TSTP Solution File: ALG226+3 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ALG226+3 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 20:11:08 EDT 2024
% Result : Theorem 64.20s 9.80s
% Output : CNFRefutation 67.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 11 unt; 0 def)
% Number of atoms : 124 ( 30 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 127 ( 47 ~; 41 |; 23 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5405,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ( r6_pboole(A,B,C)
<=> B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16950,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> B = k1_funct_4(k1_pboole(A),k7_relat_1(B,k1_closure3(A,B))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16951,conjecture,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,A) )
=> ( ( k1_closure3(A,B) = k1_closure3(A,C)
& k7_relat_1(B,k1_closure3(A,B)) = k7_relat_1(C,k1_closure3(A,C)) )
=> r6_pboole(A,B,C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16952,negated_conjecture,
~ ! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,A) )
=> ( ( k1_closure3(A,B) = k1_closure3(A,C)
& k7_relat_1(B,k1_closure3(A,B)) = k7_relat_1(C,k1_closure3(A,C)) )
=> r6_pboole(A,B,C) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16951]) ).
fof(f33054,plain,
! [A,B,C] :
( ~ m1_pboole(B,A)
| ~ m1_pboole(C,A)
| ( r6_pboole(A,B,C)
<=> B = C ) ),
inference(pre_NNF_transformation,[status(esa)],[f5405]) ).
fof(f33055,plain,
! [A,B,C] :
( ~ m1_pboole(B,A)
| ~ m1_pboole(C,A)
| ( ( ~ r6_pboole(A,B,C)
| B = C )
& ( r6_pboole(A,B,C)
| B != C ) ) ),
inference(NNF_transformation,[status(esa)],[f33054]) ).
fof(f33057,plain,
! [X0,X1,X2] :
( ~ m1_pboole(X0,X1)
| ~ m1_pboole(X2,X1)
| r6_pboole(X1,X0,X2)
| X0 != X2 ),
inference(cnf_transformation,[status(esa)],[f33055]) ).
fof(f75975,plain,
! [A] :
( v1_xboole_0(A)
| ! [B] :
( ~ v2_relat_1(B)
| ~ m1_pboole(B,A)
| B = k1_funct_4(k1_pboole(A),k7_relat_1(B,k1_closure3(A,B))) ) ),
inference(pre_NNF_transformation,[status(esa)],[f16950]) ).
fof(f75976,plain,
! [X0,X1] :
( v1_xboole_0(X0)
| ~ v2_relat_1(X1)
| ~ m1_pboole(X1,X0)
| X1 = k1_funct_4(k1_pboole(X0),k7_relat_1(X1,k1_closure3(X0,X1))) ),
inference(cnf_transformation,[status(esa)],[f75975]) ).
fof(f75977,plain,
? [A] :
( ~ v1_xboole_0(A)
& ? [B] :
( v2_relat_1(B)
& m1_pboole(B,A)
& ? [C] :
( v2_relat_1(C)
& m1_pboole(C,A)
& k1_closure3(A,B) = k1_closure3(A,C)
& k7_relat_1(B,k1_closure3(A,B)) = k7_relat_1(C,k1_closure3(A,C))
& ~ r6_pboole(A,B,C) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f16952]) ).
fof(f75978,plain,
( ~ v1_xboole_0(sk0_5437)
& v2_relat_1(sk0_5438)
& m1_pboole(sk0_5438,sk0_5437)
& v2_relat_1(sk0_5439)
& m1_pboole(sk0_5439,sk0_5437)
& k1_closure3(sk0_5437,sk0_5438) = k1_closure3(sk0_5437,sk0_5439)
& k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438)) = k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5439))
& ~ r6_pboole(sk0_5437,sk0_5438,sk0_5439) ),
inference(skolemization,[status(esa)],[f75977]) ).
fof(f75979,plain,
~ v1_xboole_0(sk0_5437),
inference(cnf_transformation,[status(esa)],[f75978]) ).
fof(f75980,plain,
v2_relat_1(sk0_5438),
inference(cnf_transformation,[status(esa)],[f75978]) ).
fof(f75981,plain,
m1_pboole(sk0_5438,sk0_5437),
inference(cnf_transformation,[status(esa)],[f75978]) ).
fof(f75982,plain,
v2_relat_1(sk0_5439),
inference(cnf_transformation,[status(esa)],[f75978]) ).
fof(f75983,plain,
m1_pboole(sk0_5439,sk0_5437),
inference(cnf_transformation,[status(esa)],[f75978]) ).
fof(f75984,plain,
k1_closure3(sk0_5437,sk0_5438) = k1_closure3(sk0_5437,sk0_5439),
inference(cnf_transformation,[status(esa)],[f75978]) ).
fof(f75985,plain,
k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438)) = k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5439)),
inference(cnf_transformation,[status(esa)],[f75978]) ).
fof(f75986,plain,
~ r6_pboole(sk0_5437,sk0_5438,sk0_5439),
inference(cnf_transformation,[status(esa)],[f75978]) ).
