TSTP Solution File: SEU422+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU422+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 20:42:18 EDT 2024
% Result : Theorem 40.90s 5.86s
% Output : CNFRefutation 41.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 25 unt; 0 def)
% Number of atoms : 178 ( 24 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 174 ( 71 ~; 65 |; 21 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 128 ( 122 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B] :
( r1_tarski(A,B)
<=> ! [C] :
( r2_hidden(C,A)
=> r2_hidden(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [A] : k4_xboole_0(A,k1_xboole_0) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [A,B,C] :
( r1_tarski(A,B)
=> r1_tarski(A,k2_xboole_0(C,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [A,B] :
( r1_tarski(A,B)
=> k2_xboole_0(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f105,axiom,
! [A,B] : r1_tarski(k4_xboole_0(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f185,axiom,
! [A,B] :
( B = k1_zfmisc_1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> r1_tarski(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f267,axiom,
! [A,B] :
( r1_tarski(A,B)
=> r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f288,axiom,
! [A] : r1_tarski(A,k1_zfmisc_1(k3_tarski(A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f540,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4486,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> B = k3_tarski(a_2_0_relset_2(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4487,conjecture,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> m1_subset_1(a_2_0_relset_2(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4488,negated_conjecture,
~ ! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> m1_subset_1(a_2_0_relset_2(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
inference(negated_conjecture,[status(cth)],[f4487]) ).
fof(f4512,plain,
! [A,B] :
( r1_tarski(A,B)
<=> ! [C] :
( ~ r2_hidden(C,A)
| r2_hidden(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f4513,plain,
! [A,B] :
( ( ~ r1_tarski(A,B)
| ! [C] :
( ~ r2_hidden(C,A)
| r2_hidden(C,B) ) )
& ( r1_tarski(A,B)
| ? [C] :
( r2_hidden(C,A)
& ~ r2_hidden(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f4512]) ).
fof(f4514,plain,
( ! [A,B] :
( ~ r1_tarski(A,B)
| ! [C] :
( ~ r2_hidden(C,A)
| r2_hidden(C,B) ) )
& ! [A,B] :
( r1_tarski(A,B)
| ? [C] :
( r2_hidden(C,A)
& ~ r2_hidden(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f4513]) ).
fof(f4515,plain,
( ! [A,B] :
( ~ r1_tarski(A,B)
| ! [C] :
( ~ r2_hidden(C,A)
| r2_hidden(C,B) ) )
& ! [A,B] :
( r1_tarski(A,B)
| ( r2_hidden(sk0_3(B,A),A)
& ~ r2_hidden(sk0_3(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f4514]) ).
fof(f4516,plain,
! [X0,X1,X2] :
( ~ r1_tarski(X0,X1)
| ~ r2_hidden(X2,X0)
| r2_hidden(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f4515]) ).
fof(f4694,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f4703,plain,
! [X0] : k4_xboole_0(X0,k1_xboole_0) = X0,
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f4729,plain,
! [A,B,C] :
( ~ r1_tarski(A,B)
| r1_tarski(A,k2_xboole_0(C,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f79]) ).
fof(f4730,plain,
! [A,B] :
( ~ r1_tarski(A,B)
| ! [C] : r1_tarski(A,k2_xboole_0(C,B)) ),
inference(miniscoping,[status(esa)],[f4729]) ).
fof(f4731,plain,
! [X0,X1,X2] :
( ~ r1_tarski(X0,X1)
| r1_tarski(X0,k2_xboole_0(X2,X1)) ),
inference(cnf_transformation,[status(esa)],[f4730]) ).
fof(f4735,plain,
! [A,B] :
( ~ r1_tarski(A,B)
| k2_xboole_0(A,B) = B ),
inference(pre_NNF_transformation,[status(esa)],[f81]) ).
fof(f4736,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| k2_xboole_0(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f4735]) ).
fof(f4786,plain,
! [X0,X1] : r1_tarski(k4_xboole_0(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f105]) ).
