TSTP Solution File: SEU420+2 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU420+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n023.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 : Wed May 31 12:37:01 EDT 2023
% Result : Theorem 0.65s 1.08s
% Output : CNFRefutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 52 ( 13 unt; 0 def)
% Number of atoms : 116 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 44 ~; 41 |; 7 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 54 (; 48 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f57,axiom,
! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [A,B] : r1_tarski(k3_xboole_0(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f88,axiom,
! [A,B,C] :
( ( r1_tarski(A,B)
& r1_tarski(A,C) )
=> r1_tarski(A,k3_xboole_0(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f563,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( r1_tarski(A,B)
=> v1_relat_1(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f729,axiom,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> ( r1_tarski(B,C)
=> r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4482,conjecture,
! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> r1_tarski(k9_relat_1(k3_xboole_0(B,C),k3_pua2mss1(A)),k3_xboole_0(k9_relat_1(B,k3_pua2mss1(A)),k9_relat_1(C,k3_pua2mss1(A)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4483,negated_conjecture,
~ ! [A,B] :
( v1_relat_1(B)
=> ! [C] :
( v1_relat_1(C)
=> r1_tarski(k9_relat_1(k3_xboole_0(B,C),k3_pua2mss1(A)),k3_xboole_0(k9_relat_1(B,k3_pua2mss1(A)),k9_relat_1(C,k3_pua2mss1(A)))) ) ),
inference(negated_conjecture,[status(cth)],[f4482]) ).
fof(f4692,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f4743,plain,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f4747,plain,
! [A,B,C] :
( ~ r1_tarski(A,B)
| ~ r1_tarski(A,C)
| r1_tarski(A,k3_xboole_0(B,C)) ),
inference(pre_NNF_transformation,[status(esa)],[f88]) ).
fof(f4748,plain,
! [X0,X1,X2] :
( ~ r1_tarski(X0,X1)
| ~ r1_tarski(X0,X2)
| r1_tarski(X0,k3_xboole_0(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f4747]) ).
fof(f5876,plain,
! [A,B] :
( ~ v1_relat_1(B)
| ~ r1_tarski(A,B)
| v1_relat_1(A) ),
inference(pre_NNF_transformation,[status(esa)],[f563]) ).
fof(f5877,plain,
! [B] :
( ~ v1_relat_1(B)
| ! [A] :
( ~ r1_tarski(A,B)
| v1_relat_1(A) ) ),
inference(miniscoping,[status(esa)],[f5876]) ).
fof(f5878,plain,
! [X0,X1] :
( ~ v1_relat_1(X0)
| ~ r1_tarski(X1,X0)
| v1_relat_1(X1) ),
inference(cnf_transformation,[status(esa)],[f5877]) ).
fof(f6333,plain,
! [A,B] :
( ~ v1_relat_1(B)
| ! [C] :
( ~ v1_relat_1(C)
| ~ r1_tarski(B,C)
| r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f729]) ).
fof(f6334,plain,
! [B] :
( ~ v1_relat_1(B)
| ! [C] :
( ~ v1_relat_1(C)
| ~ r1_tarski(B,C)
| ! [A] : r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A)) ) ),
inference(miniscoping,[status(esa)],[f6333]) ).
fof(f6335,plain,
! [X0,X1,X2] :
( ~ v1_relat_1(X0)
| ~ v1_relat_1(X1)
| ~ r1_tarski(X0,X1)
| r1_tarski(k9_relat_1(X0,X2),k9_relat_1(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f6334]) ).
fof(f17518,plain,
? [A,B] :
( v1_relat_1(B)
& ? [C] :
( v1_relat_1(C)
& ~ r1_tarski(k9_relat_1(k3_xboole_0(B,C),k3_pua2mss1(A)),k3_xboole_0(k9_relat_1(B,k3_pua2mss1(A)),k9_relat_1(C,k3_pua2mss1(A)))) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4483]) ).
fof(f17519,plain,
? [B] :
( v1_relat_1(B)
& ? [C] :
( v1_relat_1(C)
& ? [A] : ~ r1_tarski(k9_relat_1(k3_xboole_0(B,C),k3_pua2mss1(A)),k3_xboole_0(k9_relat_1(B,k3_pua2mss1(A)),k9_relat_1(C,k3_pua2mss1(A)))) ) ),
inference(miniscoping,[status(esa)],[f17518]) ).
fof(f17520,plain,
( v1_relat_1(sk0_1204)
& v1_relat_1(sk0_1205)
& ~ r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k3_xboole_0(k9_relat_1(sk0_1204,k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1205,k3_pua2mss1(sk0_1206)))) ),
inference(skolemization,[status(esa)],[f17519]) ).
fof(f17521,plain,
v1_relat_1(sk0_1204),
inference(cnf_transformation,[status(esa)],[f17520]) ).
fof(f17522,plain,
v1_relat_1(sk0_1205),
inference(cnf_transformation,[status(esa)],[f17520]) ).
fof(f17523,plain,
~ r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k3_xboole_0(k9_relat_1(sk0_1204,k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1205,k3_pua2mss1(sk0_1206)))),
inference(cnf_transformation,[status(esa)],[f17520]) ).
fof(f21722,plain,
! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X1),
inference(paramodulation,[status(thm)],[f4692,f4743]) ).
