TSTP Solution File: ALG073+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ALG073+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n020.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 20:09:26 EDT 2024
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 20 unt; 0 def)
% Number of atoms : 159 ( 56 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 157 ( 57 ~; 51 |; 25 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> sorti1(op1(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
? [U] :
( sorti1(U)
& ? [V] :
( sorti1(V)
& op1(U,U) = V
& op1(V,V) = U
& op1(U,V) != U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ ? [U] :
( sorti2(U)
& ? [V] :
( sorti2(V)
& op2(U,U) = V
& op2(V,V) = U
& op2(U,V) != U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,conjecture,
( ( ! [U] :
( sorti1(U)
=> sorti2(h(U)) )
& ! [V] :
( sorti2(V)
=> sorti1(j(V)) ) )
=> ~ ( ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) )
& ! [Y] :
( sorti2(Y)
=> ! [Z] :
( sorti2(Z)
=> j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 )
& ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ ( ( ! [U] :
( sorti1(U)
=> sorti2(h(U)) )
& ! [V] :
( sorti2(V)
=> sorti1(j(V)) ) )
=> ~ ( ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) )
& ! [Y] :
( sorti2(Y)
=> ! [Z] :
( sorti2(Z)
=> j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 )
& ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
! [U] :
( ~ sorti1(U)
| ! [V] :
( ~ sorti1(V)
| sorti1(op1(U,V)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f8,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| sorti1(op1(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f11,plain,
( sorti1(sk0_0)
& sorti1(sk0_1)
& op1(sk0_0,sk0_0) = sk0_1
& op1(sk0_1,sk0_1) = sk0_0
& op1(sk0_0,sk0_1) != sk0_0 ),
inference(skolemization,[status(esa)],[f3]) ).
fof(f12,plain,
sorti1(sk0_0),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f13,plain,
sorti1(sk0_1),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f14,plain,
op1(sk0_0,sk0_0) = sk0_1,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f15,plain,
op1(sk0_1,sk0_1) = sk0_0,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f16,plain,
op1(sk0_0,sk0_1) != sk0_0,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f17,plain,
! [U] :
( ~ sorti2(U)
| ! [V] :
( ~ sorti2(V)
| op2(U,U) != V
| op2(V,V) != U
| op2(U,V) = U ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f18,plain,
! [X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| op2(X0,X0) != X1
| op2(X1,X1) != X0
| op2(X0,X1) = X0 ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
( ! [U] :
( ~ sorti1(U)
| sorti2(h(U)) )
& ! [V] :
( ~ sorti2(V)
| sorti1(j(V)) )
& ! [W] :
( ~ sorti1(W)
| ! [X] :
( ~ sorti1(X)
| h(op1(W,X)) = op2(h(W),h(X)) ) )
& ! [Y] :
( ~ sorti2(Y)
| ! [Z] :
( ~ sorti2(Z)
| j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
& ! [X1] :
( ~ sorti2(X1)
| h(j(X1)) = X1 )
& ! [X2] :
( ~ sorti1(X2)
| j(h(X2)) = X2 ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f20,plain,
! [X0] :
( ~ sorti1(X0)
| sorti2(h(X0)) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f22,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| h(op1(X0,X1)) = op2(h(X0),h(X1)) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f25,plain,
! [X0] :
( ~ sorti1(X0)
| j(h(X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f26,plain,
! [X0] :
( ~ sorti2(X0)
| ~ sorti2(op2(X0,X0))
| op2(op2(X0,X0),op2(X0,X0)) != X0
| op2(X0,op2(X0,X0)) = X0 ),
inference(destructive_equality_resolution,[status(esa)],[f18]) ).
fof(f27,plain,
! [X0] :
( ~ sorti1(X0)
| sorti1(op1(sk0_0,X0)) ),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f28,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(sk0_0,X0)) = op2(h(sk0_0),h(X0)) ),
inference(resolution,[status(thm)],[f12,f22]) ).
fof(f29,plain,
j(h(sk0_0)) = sk0_0,
inference(resolution,[status(thm)],[f12,f25]) ).
fof(f30,plain,
sorti2(h(sk0_0)),
inference(resolution,[status(thm)],[f12,f20]) ).
fof(f47,plain,
h(op1(sk0_0,sk0_0)) = op2(h(sk0_0),h(sk0_0)),
inference(resolution,[status(thm)],[f28,f12]) ).
fof(f50,plain,
h(op1(sk0_0,sk0_1)) = op2(h(sk0_0),h(sk0_1)),
inference(resolution,[status(thm)],[f13,f28]) ).