fof(f4947,plain,
! [A,B] :
( ( B != k1_zfmisc_1(A)
| ! [C] :
( ( ~ r2_hidden(C,B)
| r1_tarski(C,A) )
& ( r2_hidden(C,B)
| ~ r1_tarski(C,A) ) ) )
& ( B = k1_zfmisc_1(A)
| ? [C] :
( ( ~ r2_hidden(C,B)
| ~ r1_tarski(C,A) )
& ( r2_hidden(C,B)
| r1_tarski(C,A) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f185]) ).
fof(f4948,plain,
( ! [A,B] :
( B != k1_zfmisc_1(A)
| ( ! [C] :
( ~ r2_hidden(C,B)
| r1_tarski(C,A) )
& ! [C] :
( r2_hidden(C,B)
| ~ r1_tarski(C,A) ) ) )
& ! [A,B] :
( B = k1_zfmisc_1(A)
| ? [C] :
( ( ~ r2_hidden(C,B)
| ~ r1_tarski(C,A) )
& ( r2_hidden(C,B)
| r1_tarski(C,A) ) ) ) ),
inference(miniscoping,[status(esa)],[f4947]) ).
fof(f4949,plain,
( ! [A,B] :
( B != k1_zfmisc_1(A)
| ( ! [C] :
( ~ r2_hidden(C,B)
| r1_tarski(C,A) )
& ! [C] :
( r2_hidden(C,B)
| ~ r1_tarski(C,A) ) ) )
& ! [A,B] :
( B = k1_zfmisc_1(A)
| ( ( ~ r2_hidden(sk0_36(B,A),B)
| ~ r1_tarski(sk0_36(B,A),A) )
& ( r2_hidden(sk0_36(B,A),B)
| r1_tarski(sk0_36(B,A),A) ) ) ) ),
inference(skolemization,[status(esa)],[f4948]) ).
fof(f4950,plain,
! [X0,X1,X2] :
( X0 != k1_zfmisc_1(X1)
| ~ r2_hidden(X2,X0)
| r1_tarski(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f4949]) ).
fof(f4951,plain,
! [X0,X1,X2] :
( X0 != k1_zfmisc_1(X1)
| r2_hidden(X2,X0)
| ~ r1_tarski(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f4949]) ).
fof(f5149,plain,
! [A,B] :
( ~ r1_tarski(A,B)
| r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)) ),
inference(pre_NNF_transformation,[status(esa)],[f267]) ).
fof(f5150,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| r1_tarski(k1_zfmisc_1(X0),k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[status(esa)],[f5149]) ).
fof(f5174,plain,
! [X0] : r1_tarski(X0,k1_zfmisc_1(k3_tarski(X0))),
inference(cnf_transformation,[status(esa)],[f288]) ).
fof(f5819,plain,
! [A,B] :
( ( ~ m1_subset_1(A,k1_zfmisc_1(B))
| r1_tarski(A,B) )
& ( m1_subset_1(A,k1_zfmisc_1(B))
| ~ r1_tarski(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f540]) ).
fof(f5820,plain,
( ! [A,B] :
( ~ m1_subset_1(A,k1_zfmisc_1(B))
| r1_tarski(A,B) )
& ! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
| ~ r1_tarski(A,B) ) ),
inference(miniscoping,[status(esa)],[f5819]) ).
fof(f5821,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5820]) ).
fof(f5822,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5820]) ).
fof(f17538,plain,
! [A] :
( v1_xboole_0(A)
| ! [B] :
( ~ m1_subset_1(B,k1_zfmisc_1(A))
| B = k3_tarski(a_2_0_relset_2(A,B)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4486]) ).
fof(f17539,plain,
! [X0,X1] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| X1 = k3_tarski(a_2_0_relset_2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f17538]) ).
fof(f17540,plain,
? [A] :
( ~ v1_xboole_0(A)
& ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ m1_subset_1(a_2_0_relset_2(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4488]) ).
