[f24,f674]) ).
fof(f676,plain,
( sQ1_spl
| ~ leq(one,one) ),
inference(forward_demodulation,[status(thm)],[f140,f675]) ).
fof(f686,plain,
( sQ1_spl
| addition(one,one) != one ),
inference(resolution,[status(thm)],[f676,f33]) ).
fof(f687,plain,
( sQ1_spl
| one != one ),
inference(forward_demodulation,[status(thm)],[f22,f686]) ).
fof(f688,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f687]) ).
fof(f689,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f688]) ).
fof(f690,plain,
$false,
inference(sat_refutation,[status(thm)],[f63,f495,f689]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.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 22:37:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.39 % Drodi V4.1.1
% 0.08/0.42 % Refutation found
% 0.08/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.47 % Elapsed time: 0.096323 seconds
% 0.14/0.47 % CPU time: 0.201659 seconds
% 0.14/0.47 % Total memory used: 27.524 MB
% 0.14/0.47 % Net memory used: 27.435 MB
%------------------------------------------------------------------------------