fof(f21874,plain,
( spl0_623
<=> r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1204,k3_pua2mss1(sk0_1206))) ),
introduced(split_symbol_definition) ).
fof(f21876,plain,
( ~ r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1204,k3_pua2mss1(sk0_1206)))
| spl0_623 ),
inference(component_clause,[status(thm)],[f21874]) ).
fof(f21877,plain,
( spl0_624
<=> r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1205,k3_pua2mss1(sk0_1206))) ),
introduced(split_symbol_definition) ).
fof(f21879,plain,
( ~ r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1205,k3_pua2mss1(sk0_1206)))
| spl0_624 ),
inference(component_clause,[status(thm)],[f21877]) ).
fof(f21880,plain,
( ~ r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1204,k3_pua2mss1(sk0_1206)))
| ~ r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1205,k3_pua2mss1(sk0_1206))) ),
inference(resolution,[status(thm)],[f4748,f17523]) ).
fof(f21881,plain,
( ~ spl0_623
| ~ spl0_624 ),
inference(split_clause,[status(thm)],[f21880,f21874,f21877]) ).
fof(f25917,plain,
! [X0,X1,X2] :
( ~ v1_relat_1(X0)
| ~ r1_tarski(X1,X0)
| r1_tarski(k9_relat_1(X1,X2),k9_relat_1(X0,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f6335,f5878]) ).
fof(f25918,plain,
( spl0_774
<=> v1_relat_1(sk0_1205) ),
introduced(split_symbol_definition) ).
fof(f25920,plain,
( ~ v1_relat_1(sk0_1205)
| spl0_774 ),
inference(component_clause,[status(thm)],[f25918]) ).
fof(f25921,plain,
( spl0_775
<=> r1_tarski(k3_xboole_0(sk0_1204,sk0_1205),sk0_1205) ),
introduced(split_symbol_definition) ).
fof(f25923,plain,
( ~ r1_tarski(k3_xboole_0(sk0_1204,sk0_1205),sk0_1205)
| spl0_775 ),
inference(component_clause,[status(thm)],[f25921]) ).
fof(f25924,plain,
( ~ v1_relat_1(sk0_1205)
| ~ r1_tarski(k3_xboole_0(sk0_1204,sk0_1205),sk0_1205)
| spl0_624 ),
inference(resolution,[status(thm)],[f25917,f21879]) ).
fof(f25925,plain,
( ~ spl0_774
| ~ spl0_775
| spl0_624 ),
inference(split_clause,[status(thm)],[f25924,f25918,f25921,f21877]) ).
fof(f25926,plain,
( spl0_776
<=> v1_relat_1(sk0_1204) ),
introduced(split_symbol_definition) ).
fof(f25928,plain,
( ~ v1_relat_1(sk0_1204)
| spl0_776 ),
inference(component_clause,[status(thm)],[f25926]) ).
fof(f25929,plain,
( spl0_777
<=> r1_tarski(k3_xboole_0(sk0_1204,sk0_1205),sk0_1204) ),
introduced(split_symbol_definition) ).
fof(f25931,plain,
( ~ r1_tarski(k3_xboole_0(sk0_1204,sk0_1205),sk0_1204)
| spl0_777 ),
inference(component_clause,[status(thm)],[f25929]) ).
fof(f25932,plain,
( ~ v1_relat_1(sk0_1204)
| ~ r1_tarski(k3_xboole_0(sk0_1204,sk0_1205),sk0_1204)
| spl0_623 ),
inference(resolution,[status(thm)],[f25917,f21876]) ).
fof(f25933,plain,
( ~ spl0_776
| ~ spl0_777
| spl0_623 ),
inference(split_clause,[status(thm)],[f25932,f25926,f25929,f21874]) ).
fof(f25945,plain,
( $false
| spl0_776 ),
inference(forward_subsumption_resolution,[status(thm)],[f25928,f17521]) ).
fof(f25946,plain,
spl0_776,
inference(contradiction_clause,[status(thm)],[f25945]) ).
fof(f25947,plain,
( $false
| spl0_777 ),
inference(forward_subsumption_resolution,[status(thm)],[f25931,f4743]) ).
fof(f25948,plain,
spl0_777,
inference(contradiction_clause,[status(thm)],[f25947]) ).
fof(f25949,plain,
( $false
| spl0_775 ),
inference(forward_subsumption_resolution,[status(thm)],[f25923,f21722]) ).
fof(f25950,plain,
spl0_775,
inference(contradiction_clause,[status(thm)],[f25949]) ).
fof(f25951,plain,
( $false
| spl0_774 ),
inference(forward_subsumption_resolution,[status(thm)],[f25920,f17522]) ).
fof(f25952,plain,
spl0_774,
inference(contradiction_clause,[status(thm)],[f25951]) ).
fof(f25953,plain,
$false,
inference(sat_refutation,[status(thm)],[f21881,f25925,f25933,f25946,f25948,f25950,f25952]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU420+2 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n023.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 : Tue May 30 09:37:08 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.46/0.66 % Drodi V3.5.1
% 0.65/1.08 % Refutation found
% 0.65/1.08 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.65/1.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.04/1.18 % Elapsed time: 0.849655 seconds
% 3.04/1.18 % CPU time: 3.515390 seconds
% 3.04/1.18 % Memory used: 658.922 MB
%------------------------------------------------------------------------------