fof(f51,plain,
sorti1(op1(sk0_0,sk0_1)),
inference(resolution,[status(thm)],[f13,f27]) ).
fof(f53,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(sk0_1,X0)) = op2(h(sk0_1),h(X0)) ),
inference(resolution,[status(thm)],[f13,f22]) ).
fof(f55,plain,
sorti2(h(sk0_1)),
inference(resolution,[status(thm)],[f13,f20]) ).
fof(f67,plain,
j(h(op1(sk0_0,sk0_1))) = op1(sk0_0,sk0_1),
inference(resolution,[status(thm)],[f51,f25]) ).
fof(f96,plain,
h(op1(sk0_1,sk0_1)) = op2(h(sk0_1),h(sk0_1)),
inference(resolution,[status(thm)],[f53,f13]) ).
fof(f97,plain,
h(sk0_0) = op2(h(sk0_1),h(sk0_1)),
inference(forward_demodulation,[status(thm)],[f15,f96]) ).
fof(f107,plain,
h(sk0_1) = op2(h(sk0_0),h(sk0_0)),
inference(forward_demodulation,[status(thm)],[f14,f47]) ).
fof(f108,plain,
( spl0_0
<=> sorti2(h(sk0_0)) ),
introduced(split_symbol_definition) ).
fof(f110,plain,
( ~ sorti2(h(sk0_0))
| spl0_0 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( spl0_1
<=> sorti2(h(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f113,plain,
( ~ sorti2(h(sk0_1))
| spl0_1 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( spl0_2
<=> op2(op2(h(sk0_0),h(sk0_0)),op2(h(sk0_0),h(sk0_0))) = h(sk0_0) ),
introduced(split_symbol_definition) ).
fof(f116,plain,
( op2(op2(h(sk0_0),h(sk0_0)),op2(h(sk0_0),h(sk0_0))) != h(sk0_0)
| spl0_2 ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,plain,
( spl0_3
<=> op2(h(sk0_0),op2(h(sk0_0),h(sk0_0))) = h(sk0_0) ),
introduced(split_symbol_definition) ).
fof(f118,plain,
( op2(h(sk0_0),op2(h(sk0_0),h(sk0_0))) = h(sk0_0)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( ~ sorti2(h(sk0_0))
| ~ sorti2(h(sk0_1))
| op2(op2(h(sk0_0),h(sk0_0)),op2(h(sk0_0),h(sk0_0))) != h(sk0_0)
| op2(h(sk0_0),op2(h(sk0_0),h(sk0_0))) = h(sk0_0) ),
inference(paramodulation,[status(thm)],[f107,f26]) ).
fof(f121,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f120,f108,f111,f114,f117]) ).
fof(f122,plain,
( op2(h(sk0_1),op2(h(sk0_0),h(sk0_0))) != h(sk0_0)
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f107,f116]) ).
fof(f123,plain,
( op2(h(sk0_1),h(sk0_1)) != h(sk0_0)
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f107,f122]) ).
fof(f282,plain,
( h(sk0_0) != h(sk0_0)
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f97,f123]) ).
fof(f283,plain,
( $false
| spl0_2 ),
inference(trivial_equality_resolution,[status(esa)],[f282]) ).
fof(f284,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f283]) ).
fof(f285,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f30]) ).
fof(f286,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f285]) ).
fof(f289,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f113,f55]) ).
fof(f290,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f289]) ).
fof(f296,plain,
( op2(h(sk0_0),h(sk0_1)) = h(sk0_0)
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f107,f118]) ).
fof(f297,plain,
( h(op1(sk0_0,sk0_1)) = h(sk0_0)
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f50,f296]) ).
fof(f410,plain,
( j(h(sk0_0)) = op1(sk0_0,sk0_1)
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f297,f67]) ).
fof(f411,plain,
( sk0_0 = op1(sk0_0,sk0_1)
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f29,f410]) ).
fof(f412,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f411,f16]) ).
fof(f413,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f412]) ).
fof(f414,plain,
$false,
inference(sat_refutation,[status(thm)],[f121,f284,f286,f290,f413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG073+1 : TPTP v8.1.2. Released v2.7.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 23:27:32 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.042214 seconds
% 0.13/0.40 % CPU time: 0.196552 seconds
% 0.13/0.40 % Total memory used: 32.529 MB
% 0.13/0.40 % Net memory used: 32.281 MB
%------------------------------------------------------------------------------