TSTP Solution File: ALG071+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ALG071+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.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 0.10s 0.37s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 64 ( 19 unt; 0 def)
% Number of atoms : 166 ( 57 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 165 ( 63 ~; 53 |; 23 &)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 67 ( 63 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> sorti1(op1(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> sorti2(op2(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U] :
( sorti1(U)
=> ? [V] :
( sorti1(V)
& op1(V,op1(V,U)) != U
& op1(U,op1(V,U)) = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ ! [U] :
( sorti2(U)
=> ? [V] :
( sorti2(V)
& op2(V,op2(V,U)) != U
& op2(U,op2(V,U)) = V ) ),
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(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(f9,plain,
! [U] :
( ~ sorti2(U)
| ! [V] :
( ~ sorti2(V)
| sorti2(op2(U,V)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f10,plain,
! [X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| sorti2(op2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f11,plain,
! [U] :
( ~ sorti1(U)
| ? [V] :
( sorti1(V)
& op1(V,op1(V,U)) != U
& op1(U,op1(V,U)) = V ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f12,plain,
! [U] :
( ~ sorti1(U)
| ( sorti1(sk0_0(U))
& op1(sk0_0(U),op1(sk0_0(U),U)) != U
& op1(U,op1(sk0_0(U),U)) = sk0_0(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),op1(sk0_0(X0),X0)) != X0 ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f15,plain,
! [X0] :
( ~ sorti1(X0)
| op1(X0,op1(sk0_0(X0),X0)) = sk0_0(X0) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f16,plain,
? [U] :
( sorti2(U)
& ! [V] :
( ~ sorti2(V)
| op2(V,op2(V,U)) = U
| op2(U,op2(V,U)) != V ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f17,plain,
( sorti2(sk0_1)
& ! [V] :
( ~ sorti2(V)
| op2(V,op2(V,sk0_1)) = sk0_1
| op2(sk0_1,op2(V,sk0_1)) != V ) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f18,plain,
sorti2(sk0_1),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0] :
( ~ sorti2(X0)
| op2(X0,op2(X0,sk0_1)) = sk0_1
| op2(sk0_1,op2(X0,sk0_1)) != X0 ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f20,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(f21,plain,
! [X0] :
( ~ sorti1(X0)
| sorti2(h(X0)) ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f22,plain,
! [X0] :
( ~ sorti2(X0)
| sorti1(j(X0)) ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f23,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| h(op1(X0,X1)) = op2(h(X0),h(X1)) ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f24,plain,
! [X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| j(op2(X0,X1)) = op1(j(X0),j(X1)) ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f25,plain,
! [X0] :
( ~ sorti2(X0)
| h(j(X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f26,plain,
! [X0] :
( ~ sorti1(X0)
| j(h(X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f28,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,sk0_1)) = op1(j(X0),j(sk0_1)) ),
inference(resolution,[status(thm)],[f18,f24]) ).
fof(f29,plain,
h(j(sk0_1)) = sk0_1,
inference(resolution,[status(thm)],[f18,f25]) ).
fof(f30,plain,
sorti1(j(sk0_1)),
inference(resolution,[status(thm)],[f18,f22]) ).
fof(f32,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(X0,j(sk0_1))) = op2(h(X0),h(j(sk0_1))) ),
inference(resolution,[status(thm)],[f30,f23]) ).
fof(f43,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(X0,j(sk0_1))) = op2(h(X0),sk0_1) ),
inference(forward_demodulation,[status(thm)],[f29,f32]) ).
fof(f49,plain,
sorti1(sk0_0(j(sk0_1))),
inference(resolution,[status(thm)],[f13,f30]) ).
fof(f51,plain,
h(op1(sk0_0(j(sk0_1)),j(sk0_1))) = op2(h(sk0_0(j(sk0_1))),sk0_1),
inference(resolution,[status(thm)],[f49,f43]) ).
fof(f53,plain,
! [X0] :
( ~ sorti1(X0)
| sorti1(op1(sk0_0(j(sk0_1)),X0)) ),
inference(resolution,[status(thm)],[f49,f8]) ).
fof(f55,plain,
j(h(sk0_0(j(sk0_1)))) = sk0_0(j(sk0_1)),
inference(resolution,[status(thm)],[f49,f26]) ).
fof(f56,plain,
sorti2(h(sk0_0(j(sk0_1)))),
inference(resolution,[status(thm)],[f49,f21]) ).
fof(f57,plain,
j(op2(h(sk0_0(j(sk0_1))),sk0_1)) = op1(j(h(sk0_0(j(sk0_1)))),j(sk0_1)),
inference(resolution,[status(thm)],[f56,f28]) ).
fof(f59,plain,
! [X0] :
( ~ sorti2(X0)
| sorti2(op2(h(sk0_0(j(sk0_1))),X0)) ),
inference(resolution,[status(thm)],[f56,f10]) ).
fof(f73,plain,
sorti1(op1(sk0_0(j(sk0_1)),j(sk0_1))),
inference(resolution,[status(thm)],[f53,f30]) ).
fof(f85,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(X0,op1(sk0_0(j(sk0_1)),j(sk0_1)))) = op2(h(X0),h(op1(sk0_0(j(sk0_1)),j(sk0_1)))) ),
inference(resolution,[status(thm)],[f73,f23]) ).
