TSTP Solution File: ALG227+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG227+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.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 : Sun May 5 04:29:23 EDT 2024
% Result : Theorem 0.15s 0.38s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 156 ( 55 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 192 ( 72 ~; 49 |; 51 &)
% ( 5 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 72 ( 51 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f278,plain,
$false,
inference(trivial_inequality_removal,[],[f277]) ).
fof(f277,plain,
k1_xboole_0 != k1_xboole_0,
inference(superposition,[],[f90,f270]) ).
fof(f270,plain,
k1_xboole_0 = k1_funct_1(sK1,sK2),
inference(resolution,[],[f269,f86]) ).
fof(f86,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
( k1_xboole_0 != k1_funct_1(sK1,sK2)
& ~ r2_hidden(sK2,k1_closure3(sK0,sK1))
& m1_subset_1(sK2,sK0)
& m1_pboole(sK1,sK0)
& ~ v1_xboole_0(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f40,f58,f57,f56]) ).
fof(f56,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( k1_funct_1(X1,X2) != k1_xboole_0
& ~ r2_hidden(X2,k1_closure3(X0,X1))
& m1_subset_1(X2,X0) )
& m1_pboole(X1,X0) )
& ~ v1_xboole_0(X0) )
=> ( ? [X1] :
( ? [X2] :
( k1_funct_1(X1,X2) != k1_xboole_0
& ~ r2_hidden(X2,k1_closure3(sK0,X1))
& m1_subset_1(X2,sK0) )
& m1_pboole(X1,sK0) )
& ~ v1_xboole_0(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
( ? [X1] :
( ? [X2] :
( k1_funct_1(X1,X2) != k1_xboole_0
& ~ r2_hidden(X2,k1_closure3(sK0,X1))
& m1_subset_1(X2,sK0) )
& m1_pboole(X1,sK0) )
=> ( ? [X2] :
( k1_xboole_0 != k1_funct_1(sK1,X2)
& ~ r2_hidden(X2,k1_closure3(sK0,sK1))
& m1_subset_1(X2,sK0) )
& m1_pboole(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
( ? [X2] :
( k1_xboole_0 != k1_funct_1(sK1,X2)
& ~ r2_hidden(X2,k1_closure3(sK0,sK1))
& m1_subset_1(X2,sK0) )
=> ( k1_xboole_0 != k1_funct_1(sK1,sK2)
& ~ r2_hidden(sK2,k1_closure3(sK0,sK1))
& m1_subset_1(sK2,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_funct_1(X1,X2) != k1_xboole_0
& ~ r2_hidden(X2,k1_closure3(X0,X1))
& m1_subset_1(X2,X0) )
& m1_pboole(X1,X0) )
& ~ v1_xboole_0(X0) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_funct_1(X1,X2) != k1_xboole_0
& ~ r2_hidden(X2,k1_closure3(X0,X1))
& m1_subset_1(X2,X0) )
& m1_pboole(X1,X0) )
& ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,X0)
=> ( ~ r2_hidden(X2,k1_closure3(X0,X1))
=> k1_funct_1(X1,X2) = k1_xboole_0 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,X0)
=> ( ~ r2_hidden(X2,k1_closure3(X0,X1))
=> k1_funct_1(X1,X2) = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_closure3) ).
fof(f269,plain,
( v1_xboole_0(sK0)
| k1_xboole_0 = k1_funct_1(sK1,sK2) ),
inference(resolution,[],[f267,f87]) ).
fof(f87,plain,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f59]) ).
fof(f267,plain,
( ~ m1_pboole(sK1,sK0)
| k1_xboole_0 = k1_funct_1(sK1,sK2)
| v1_xboole_0(sK0) ),
inference(resolution,[],[f261,f88]) ).
fof(f88,plain,
m1_subset_1(sK2,sK0),
inference(cnf_transformation,[],[f59]) ).
fof(f261,plain,
( ~ m1_subset_1(sK2,sK0)
| k1_xboole_0 = k1_funct_1(sK1,sK2)
| ~ m1_pboole(sK1,sK0)
| v1_xboole_0(sK0) ),
inference(resolution,[],[f128,f158]) ).
fof(f158,plain,
~ r2_hidden(sK2,a_2_0_closure3(sK0,sK1)),
inference(backward_demodulation,[],[f89,f153]) ).
fof(f153,plain,
k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1),
inference(resolution,[],[f150,f86]) ).
fof(f150,plain,
( v1_xboole_0(sK0)
| k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1) ),
inference(resolution,[],[f126,f87]) ).
