TSTP Solution File: KLE025+2 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : KLE025+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:24:12 EDT 2024
% Result : Theorem 0.12s 0.33s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 19 unt; 0 def)
% Number of atoms : 82 ( 49 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 72 ( 24 ~; 19 |; 21 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 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)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
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(X1)
& test(X2) )
=> ( 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(X1)
& test(X2) )
=> ( 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(esa)],[f1]) ).
fof(f23,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f41,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) )
& ( complement(X1,X0)
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| addition(X0,X1) != one ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f42,plain,
( ! [X0,X1] :
( ~ complement(X1,X0)
| ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) )
& ! [X0,X1] :
( complement(X1,X0)
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| addition(X0,X1) != one ) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f47,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f48,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(NNF_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0] :
( ~ test(X0)
| ( ! [X1] :
( c(X0) != X1
| complement(X0,X1) )
& ! [X1] :
( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(miniscoping,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f58,plain,
? [X0,X1,X2] :
( test(X1)
& test(X2)
& multiplication(multiplication(X1,X0),c(X2)) = zero
& multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f59,plain,
? [X1,X2] :
( test(X1)
& test(X2)
& ? [X0] :
( multiplication(multiplication(X1,X0),c(X2)) = zero
& multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2) ) ),
inference(miniscoping,[status(esa)],[f58]) ).
fof(f60,plain,
( test(sk0_1)
& test(sk0_2)
& multiplication(multiplication(sk0_1,sk0_3),c(sk0_2)) = zero
& multiplication(sk0_1,sk0_3) != multiplication(multiplication(sk0_1,sk0_3),sk0_2) ),
inference(skolemization,[status(esa)],[f59]) ).
fof(f62,plain,
test(sk0_2),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f63,plain,
multiplication(multiplication(sk0_1,sk0_3),c(sk0_2)) = zero,
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f64,plain,
multiplication(sk0_1,sk0_3) != multiplication(multiplication(sk0_1,sk0_3),sk0_2),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f65,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f50]) ).
fof(f146,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f197,plain,
! [X0] : multiplication(multiplication(sk0_1,sk0_3),addition(c(sk0_2),X0)) = addition(zero,multiplication(multiplication(sk0_1,sk0_3),X0)),
inference(paramodulation,[status(thm)],[f63,f28]) ).
fof(f198,plain,
! [X0] : multiplication(multiplication(sk0_1,sk0_3),addition(c(sk0_2),X0)) = multiplication(multiplication(sk0_1,sk0_3),X0),
inference(forward_demodulation,[status(thm)],[f146,f197]) ).
fof(f676,plain,
complement(sk0_2,c(sk0_2)),
inference(resolution,[status(thm)],[f65,f62]) ).
fof(f738,plain,
addition(c(sk0_2),sk0_2) = one,
inference(resolution,[status(thm)],[f45,f676]) ).
fof(f1893,plain,
multiplication(multiplication(sk0_1,sk0_3),one) = multiplication(multiplication(sk0_1,sk0_3),sk0_2),
inference(paramodulation,[status(thm)],[f738,f198]) ).
fof(f1894,plain,
multiplication(sk0_1,sk0_3) = multiplication(multiplication(sk0_1,sk0_3),sk0_2),
inference(forward_demodulation,[status(thm)],[f26,f1893]) ).
fof(f1895,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1894,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : KLE025+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Tue Apr 30 01:06:05 EDT 2024
% 0.08/0.28 % CPUTime :
% 0.08/0.28 % Drodi V3.6.0
% 0.12/0.33 % Refutation found
% 0.12/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.34 % Elapsed time: 0.062437 seconds
% 0.12/0.34 % CPU time: 0.415701 seconds
% 0.12/0.34 % Total memory used: 71.965 MB
% 0.12/0.34 % Net memory used: 71.395 MB
%------------------------------------------------------------------------------