fof(f92,plain,
op1(j(sk0_1),op1(sk0_0(j(sk0_1)),j(sk0_1))) = sk0_0(j(sk0_1)),
inference(resolution,[status(thm)],[f15,f30]) ).
fof(f95,plain,
sorti2(op2(h(sk0_0(j(sk0_1))),sk0_1)),
inference(resolution,[status(thm)],[f59,f18]) ).
fof(f100,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,op2(h(sk0_0(j(sk0_1))),sk0_1))) = op1(j(X0),j(op2(h(sk0_0(j(sk0_1))),sk0_1))) ),
inference(resolution,[status(thm)],[f95,f24]) ).
fof(f119,plain,
( spl0_4
<=> op2(h(sk0_0(j(sk0_1))),op2(h(sk0_0(j(sk0_1))),sk0_1)) = sk0_1 ),
introduced(split_symbol_definition) ).
fof(f120,plain,
( op2(h(sk0_0(j(sk0_1))),op2(h(sk0_0(j(sk0_1))),sk0_1)) = sk0_1
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( spl0_5
<=> op2(sk0_1,op2(h(sk0_0(j(sk0_1))),sk0_1)) = h(sk0_0(j(sk0_1))) ),
introduced(split_symbol_definition) ).
fof(f124,plain,
( op2(sk0_1,op2(h(sk0_0(j(sk0_1))),sk0_1)) != h(sk0_0(j(sk0_1)))
| spl0_5 ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,plain,
( op2(h(sk0_0(j(sk0_1))),op2(h(sk0_0(j(sk0_1))),sk0_1)) = sk0_1
| op2(sk0_1,op2(h(sk0_0(j(sk0_1))),sk0_1)) != h(sk0_0(j(sk0_1))) ),
inference(resolution,[status(thm)],[f19,f56]) ).
fof(f126,plain,
( spl0_4
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f125,f119,f122]) ).
fof(f155,plain,
j(op2(h(sk0_0(j(sk0_1))),sk0_1)) = op1(sk0_0(j(sk0_1)),j(sk0_1)),
inference(forward_demodulation,[status(thm)],[f55,f57]) ).
fof(f203,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(X0,op1(sk0_0(j(sk0_1)),j(sk0_1)))) = op2(h(X0),op2(h(sk0_0(j(sk0_1))),sk0_1)) ),
inference(forward_demodulation,[status(thm)],[f51,f85]) ).
fof(f210,plain,
h(op1(j(sk0_1),op1(sk0_0(j(sk0_1)),j(sk0_1)))) = op2(h(j(sk0_1)),op2(h(sk0_0(j(sk0_1))),sk0_1)),
inference(resolution,[status(thm)],[f203,f30]) ).
fof(f211,plain,
h(sk0_0(j(sk0_1))) = op2(h(j(sk0_1)),op2(h(sk0_0(j(sk0_1))),sk0_1)),
inference(forward_demodulation,[status(thm)],[f92,f210]) ).
fof(f212,plain,
h(sk0_0(j(sk0_1))) = op2(sk0_1,op2(h(sk0_0(j(sk0_1))),sk0_1)),
inference(forward_demodulation,[status(thm)],[f29,f211]) ).
fof(f213,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f212,f124]) ).
fof(f214,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f213]) ).
fof(f215,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,op2(h(sk0_0(j(sk0_1))),sk0_1))) = op1(j(X0),op1(sk0_0(j(sk0_1)),j(sk0_1))) ),
inference(forward_demodulation,[status(thm)],[f155,f100]) ).
fof(f221,plain,
j(op2(h(sk0_0(j(sk0_1))),op2(h(sk0_0(j(sk0_1))),sk0_1))) = op1(j(h(sk0_0(j(sk0_1)))),op1(sk0_0(j(sk0_1)),j(sk0_1))),
inference(resolution,[status(thm)],[f215,f56]) ).
fof(f222,plain,
( j(sk0_1) = op1(j(h(sk0_0(j(sk0_1)))),op1(sk0_0(j(sk0_1)),j(sk0_1)))
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f120,f221]) ).
fof(f223,plain,
( j(sk0_1) = op1(sk0_0(j(sk0_1)),op1(sk0_0(j(sk0_1)),j(sk0_1)))
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f55,f222]) ).
fof(f227,plain,
( ~ sorti1(j(sk0_1))
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f223,f14]) ).
fof(f228,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f227,f30]) ).
fof(f229,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f228]) ).
fof(f230,plain,
$false,
inference(sat_refutation,[status(thm)],[f126,f214,f229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.13 % Problem : ALG071+1 : TPTP v8.1.2. Released v2.7.0.
% 0.02/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.34 % Computer : n027.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8042.1875MB
% 0.10/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Mon Apr 29 23:57:17 EDT 2024
% 0.10/0.34 % CPUTime :
% 0.10/0.35 % Drodi V3.6.0
% 0.10/0.37 % Refutation found
% 0.10/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.38 % Elapsed time: 0.028044 seconds
% 0.16/0.38 % CPU time: 0.085632 seconds
% 0.16/0.38 % Total memory used: 9.867 MB
% 0.16/0.38 % Net memory used: 9.774 MB
%------------------------------------------------------------------------------