fof(f126,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| k1_closure3(X0,X1) = a_2_0_closure3(X0,X1)
| v1_xboole_0(X0) ),
inference(equality_resolution,[],[f93]) ).
fof(f93,plain,
! [X2,X0,X1] :
( k1_closure3(X0,X1) = X2
| a_2_0_closure3(X0,X1) != X2
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( k1_closure3(X0,X1) = X2
| a_2_0_closure3(X0,X1) != X2 )
& ( a_2_0_closure3(X0,X1) = X2
| k1_closure3(X0,X1) != X2 ) )
| ~ m1_pboole(X1,X0) )
| v1_xboole_0(X0) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k1_closure3(X0,X1) = X2
<=> a_2_0_closure3(X0,X1) = X2 )
| ~ m1_pboole(X1,X0) )
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( k1_closure3(X0,X1) = X2
<=> a_2_0_closure3(X0,X1) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_closure3) ).
fof(f89,plain,
~ r2_hidden(sK2,k1_closure3(sK0,sK1)),
inference(cnf_transformation,[],[f59]) ).
fof(f128,plain,
! [X2,X3,X1] :
( r2_hidden(X3,a_2_0_closure3(X1,X2))
| k1_xboole_0 = k1_funct_1(X2,X3)
| ~ m1_subset_1(X3,X1)
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(equality_resolution,[],[f112]) ).
fof(f112,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X0,a_2_0_closure3(X1,X2))
| k1_xboole_0 = k1_funct_1(X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,X1)
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( k1_xboole_0 = k1_funct_1(X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,X1) ) )
& ( ( k1_xboole_0 != k1_funct_1(X2,sK6(X0,X1,X2))
& sK6(X0,X1,X2) = X0
& m1_subset_1(sK6(X0,X1,X2),X1) )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f69,f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ? [X4] :
( k1_xboole_0 != k1_funct_1(X2,X4)
& X0 = X4
& m1_subset_1(X4,X1) )
=> ( k1_xboole_0 != k1_funct_1(X2,sK6(X0,X1,X2))
& sK6(X0,X1,X2) = X0
& m1_subset_1(sK6(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( k1_xboole_0 = k1_funct_1(X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,X1) ) )
& ( ? [X4] :
( k1_xboole_0 != k1_funct_1(X2,X4)
& X0 = X4
& m1_subset_1(X4,X1) )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(rectify,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( k1_xboole_0 = k1_funct_1(X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,X1) ) )
& ( ? [X3] :
( k1_xboole_0 != k1_funct_1(X2,X3)
& X0 = X3
& m1_subset_1(X3,X1) )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( k1_xboole_0 != k1_funct_1(X2,X3)
& X0 = X3
& m1_subset_1(X3,X1) ) )
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( k1_xboole_0 != k1_funct_1(X2,X3)
& X0 = X3
& m1_subset_1(X3,X1) ) )
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1,X2] :
( ( m1_pboole(X2,X1)
& ~ v1_xboole_0(X1) )
=> ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( k1_xboole_0 != k1_funct_1(X2,X3)
& X0 = X3
& m1_subset_1(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
fof(f90,plain,
k1_xboole_0 != k1_funct_1(sK1,sK2),
inference(cnf_transformation,[],[f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG227+1 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.34 % Computer : n004.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Fri May 3 19:57:08 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (915)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.36 % (917)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (918)WARNING: value z3 for option sas not known
% 0.15/0.37 % (916)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (919)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (918)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.37 % (920)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.37 % (921)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.37 % (922)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.37 TRYING [1]
% 0.15/0.37 TRYING [2]
% 0.15/0.37 TRYING [3]
% 0.15/0.37 TRYING [1]
% 0.15/0.37 TRYING [2]
% 0.15/0.37 TRYING [3]
% 0.15/0.37 TRYING [1]
% 0.15/0.37 TRYING [2]
% 0.15/0.37 TRYING [4]
% 0.15/0.38 TRYING [4]
% 0.15/0.38 % (921)First to succeed.
% 0.15/0.38 % (921)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-915"
% 0.15/0.38 % (922)Also succeeded, but the first one will report.
% 0.15/0.38 % (921)Refutation found. Thanks to Tanya!
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38 % (921)------------------------------
% 0.15/0.38 % (921)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38 % (921)Termination reason: Refutation
% 0.15/0.38
% 0.15/0.38 % (921)Memory used [KB]: 923
% 0.15/0.38 % (921)Time elapsed: 0.012 s
% 0.15/0.38 % (921)Instructions burned: 15 (million)
% 0.15/0.38 % (915)Success in time 0.017 s
%------------------------------------------------------------------------------