TSTP Solution File: ALG074+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ALG074+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 0.41s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 26 unt; 0 def)
% Number of atoms : 172 ( 71 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 166 ( 63 ~; 55 |; 25 &)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 47 !; 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(V,U) != op1(U,V)
& op1(op1(U,V),V) = U
& op1(op1(U,V),U) != V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ ? [U] :
( sorti2(U)
& ? [V] :
( sorti2(V)
& op2(V,U) != op2(U,V)
& op2(op2(U,V),V) = U
& op2(op2(U,V),U) != V ) ),
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_1,sk0_0) != op1(sk0_0,sk0_1)
& op1(op1(sk0_0,sk0_1),sk0_1) = sk0_0
& op1(op1(sk0_0,sk0_1),sk0_0) != sk0_1 ),
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_1,sk0_0) != op1(sk0_0,sk0_1),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f15,plain,
op1(op1(sk0_0,sk0_1),sk0_1) = sk0_0,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f16,plain,
op1(op1(sk0_0,sk0_1),sk0_0) != sk0_1,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f17,plain,
! [U] :
( ~ sorti2(U)
| ! [V] :
( ~ sorti2(V)
| op2(V,U) = op2(U,V)
| op2(op2(U,V),V) != U
| op2(op2(U,V),U) = V ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f18,plain,
! [X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| op2(X1,X0) = op2(X0,X1)
| op2(op2(X0,X1),X1) != X0
| op2(op2(X0,X1),X0) = X1 ),
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(f23,plain,
! [X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| j(op2(X0,X1)) = op1(j(X0),j(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] :
( ~ sorti1(X0)
| sorti1(op1(sk0_0,X0)) ),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f27,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(X0,sk0_0)) = op2(h(X0),h(sk0_0)) ),
inference(resolution,[status(thm)],[f12,f22]) ).
fof(f28,plain,
j(h(sk0_0)) = sk0_0,
inference(resolution,[status(thm)],[f12,f25]) ).
fof(f29,plain,
sorti2(h(sk0_0)),
inference(resolution,[status(thm)],[f12,f20]) ).
fof(f32,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,h(sk0_0))) = op1(j(X0),j(h(sk0_0))) ),
inference(resolution,[status(thm)],[f29,f23]) ).
fof(f33,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,h(sk0_0))) = op1(j(X0),sk0_0) ),
inference(forward_demodulation,[status(thm)],[f28,f32]) ).
fof(f72,plain,
h(op1(sk0_1,sk0_0)) = op2(h(sk0_1),h(sk0_0)),
inference(resolution,[status(thm)],[f13,f27]) ).
fof(f73,plain,
sorti1(op1(sk0_0,sk0_1)),
inference(resolution,[status(thm)],[f13,f26]) ).
fof(f74,plain,
! [X0] :
( ~ sorti1(X0)
| sorti1(op1(sk0_1,X0)) ),
inference(resolution,[status(thm)],[f13,f8]) ).
fof(f75,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(X0,sk0_1)) = op2(h(X0),h(sk0_1)) ),
inference(resolution,[status(thm)],[f13,f22]) ).
fof(f76,plain,
j(h(sk0_1)) = sk0_1,
inference(resolution,[status(thm)],[f13,f25]) ).
fof(f77,plain,
sorti2(h(sk0_1)),
inference(resolution,[status(thm)],[f13,f20]) ).
fof(f78,plain,
( spl0_5
<=> op2(h(sk0_0),h(sk0_1)) = op2(h(sk0_1),h(sk0_0)) ),
introduced(split_symbol_definition) ).
fof(f79,plain,
( op2(h(sk0_0),h(sk0_1)) = op2(h(sk0_1),h(sk0_0))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f89,plain,
! [X0] :
( ~ sorti2(X0)
| op2(h(sk0_1),X0) = op2(X0,h(sk0_1))
| op2(op2(X0,h(sk0_1)),h(sk0_1)) != X0
| op2(op2(X0,h(sk0_1)),X0) = h(sk0_1) ),
inference(resolution,[status(thm)],[f77,f18]) ).
fof(f97,plain,
h(op1(op1(sk0_0,sk0_1),sk0_0)) = op2(h(op1(sk0_0,sk0_1)),h(sk0_0)),
inference(resolution,[status(thm)],[f73,f27]) ).
fof(f101,plain,
j(h(op1(sk0_0,sk0_1))) = op1(sk0_0,sk0_1),
inference(resolution,[status(thm)],[f73,f25]) ).
fof(f102,plain,
sorti2(h(op1(sk0_0,sk0_1))),
inference(resolution,[status(thm)],[f73,f20]) ).
fof(f106,plain,
sorti1(op1(sk0_1,sk0_0)),
inference(resolution,[status(thm)],[f74,f12]) ).
fof(f119,plain,
j(h(op1(sk0_1,sk0_0))) = op1(sk0_1,sk0_0),
inference(resolution,[status(thm)],[f106,f25]) ).
fof(f182,plain,
h(op1(op1(sk0_0,sk0_1),sk0_1)) = op2(h(op1(sk0_0,sk0_1)),h(sk0_1)),
inference(resolution,[status(thm)],[f75,f73]) ).
