%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE007+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 : n012.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 12:57:43 PM UTC 2026
% Result : Theorem 0.04s 0.32s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 17 unt; 2 def)
% Number of atoms : 130 ( 46 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 122 ( 48 ~; 45 |; 20 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 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 : 53 ( 51 !; 2 ?)
% 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(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,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(X0)
& test(X1) )
=> ( leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
& leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
& leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,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(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(f26,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
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(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
| ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) )
& test(X0)
& test(X1) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( ( ~ leq(addition(multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl),multiplication(addition(sK1_skl,c(sK1_skl)),c(sK2_skl))),one)
| ~ leq(one,addition(multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl),multiplication(addition(sK1_skl,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(multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl),multiplication(addition(sK1_skl,c(sK1_skl)),c(sK2_skl))),one)
| ~ leq(one,addition(multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl),multiplication(addition(sK1_skl,c(sK1_skl)),c(sK2_skl)))) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f57,definition,
( sQ0_spl
<=> leq(one,addition(multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl),multiplication(addition(sK1_skl,c(sK1_skl)),c(sK2_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( sQ0_spl
| ~ leq(one,addition(multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl),multiplication(addition(sK1_skl,c(sK1_skl)),c(sK2_skl)))) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,definition,
( sQ1_spl
<=> leq(addition(multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl),multiplication(addition(sK1_skl,c(sK1_skl)),c(sK2_skl))),one) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( sQ1_spl
| ~ leq(addition(multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl),multiplication(addition(sK1_skl,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(f73,plain,
! [X0] :
( ~ test(X0)
| addition(c(X0),X0) = one ),
inference(resolution,[status(thm)],[f43,f64]) ).
fof(f133,plain,
addition(c(sK1_skl),sK1_skl) = one,
inference(resolution,[status(thm)],[f73,f55]) ).
fof(f134,plain,
addition(c(sK2_skl),sK2_skl) = one,
inference(resolution,[status(thm)],[f73,f54]) ).
fof(f137,plain,
( sQ0_spl
| ~ leq(one,multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl)))) ),
inference(backward_demodulation,[status(thm)],[f26,f59]) ).
fof(f210,plain,
addition(sK1_skl,c(sK1_skl)) = one,
inference(paramodulation,[status(thm)],[f19,f133]) ).
fof(f215,plain,
addition(sK2_skl,c(sK2_skl)) = one,
inference(paramodulation,[status(thm)],[f19,f134]) ).
fof(f221,plain,
( sQ0_spl
| ~ leq(one,multiplication(one,addition(sK2_skl,c(sK2_skl)))) ),
inference(forward_demodulation,[status(thm)],[f210,f137]) ).
fof(f222,plain,
( sQ0_spl
| ~ leq(one,addition(sK2_skl,c(sK2_skl))) ),
inference(forward_demodulation,[status(thm)],[f25,f221]) ).
fof(f224,plain,
( sQ0_spl
| ~ leq(one,one) ),
inference(backward_demodulation,[status(thm)],[f215,f222]) ).
fof(f226,plain,
( sQ0_spl
| addition(one,one) != one ),
inference(resolution,[status(thm)],[f224,f33]) ).
fof(f227,plain,
( sQ0_spl
| one != one ),
inference(forward_demodulation,[status(thm)],[f22,f226]) ).
fof(f228,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f227]) ).
fof(f229,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f228]) ).
fof(f230,plain,
( sQ1_spl
| ~ leq(multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl))),one) ),
inference(forward_demodulation,[status(thm)],[f26,f62]) ).
fof(f231,plain,
( sQ1_spl
| ~ leq(multiplication(one,addition(sK2_skl,c(sK2_skl))),one) ),
inference(forward_demodulation,[status(thm)],[f210,f230]) ).
fof(f232,plain,
( sQ1_spl
| ~ leq(addition(sK2_skl,c(sK2_skl)),one) ),
inference(forward_demodulation,[status(thm)],[f25,f231]) ).
fof(f233,plain,
( sQ1_spl
| ~ leq(one,one) ),
inference(forward_demodulation,[status(thm)],[f215,f232]) ).
fof(f238,plain,
( sQ1_spl
| addition(one,one) != one ),
inference(resolution,[status(thm)],[f233,f33]) ).
fof(f239,plain,
( sQ1_spl
| one != one ),
inference(forward_demodulation,[status(thm)],[f22,f238]) ).
fof(f240,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f239]) ).
fof(f241,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f240]) ).
fof(f242,plain,
$false,
inference(sat_refutation,[status(thm)],[f63,f229,f241]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE007+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 20 22:37:37 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.31 % Drodi V4.1.1
% 0.04/0.32 % Refutation found
% 0.04/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.04/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.34 % Elapsed time: 0.036018 seconds
% 0.08/0.34 % CPU time: 0.095732 seconds
% 0.08/0.34 % Total memory used: 102.583 MB
% 0.08/0.34 % Net memory used: 102.265 MB
%------------------------------------------------------------------------------