fof(f17541,plain,
( ~ v1_xboole_0(sk0_1205)
& m1_subset_1(sk0_1206,k1_zfmisc_1(sk0_1205))
& ~ m1_subset_1(a_2_0_relset_2(sk0_1205,sk0_1206),k1_zfmisc_1(k1_zfmisc_1(sk0_1205))) ),
inference(skolemization,[status(esa)],[f17540]) ).
fof(f17542,plain,
~ v1_xboole_0(sk0_1205),
inference(cnf_transformation,[status(esa)],[f17541]) ).
fof(f17543,plain,
m1_subset_1(sk0_1206,k1_zfmisc_1(sk0_1205)),
inference(cnf_transformation,[status(esa)],[f17541]) ).
fof(f17544,plain,
~ m1_subset_1(a_2_0_relset_2(sk0_1205,sk0_1206),k1_zfmisc_1(k1_zfmisc_1(sk0_1205))),
inference(cnf_transformation,[status(esa)],[f17541]) ).
fof(f20831,plain,
! [X0,X1] :
( ~ r2_hidden(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f4950]) ).
fof(f20832,plain,
! [X0,X1] :
( r2_hidden(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f4951]) ).
fof(f21745,plain,
r1_tarski(sk0_1206,sk0_1205),
inference(resolution,[status(thm)],[f5821,f17543]) ).
fof(f21761,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| r2_hidden(k1_zfmisc_1(X0),k1_zfmisc_1(k1_zfmisc_1(X1))) ),
inference(resolution,[status(thm)],[f5150,f20832]) ).
fof(f21781,plain,
r2_hidden(k1_zfmisc_1(sk0_1206),k1_zfmisc_1(k1_zfmisc_1(sk0_1205))),
inference(resolution,[status(thm)],[f21761,f21745]) ).
fof(f21782,plain,
r1_tarski(k1_zfmisc_1(sk0_1206),k1_zfmisc_1(sk0_1205)),
inference(resolution,[status(thm)],[f21781,f20831]) ).
fof(f21889,plain,
~ r1_tarski(a_2_0_relset_2(sk0_1205,sk0_1206),k1_zfmisc_1(sk0_1205)),
inference(resolution,[status(thm)],[f5822,f17544]) ).
fof(f21960,plain,
( spl0_641
<=> v1_xboole_0(sk0_1205) ),
introduced(split_symbol_definition) ).
fof(f21961,plain,
( v1_xboole_0(sk0_1205)
| ~ spl0_641 ),
inference(component_clause,[status(thm)],[f21960]) ).
fof(f21963,plain,
( spl0_642
<=> sk0_1206 = k3_tarski(a_2_0_relset_2(sk0_1205,sk0_1206)) ),
introduced(split_symbol_definition) ).
fof(f21964,plain,
( sk0_1206 = k3_tarski(a_2_0_relset_2(sk0_1205,sk0_1206))
| ~ spl0_642 ),
inference(component_clause,[status(thm)],[f21963]) ).
fof(f21966,plain,
( v1_xboole_0(sk0_1205)
| sk0_1206 = k3_tarski(a_2_0_relset_2(sk0_1205,sk0_1206)) ),
inference(resolution,[status(thm)],[f17539,f17543]) ).
fof(f21967,plain,
( spl0_641
| spl0_642 ),
inference(split_clause,[status(thm)],[f21966,f21960,f21963]) ).
fof(f21969,plain,
( $false
| ~ spl0_641 ),
inference(forward_subsumption_resolution,[status(thm)],[f21961,f17542]) ).
fof(f21970,plain,
~ spl0_641,
inference(contradiction_clause,[status(thm)],[f21969]) ).
fof(f24250,plain,
! [X0,X1] : r2_hidden(k4_xboole_0(X0,X1),k1_zfmisc_1(X0)),
inference(resolution,[status(thm)],[f4786,f20832]) ).
fof(f24509,plain,
! [X0] :
( ~ r2_hidden(X0,k1_zfmisc_1(sk0_1206))
| r2_hidden(X0,k1_zfmisc_1(sk0_1205)) ),
inference(resolution,[status(thm)],[f21782,f4516]) ).