fof(f183,plain,
h(sk0_0) = op2(h(op1(sk0_0,sk0_1)),h(sk0_1)),
inference(forward_demodulation,[status(thm)],[f15,f182]) ).
fof(f185,plain,
h(op1(sk0_0,sk0_1)) = op2(h(sk0_0),h(sk0_1)),
inference(resolution,[status(thm)],[f75,f12]) ).
fof(f203,plain,
j(op2(h(op1(sk0_0,sk0_1)),h(sk0_0))) = op1(j(h(op1(sk0_0,sk0_1))),sk0_0),
inference(resolution,[status(thm)],[f33,f102]) ).
fof(f204,plain,
j(h(op1(op1(sk0_0,sk0_1),sk0_0))) = op1(j(h(op1(sk0_0,sk0_1))),sk0_0),
inference(forward_demodulation,[status(thm)],[f97,f203]) ).
fof(f205,plain,
j(h(op1(op1(sk0_0,sk0_1),sk0_0))) = op1(op1(sk0_0,sk0_1),sk0_0),
inference(forward_demodulation,[status(thm)],[f101,f204]) ).
fof(f283,plain,
( spl0_31
<=> op2(op2(h(sk0_0),h(sk0_1)),h(sk0_1)) = h(sk0_0) ),
introduced(split_symbol_definition) ).
fof(f285,plain,
( op2(op2(h(sk0_0),h(sk0_1)),h(sk0_1)) != h(sk0_0)
| spl0_31 ),
inference(component_clause,[status(thm)],[f283]) ).
fof(f286,plain,
( spl0_32
<=> op2(op2(h(sk0_0),h(sk0_1)),h(sk0_0)) = h(sk0_1) ),
introduced(split_symbol_definition) ).
fof(f287,plain,
( op2(op2(h(sk0_0),h(sk0_1)),h(sk0_0)) = h(sk0_1)
| ~ spl0_32 ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,plain,
( op2(h(sk0_1),h(sk0_0)) = op2(h(sk0_0),h(sk0_1))
| op2(op2(h(sk0_0),h(sk0_1)),h(sk0_1)) != h(sk0_0)
| op2(op2(h(sk0_0),h(sk0_1)),h(sk0_0)) = h(sk0_1) ),
inference(resolution,[status(thm)],[f89,f29]) ).
fof(f290,plain,
( spl0_5
| ~ spl0_31
| spl0_32 ),
inference(split_clause,[status(thm)],[f289,f78,f283,f286]) ).
fof(f291,plain,
( op2(h(op1(sk0_0,sk0_1)),h(sk0_1)) != h(sk0_0)
| spl0_31 ),
inference(forward_demodulation,[status(thm)],[f185,f285]) ).
fof(f292,plain,
( h(sk0_0) != h(sk0_0)
| spl0_31 ),
inference(forward_demodulation,[status(thm)],[f183,f291]) ).
fof(f293,plain,
( $false
| spl0_31 ),
inference(trivial_equality_resolution,[status(esa)],[f292]) ).
fof(f294,plain,
spl0_31,
inference(contradiction_clause,[status(thm)],[f293]) ).
fof(f302,plain,
( h(op1(sk0_0,sk0_1)) = op2(h(sk0_1),h(sk0_0))
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f185,f79]) ).
fof(f303,plain,
( h(op1(sk0_0,sk0_1)) = h(op1(sk0_1,sk0_0))
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f72,f302]) ).
fof(f309,plain,
( j(h(op1(sk0_0,sk0_1))) = op1(sk0_1,sk0_0)
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f303,f119]) ).
fof(f310,plain,
( op1(sk0_0,sk0_1) = op1(sk0_1,sk0_0)
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f101,f309]) ).
fof(f311,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f14]) ).
fof(f312,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f311]) ).
fof(f313,plain,
( op2(h(op1(sk0_0,sk0_1)),h(sk0_0)) = h(sk0_1)
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f185,f287]) ).
fof(f314,plain,
( h(op1(op1(sk0_0,sk0_1),sk0_0)) = h(sk0_1)
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f97,f313]) ).
fof(f317,plain,
( j(h(sk0_1)) = op1(op1(sk0_0,sk0_1),sk0_0)
| ~ spl0_32 ),
inference(backward_demodulation,[status(thm)],[f314,f205]) ).
fof(f318,plain,
( sk0_1 = op1(op1(sk0_0,sk0_1),sk0_0)
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f76,f317]) ).
fof(f319,plain,
( $false
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[status(thm)],[f318,f16]) ).
fof(f320,plain,
~ spl0_32,
inference(contradiction_clause,[status(thm)],[f319]) ).
fof(f321,plain,
$false,
inference(sat_refutation,[status(thm)],[f290,f294,f312,f320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG074+1 : TPTP v8.1.2. Released v2.7.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 23:07:33 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.42 % Elapsed time: 0.068059 seconds
% 0.20/0.42 % CPU time: 0.431460 seconds
% 0.20/0.42 % Total memory used: 66.065 MB
% 0.20/0.42 % Net memory used: 65.757 MB
%------------------------------------------------------------------------------