fof(f85348,plain,
! [X2,X1] :
( ~ m1_pboole(X2,X1)
| ~ m1_pboole(X2,X1)
| r6_pboole(X1,X2,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f33057]) ).
fof(f85349,plain,
! [X0,X1] :
( ~ m1_pboole(X0,X1)
| r6_pboole(X1,X0,X0) ),
inference(duplicate_literals_removal,[status(esa)],[f85348]) ).
fof(f87967,plain,
k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438)) = k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5438)),
inference(forward_demodulation,[status(thm)],[f75984,f75985]) ).
fof(f87971,plain,
! [X0] :
( v1_xboole_0(X0)
| ~ m1_pboole(sk0_5439,X0)
| sk0_5439 = k1_funct_4(k1_pboole(X0),k7_relat_1(sk0_5439,k1_closure3(X0,sk0_5439))) ),
inference(resolution,[status(thm)],[f75976,f75982]) ).
fof(f87972,plain,
! [X0] :
( v1_xboole_0(X0)
| ~ m1_pboole(sk0_5438,X0)
| sk0_5438 = k1_funct_4(k1_pboole(X0),k7_relat_1(sk0_5438,k1_closure3(X0,sk0_5438))) ),
inference(resolution,[status(thm)],[f75976,f75980]) ).
fof(f87974,plain,
( spl0_1356
<=> v1_xboole_0(sk0_5437) ),
introduced(split_symbol_definition) ).
fof(f87975,plain,
( v1_xboole_0(sk0_5437)
| ~ spl0_1356 ),
inference(component_clause,[status(thm)],[f87974]) ).
fof(f87977,plain,
( spl0_1357
<=> sk0_5439 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5439))) ),
introduced(split_symbol_definition) ).
fof(f87978,plain,
( sk0_5439 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5439)))
| ~ spl0_1357 ),
inference(component_clause,[status(thm)],[f87977]) ).
fof(f87980,plain,
( v1_xboole_0(sk0_5437)
| sk0_5439 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5439))) ),
inference(resolution,[status(thm)],[f87971,f75983]) ).
fof(f87981,plain,
( spl0_1356
| spl0_1357 ),
inference(split_clause,[status(thm)],[f87980,f87974,f87977]) ).
fof(f87996,plain,
( $false
| ~ spl0_1356 ),
inference(forward_subsumption_resolution,[status(thm)],[f87975,f75979]) ).
fof(f87997,plain,
~ spl0_1356,
inference(contradiction_clause,[status(thm)],[f87996]) ).
fof(f87998,plain,
( sk0_5439 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5438)))
| ~ spl0_1357 ),
inference(forward_demodulation,[status(thm)],[f75984,f87978]) ).
fof(f87999,plain,
( sk0_5439 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438)))
| ~ spl0_1357 ),
inference(forward_demodulation,[status(thm)],[f87967,f87998]) ).
fof(f88007,plain,
( spl0_1362
<=> sk0_5438 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438))) ),
introduced(split_symbol_definition) ).
fof(f88008,plain,
( sk0_5438 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438)))
| ~ spl0_1362 ),
inference(component_clause,[status(thm)],[f88007]) ).
fof(f88010,plain,
( v1_xboole_0(sk0_5437)
| sk0_5438 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438))) ),
inference(resolution,[status(thm)],[f87972,f75981]) ).
fof(f88011,plain,
( spl0_1356
| spl0_1362 ),
inference(split_clause,[status(thm)],[f88010,f87974,f88007]) ).
fof(f88026,plain,
( sk0_5438 = sk0_5439
| ~ spl0_1357
| ~ spl0_1362 ),
inference(forward_demodulation,[status(thm)],[f87999,f88008]) ).
fof(f88043,plain,
( ~ r6_pboole(sk0_5437,sk0_5438,sk0_5438)
| ~ spl0_1357
| ~ spl0_1362 ),
inference(backward_demodulation,[status(thm)],[f88026,f75986]) ).
fof(f88046,plain,
( ~ m1_pboole(sk0_5438,sk0_5437)
| ~ spl0_1357
| ~ spl0_1362 ),
inference(resolution,[status(thm)],[f88043,f85349]) ).
fof(f88047,plain,
( $false
| ~ spl0_1357
| ~ spl0_1362 ),
inference(forward_subsumption_resolution,[status(thm)],[f88046,f75981]) ).
fof(f88048,plain,
( ~ spl0_1357
| ~ spl0_1362 ),
inference(contradiction_clause,[status(thm)],[f88047]) ).
fof(f88049,plain,
$false,
inference(sat_refutation,[status(thm)],[f87981,f87997,f88011,f88048]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : ALG226+3 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 29 23:23:52 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.60/1.80 % Drodi V3.6.0
% 64.20/9.80 % Refutation found
% 64.20/9.80 % SZS status Theorem for theBenchmark: Theorem is valid
% 64.20/9.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 68.00/10.21 % Elapsed time: 9.831143 seconds
% 68.00/10.21 % CPU time: 65.772336 seconds
% 68.00/10.21 % Total memory used: 4.495 GB
% 68.00/10.21 % Net memory used: 4.472 GB
%------------------------------------------------------------------------------