TSTP Solution File: SEU110+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU110+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.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 20:41:02 EDT 2024
% Result : Theorem 3.69s 0.85s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 7 unt; 0 def)
% Number of atoms : 170 ( 11 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 196 ( 76 ~; 81 |; 26 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 95 ( 89 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : preboolean(finite_subsets(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f50,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f51,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f51]) ).
fof(f53,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_0(B,A),A)
& ~ in(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f52]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f57,plain,
! [A,B] :
( ~ preboolean(B)
| ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f58,plain,
! [A,B] :
( ~ preboolean(B)
| ( ( B != finite_subsets(A)
| ! [C] :
( ( ~ in(C,B)
| ( subset(C,A)
& finite(C) ) )
& ( in(C,B)
| ~ subset(C,A)
| ~ finite(C) ) ) )
& ( B = finite_subsets(A)
| ? [C] :
( ( ~ in(C,B)
| ~ subset(C,A)
| ~ finite(C) )
& ( in(C,B)
| ( subset(C,A)
& finite(C) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f57]) ).
fof(f59,plain,
! [B] :
( ~ preboolean(B)
| ( ! [A] :
( B != finite_subsets(A)
| ( ! [C] :
( ~ in(C,B)
| ( subset(C,A)
& finite(C) ) )
& ! [C] :
( in(C,B)
| ~ subset(C,A)
| ~ finite(C) ) ) )
& ! [A] :
( B = finite_subsets(A)
| ? [C] :
( ( ~ in(C,B)
| ~ subset(C,A)
| ~ finite(C) )
& ( in(C,B)
| ( subset(C,A)
& finite(C) ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f58]) ).
fof(f60,plain,
! [B] :
( ~ preboolean(B)
| ( ! [A] :
( B != finite_subsets(A)
| ( ! [C] :
( ~ in(C,B)
| ( subset(C,A)
& finite(C) ) )
& ! [C] :
( in(C,B)
| ~ subset(C,A)
| ~ finite(C) ) ) )
& ! [A] :
( B = finite_subsets(A)
| ( ( ~ in(sk0_1(A,B),B)
| ~ subset(sk0_1(A,B),A)
| ~ finite(sk0_1(A,B)) )
& ( in(sk0_1(A,B),B)
| ( subset(sk0_1(A,B),A)
& finite(sk0_1(A,B)) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ preboolean(X0)
| X0 != finite_subsets(X1)
| ~ in(X2,X0)
| subset(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ preboolean(X0)
| X0 != finite_subsets(X1)
| ~ in(X2,X0)
| finite(X2) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ preboolean(X0)
| X0 != finite_subsets(X1)
| in(X2,X0)
| ~ subset(X2,X1)
| ~ finite(X2) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f67,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f127,plain,
! [A,B,C] :
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(pre_NNF_transformation,[status(esa)],[f26]) ).
fof(f128,plain,
! [A,C] :
( ! [B] :
( ~ subset(A,B)
| ~ subset(B,C) )
| subset(A,C) ),
inference(miniscoping,[status(esa)],[f127]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| subset(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f128]) ).
fof(f130,plain,
? [A,B] :
( subset(A,B)
& ~ subset(finite_subsets(A),finite_subsets(B)) ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f131,plain,
( subset(sk0_12,sk0_13)
& ~ subset(finite_subsets(sk0_12),finite_subsets(sk0_13)) ),
inference(skolemization,[status(esa)],[f130]) ).
fof(f132,plain,
subset(sk0_12,sk0_13),
inference(cnf_transformation,[status(esa)],[f131]) ).
fof(f133,plain,
~ subset(finite_subsets(sk0_12),finite_subsets(sk0_13)),
inference(cnf_transformation,[status(esa)],[f131]) ).
fof(f154,plain,
! [X0,X1] :
( ~ preboolean(finite_subsets(X0))
| ~ in(X1,finite_subsets(X0))
| subset(X1,X0) ),
inference(destructive_equality_resolution,[status(esa)],[f61]) ).
fof(f155,plain,
! [X0,X1] :
( ~ preboolean(finite_subsets(X0))
| ~ in(X1,finite_subsets(X0))
| finite(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f62]) ).
fof(f156,plain,
! [X0,X1] :
( ~ preboolean(finite_subsets(X0))
| in(X1,finite_subsets(X0))
| ~ subset(X1,X0)
| ~ finite(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f63]) ).