fof(f25786,plain,
( r1_tarski(a_2_0_relset_2(sk0_1205,sk0_1206),k1_zfmisc_1(sk0_1206))
| ~ spl0_642 ),
inference(paramodulation,[status(thm)],[f21964,f5174]) ).
fof(f26510,plain,
! [X0] : r2_hidden(k4_xboole_0(sk0_1206,X0),k1_zfmisc_1(sk0_1205)),
inference(resolution,[status(thm)],[f24509,f24250]) ).
fof(f26541,plain,
! [X0] : r1_tarski(k4_xboole_0(sk0_1206,X0),sk0_1205),
inference(resolution,[status(thm)],[f26510,f20831]) ).
fof(f26551,plain,
! [X0] : r2_hidden(k1_zfmisc_1(k4_xboole_0(sk0_1206,X0)),k1_zfmisc_1(k1_zfmisc_1(sk0_1205))),
inference(resolution,[status(thm)],[f26541,f21761]) ).
fof(f26563,plain,
! [X0] : r1_tarski(k1_zfmisc_1(k4_xboole_0(sk0_1206,X0)),k1_zfmisc_1(sk0_1205)),
inference(resolution,[status(thm)],[f26551,f20831]) ).
fof(f33794,plain,
! [X0] : k2_xboole_0(k1_zfmisc_1(k4_xboole_0(sk0_1206,X0)),k1_zfmisc_1(sk0_1205)) = k1_zfmisc_1(sk0_1205),
inference(resolution,[status(thm)],[f4736,f26563]) ).
fof(f33795,plain,
! [X0] : k2_xboole_0(k1_zfmisc_1(sk0_1205),k1_zfmisc_1(k4_xboole_0(sk0_1206,X0))) = k1_zfmisc_1(sk0_1205),
inference(forward_demodulation,[status(thm)],[f4694,f33794]) ).
fof(f34042,plain,
! [X0,X1] :
( ~ r1_tarski(X0,k1_zfmisc_1(k4_xboole_0(sk0_1206,X1)))
| r1_tarski(X0,k1_zfmisc_1(sk0_1205)) ),
inference(paramodulation,[status(thm)],[f33795,f4731]) ).
fof(f34074,plain,
! [X0] :
( ~ r1_tarski(X0,k1_zfmisc_1(sk0_1206))
| r1_tarski(X0,k1_zfmisc_1(sk0_1205)) ),
inference(paramodulation,[status(thm)],[f4703,f34042]) ).
fof(f34548,plain,
( r1_tarski(a_2_0_relset_2(sk0_1205,sk0_1206),k1_zfmisc_1(sk0_1205))
| ~ spl0_642 ),
inference(resolution,[status(thm)],[f25786,f34074]) ).
fof(f34549,plain,
( $false
| ~ spl0_642 ),
inference(forward_subsumption_resolution,[status(thm)],[f34548,f21889]) ).
fof(f34550,plain,
~ spl0_642,
inference(contradiction_clause,[status(thm)],[f34549]) ).
fof(f34551,plain,
$false,
inference(sat_refutation,[status(thm)],[f21967,f21970,f34550]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU422+2 : TPTP v8.1.2. Released v3.4.0.
% 0.08/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.33 % Computer : n032.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Mon Apr 29 19:48:51 EDT 2024
% 0.10/0.33 % CPUTime :
% 0.43/0.67 % Drodi V3.6.0
% 40.90/5.86 % Refutation found
% 40.90/5.86 % SZS status Theorem for theBenchmark: Theorem is valid
% 40.90/5.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 42.39/6.03 % Elapsed time: 5.677651 seconds
% 42.39/6.03 % CPU time: 41.922589 seconds
% 42.39/6.03 % Total memory used: 837.087 MB
% 42.39/6.03 % Net memory used: 828.731 MB
%------------------------------------------------------------------------------