%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE004+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 : 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 12:57:42 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 17 unt; 2 def)
% Number of atoms : 115 ( 54 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 118 ( 50 ~; 48 |; 13 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 52 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
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,
c(zero) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
c(zero) != one,
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f29,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f34,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f35,plain,
( ! [X0] :
( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ! [X0] :
( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,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))],[f35]) ).
fof(f38,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| test(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
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(f44,plain,
! [X0,X1] :
( addition(X1,X0) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| 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,
c(zero) != one,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f66,definition,
( sQ1_spl
<=> test(zero) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( sQ1_spl
| ~ test(zero) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f71,plain,
! [X0] :
( X0 = one
| ~ complement(zero,X0) ),
inference(paramodulation,[status(thm)],[f21,f43]) ).
fof(f72,plain,
( ~ test(zero)
| c(zero) = one ),
inference(resolution,[status(thm)],[f71,f53]) ).
fof(f73,definition,
( sQ2_spl
<=> c(zero) = one ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ2_spl
| c(zero) = one ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f72,f73,f66]) ).
fof(f77,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f52]) ).
fof(f78,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f77]) ).
fof(f104,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f21,f19]) ).
fof(f123,plain,
! [X0] :
( X0 != one
| multiplication(X0,zero) != zero
| multiplication(zero,X0) != zero
| complement(X0,zero) ),
inference(paramodulation,[status(thm)],[f104,f44]) ).
fof(f129,plain,
! [X0] :
( X0 != one
| multiplication(X0,zero) != zero
| zero != zero
| complement(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f29,f123]) ).
fof(f130,plain,
! [X0] :
( X0 != one
| zero != zero
| zero != zero
| complement(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f28,f129]) ).
fof(f131,plain,
! [X0] :
( X0 != one
| zero != zero
| complement(X0,zero) ),
inference(duplicate_literals_removal,[status(thm)],[f130]) ).
fof(f132,plain,
! [X0] :
( X0 != one
| complement(X0,zero) ),
inference(trivial_equality_resolution,[status(thm)],[f131]) ).
fof(f133,plain,
complement(one,zero),
inference(destructive_equality_resolution,[status(thm)],[f132]) ).
fof(f167,plain,
test(zero),
inference(resolution,[status(thm)],[f38,f133]) ).
fof(f170,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f68]) ).
fof(f171,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f170]) ).
fof(f172,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f78,f171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE004+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 22:37:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.053670 seconds
% 0.10/0.43 % CPU time: 0.149594 seconds
% 0.10/0.43 % Total memory used: 102.001 MB
% 0.10/0.43 % Net memory used: 101.678 MB
%------------------------------------------------------------------------------