TSTP Solution File: ALG069+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ALG069+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.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 20:09:25 EDT 2024
% Result : Theorem 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 88 ( 29 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 89 ( 29 ~; 21 |; 19 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 43 ( 39 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [U] :
( sorti1(U)
=> ? [V] :
( sorti1(V)
& op1(V,V) = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ ! [U] :
( sorti2(U)
=> ? [V] :
( sorti2(V)
& op2(V,V) = U ) ),
file('/export/starexec/sandbox/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/sandbox/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(f11,plain,
! [U] :
( ~ sorti1(U)
| ? [V] :
( sorti1(V)
& op1(V,V) = U ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f12,plain,
! [U] :
( ~ sorti1(U)
| ( sorti1(sk0_0(U))
& op1(sk0_0(U),sk0_0(U)) = U ) ),
inference(skolemization,[status(esa)],[f11]) ).
fof(f13,plain,
! [X0] :
( ~ sorti1(X0)
| sorti1(sk0_0(X0)) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f14,plain,
! [X0] :
( ~ sorti1(X0)
| op1(sk0_0(X0),sk0_0(X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f15,plain,
? [U] :
( sorti2(U)
& ! [V] :
( ~ sorti2(V)
| op2(V,V) != U ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f16,plain,
( sorti2(sk0_1)
& ! [V] :
( ~ sorti2(V)
| op2(V,V) != sk0_1 ) ),
inference(skolemization,[status(esa)],[f15]) ).
fof(f17,plain,
sorti2(sk0_1),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0] :
( ~ sorti2(X0)
| op2(X0,X0) != sk0_1 ),
inference(cnf_transformation,[status(esa)],[f16]) ).
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(f21,plain,
! [X0] :
( ~ sorti2(X0)
| sorti1(j(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(f24,plain,
! [X0] :
( ~ sorti2(X0)
| h(j(X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f28,plain,
h(j(sk0_1)) = sk0_1,
inference(resolution,[status(thm)],[f17,f24]) ).
fof(f29,plain,
sorti1(j(sk0_1)),
inference(resolution,[status(thm)],[f17,f21]) ).
fof(f46,plain,
sorti1(sk0_0(j(sk0_1))),
inference(resolution,[status(thm)],[f13,f29]) ).
fof(f51,plain,
sorti2(h(sk0_0(j(sk0_1)))),
inference(resolution,[status(thm)],[f46,f20]) ).
fof(f52,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(sk0_0(j(sk0_1)),X0)) = op2(h(sk0_0(j(sk0_1))),h(X0)) ),
inference(resolution,[status(thm)],[f46,f22]) ).
fof(f68,plain,
op2(h(sk0_0(j(sk0_1))),h(sk0_0(j(sk0_1)))) != sk0_1,
inference(resolution,[status(thm)],[f51,f18]) ).
fof(f76,plain,
op1(sk0_0(j(sk0_1)),sk0_0(j(sk0_1))) = j(sk0_1),
inference(resolution,[status(thm)],[f14,f29]) ).
fof(f161,plain,
h(op1(sk0_0(j(sk0_1)),sk0_0(j(sk0_1)))) = op2(h(sk0_0(j(sk0_1))),h(sk0_0(j(sk0_1)))),
inference(resolution,[status(thm)],[f52,f46]) ).
fof(f162,plain,
h(j(sk0_1)) = op2(h(sk0_0(j(sk0_1))),h(sk0_0(j(sk0_1)))),
inference(forward_demodulation,[status(thm)],[f76,f161]) ).
fof(f163,plain,
sk0_1 = op2(h(sk0_0(j(sk0_1))),h(sk0_0(j(sk0_1)))),
inference(forward_demodulation,[status(thm)],[f28,f162]) ).
fof(f164,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f163,f68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG069+1 : TPTP v8.1.2. Released v2.7.0.
% 0.13/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n024.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 23:31:06 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.35 % Drodi V3.6.0
% 0.19/0.41 % Refutation found
% 0.19/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.43 % Elapsed time: 0.079174 seconds
% 0.19/0.43 % CPU time: 0.545278 seconds
% 0.19/0.43 % Total memory used: 32.476 MB
% 0.19/0.43 % Net memory used: 31.817 MB
%------------------------------------------------------------------------------