%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE025+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 : n008.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 12:57:47 PM UTC 2026
% Result : Theorem 2.62s 0.78s
% Output : CNFRefutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 17 unt; 2 def)
% Number of atoms : 104 ( 51 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 94 ( 34 ~; 29 |; 21 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 51 ( 45 !; 6 ?)
% 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(f6,axiom,
! [A] : multiplication(A,one) = 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(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(f19,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f23,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
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(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,X2] :
( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
& multiplication(multiplication(X1,X0),c(X2)) = zero
& test(X2)
& test(X1) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f59,plain,
? [X1,X2] :
( ? [X0] :
( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
& multiplication(multiplication(X1,X0),c(X2)) = zero )
& test(X2)
& test(X1) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f60,plain,
( multiplication(sK1_skl,sK3_skl) != multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl)
& multiplication(multiplication(sK1_skl,sK3_skl),c(sK2_skl)) = zero
& test(sK2_skl)
& test(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(X1,sK1_skl),skolemize(X2,sK2_skl),skolemize(X0,sK3_skl)],[f59]) ).
fof(f62,plain,
test(sK2_skl),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f63,plain,
multiplication(multiplication(sK1_skl,sK3_skl),c(sK2_skl)) = zero,
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f64,plain,
multiplication(sK1_skl,sK3_skl) != multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f65,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f50]) ).
fof(f119,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f175,plain,
! [X0] : multiplication(multiplication(sK1_skl,sK3_skl),addition(c(sK2_skl),X0)) = addition(zero,multiplication(multiplication(sK1_skl,sK3_skl),X0)),
inference(paramodulation,[status(thm)],[f63,f28]) ).
fof(f197,plain,
! [X0] : multiplication(multiplication(sK1_skl,sK3_skl),addition(c(sK2_skl),X0)) = multiplication(multiplication(sK1_skl,sK3_skl),X0),
inference(forward_demodulation,[status(thm)],[f119,f175]) ).
fof(f5737,definition,
( sQ131_spl
<=> test(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f5739,plain,
( sQ131_spl
| ~ test(sK2_skl) ),
inference(component_clause,[status(thm)],[f5737]) ).
fof(f5760,plain,
( sQ131_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5739,f62]) ).
fof(f5761,plain,
sQ131_spl,
inference(contradiction_clause,[status(thm)],[f5760]) ).
fof(f7284,definition,
( sQ182_spl
<=> addition(c(sK2_skl),sK2_skl) = one ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f7285,plain,
( ~ sQ182_spl
| addition(c(sK2_skl),sK2_skl) = one ),
inference(component_clause,[status(thm)],[f7284]) ).
fof(f7286,plain,
( sQ182_spl
| addition(c(sK2_skl),sK2_skl) != one ),
inference(component_clause,[status(thm)],[f7284]) ).
fof(f7772,plain,
( sQ182_spl
| ~ complement(sK2_skl,c(sK2_skl)) ),
inference(resolution,[status(thm)],[f7286,f45]) ).
fof(f7776,plain,
( sQ182_spl
| ~ test(sK2_skl) ),
inference(resolution,[status(thm)],[f7772,f65]) ).
fof(f7777,plain,
( sQ182_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f7776,f5737,f7284]) ).
fof(f7780,plain,
( ~ sQ182_spl
| multiplication(multiplication(sK1_skl,sK3_skl),one) = multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl) ),
inference(paramodulation,[status(thm)],[f7285,f197]) ).
fof(f7788,plain,
( ~ sQ182_spl
| multiplication(sK1_skl,sK3_skl) = multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f26,f7780]) ).
fof(f7789,plain,
( ~ sQ182_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7788,f64]) ).
fof(f7790,plain,
~ sQ182_spl,
inference(contradiction_clause,[status(thm)],[f7789]) ).
fof(f7791,plain,
$false,
inference(sat_refutation,[status(thm)],[f5761,f7777,f7790]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE025+2 : 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 : n008.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 22:40:08 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 2.62/0.78 % Refutation found
% 2.62/0.78 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.62/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.62/0.81 % Elapsed time: 0.424942 seconds
% 2.62/0.81 % CPU time: 2.989502 seconds
% 2.62/0.81 % Total memory used: 150.675 MB
% 2.62/0.81 % Net memory used: 149.137 MB
%------------------------------------------------------------------------------