fof(f158,plain,
! [X0] :
( ~ subset(X0,sk0_12)
| subset(X0,sk0_13) ),
inference(resolution,[status(thm)],[f129,f132]) ).
fof(f1485,plain,
! [X0,X1] :
( ~ in(X0,finite_subsets(X1))
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f67]) ).
fof(f1487,plain,
! [X0,X1] :
( subset(sk0_0(X0,finite_subsets(X1)),X1)
| subset(finite_subsets(X1),X0) ),
inference(resolution,[status(thm)],[f1485,f55]) ).
fof(f1488,plain,
! [X0,X1] :
( ~ in(X0,finite_subsets(X1))
| finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f67]) ).
fof(f1490,plain,
! [X0,X1] :
( finite(sk0_0(X0,finite_subsets(X1)))
| subset(finite_subsets(X1),X0) ),
inference(resolution,[status(thm)],[f1488,f55]) ).
fof(f1491,plain,
! [X0,X1] :
( in(X0,finite_subsets(X1))
| ~ subset(X0,X1)
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f67]) ).
fof(f1493,plain,
! [X0,X1] :
( ~ subset(sk0_0(finite_subsets(X0),X1),X0)
| ~ finite(sk0_0(finite_subsets(X0),X1))
| subset(X1,finite_subsets(X0)) ),
inference(resolution,[status(thm)],[f1491,f56]) ).
fof(f4760,plain,
! [X0] :
( subset(finite_subsets(sk0_12),X0)
| subset(sk0_0(X0,finite_subsets(sk0_12)),sk0_13) ),
inference(resolution,[status(thm)],[f1487,f158]) ).
fof(f5237,plain,
( spl0_454
<=> finite(sk0_0(finite_subsets(sk0_13),finite_subsets(sk0_12))) ),
introduced(split_symbol_definition) ).
fof(f5239,plain,
( ~ finite(sk0_0(finite_subsets(sk0_13),finite_subsets(sk0_12)))
| spl0_454 ),
inference(component_clause,[status(thm)],[f5237]) ).
fof(f5240,plain,
( spl0_455
<=> subset(finite_subsets(sk0_12),finite_subsets(sk0_13)) ),
introduced(split_symbol_definition) ).
fof(f5241,plain,
( subset(finite_subsets(sk0_12),finite_subsets(sk0_13))
| ~ spl0_455 ),
inference(component_clause,[status(thm)],[f5240]) ).
fof(f5243,plain,
( ~ finite(sk0_0(finite_subsets(sk0_13),finite_subsets(sk0_12)))
| subset(finite_subsets(sk0_12),finite_subsets(sk0_13))
| subset(finite_subsets(sk0_12),finite_subsets(sk0_13)) ),
inference(resolution,[status(thm)],[f1493,f4760]) ).
fof(f5244,plain,
( ~ spl0_454
| spl0_455 ),
inference(split_clause,[status(thm)],[f5243,f5237,f5240]) ).
fof(f5362,plain,
( subset(finite_subsets(sk0_12),finite_subsets(sk0_13))
| spl0_454 ),
inference(resolution,[status(thm)],[f5239,f1490]) ).
fof(f5363,plain,
( $false
| spl0_454 ),
inference(forward_subsumption_resolution,[status(thm)],[f5362,f133]) ).
fof(f5364,plain,
spl0_454,
inference(contradiction_clause,[status(thm)],[f5363]) ).
fof(f5365,plain,
( $false
| ~ spl0_455 ),
inference(forward_subsumption_resolution,[status(thm)],[f5241,f133]) ).
fof(f5366,plain,
~ spl0_455,
inference(contradiction_clause,[status(thm)],[f5365]) ).
fof(f5367,plain,
$false,
inference(sat_refutation,[status(thm)],[f5244,f5364,f5366]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SEU110+1 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n005.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 19:44:26 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % Drodi V3.6.0
% 3.69/0.85 % Refutation found
% 3.69/0.85 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.69/0.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.69/0.88 % Elapsed time: 0.550373 seconds
% 3.69/0.88 % CPU time: 4.194538 seconds
% 3.69/0.88 % Total memory used: 81.055 MB
% 3.69/0.88 % Net memory used: 79.139 MB
%------------------------------------------------------------------------------