TSTP Solution File: SET020+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n008.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 Aug 31 18:23:11 EDT 2022
% Result : Theorem 1.28s 0.54s
% Output : Refutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 19 unt; 0 def)
% Number of atoms : 110 ( 63 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 103 ( 35 ~; 28 |; 34 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 45 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f493,plain,
$false,
inference(subsumption_resolution,[],[f492,f424]) ).
fof(f424,plain,
first(sK2) = sK1,
inference(forward_demodulation,[],[f420,f258]) ).
fof(f258,plain,
sK2 = unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0))),
inference(definition_unfolding,[],[f164,f251]) ).
fof(f251,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f204,f245,f245]) ).
fof(f245,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f204,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(rectify,[],[f54]) ).
fof(f54,plain,
! [X1,X0] : unordered_pair(singleton(X1),unordered_pair(X1,singleton(X0))) = ordered_pair(X1,X0),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_defn) ).
fof(f164,plain,
sK2 = ordered_pair(sK1,sK0),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
( ( second(sK2) != sK0
| first(sK2) != sK1 )
& member(sK0,universal_class)
& sK2 = ordered_pair(sK1,sK0)
& member(sK1,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f94,f95]) ).
fof(f95,plain,
( ? [X0,X1,X2] :
( ( second(X2) != X0
| first(X2) != X1 )
& member(X0,universal_class)
& ordered_pair(X1,X0) = X2
& member(X1,universal_class) )
=> ( ( second(sK2) != sK0
| first(sK2) != sK1 )
& member(sK0,universal_class)
& sK2 = ordered_pair(sK1,sK0)
& member(sK1,universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
? [X0,X1,X2] :
( ( second(X2) != X0
| first(X2) != X1 )
& member(X0,universal_class)
& ordered_pair(X1,X0) = X2
& member(X1,universal_class) ),
inference(rectify,[],[f83]) ).
fof(f83,plain,
? [X1,X2,X0] :
( ( second(X0) != X1
| first(X0) != X2 )
& member(X1,universal_class)
& ordered_pair(X2,X1) = X0
& member(X2,universal_class) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
? [X1,X2,X0] :
( ( second(X0) != X1
| first(X0) != X2 )
& member(X1,universal_class)
& member(X2,universal_class)
& ordered_pair(X2,X1) = X0 ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,plain,
~ ! [X1,X2,X0] :
( ( member(X1,universal_class)
& member(X2,universal_class)
& ordered_pair(X2,X1) = X0 )
=> ( first(X0) = X2
& second(X0) = X1 ) ),
inference(rectify,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X0,X3,X2] :
( ( ordered_pair(X2,X3) = X0
& member(X2,universal_class)
& member(X3,universal_class) )
=> ( first(X0) = X2
& second(X0) = X3 ) ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X0,X3,X2] :
( ( ordered_pair(X2,X3) = X0
& member(X2,universal_class)
& member(X3,universal_class) )
=> ( first(X0) = X2
& second(X0) = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).
fof(f420,plain,
sK1 = first(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0)))),
inference(resolution,[],[f372,f313]) ).
fof(f313,plain,
~ member(sK1,universal_class),
inference(consistent_polarity_flipping,[],[f163]) ).
fof(f163,plain,
member(sK1,universal_class),
inference(cnf_transformation,[],[f96]) ).
fof(f372,plain,
! [X3] :
( member(X3,universal_class)
| first(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(sK0,sK0)))) = X3 ),
inference(resolution,[],[f305,f347]) ).
fof(f347,plain,
~ member(sK0,universal_class),
inference(consistent_polarity_flipping,[],[f165]) ).
fof(f165,plain,
member(sK0,universal_class),
inference(cnf_transformation,[],[f96]) ).
fof(f305,plain,
! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0 ),
inference(consistent_polarity_flipping,[],[f272]) ).
fof(f272,plain,
! [X0,X1] :
( ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0 ),
inference(definition_unfolding,[],[f224,f251]) ).
fof(f224,plain,
! [X0,X1] :
( first(ordered_pair(X0,X1)) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0,X1] :
( ( first(ordered_pair(X0,X1)) = X0
& second(ordered_pair(X0,X1)) = X1 )
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
! [X1,X0] :
( ( first(ordered_pair(X1,X0)) = X1
& second(ordered_pair(X1,X0)) = X0 )
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ( first(ordered_pair(X1,X0)) = X1
& second(ordered_pair(X1,X0)) = X0 )
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ( member(X0,universal_class)
& member(X1,universal_class) )
=> ( first(ordered_pair(X1,X0)) = X1
& second(ordered_pair(X1,X0)) = X0 ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X1,X0] :
( ( member(X0,universal_class)
& member(X1,universal_class) )
=> ( first(ordered_pair(X0,X1)) = X0
& second(ordered_pair(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_second) ).
fof(f492,plain,
first(sK2) != sK1,
inference(trivial_inequality_removal,[],[f491]) ).
fof(f491,plain,
( first(sK2) != sK1
| sK0 != sK0 ),
inference(superposition,[],[f166,f490]) ).
fof(f490,plain,
second(sK2) = sK0,
inference(forward_demodulation,[],[f485,f258]) ).
fof(f485,plain,
sK0 = second(unordered_pair(unordered_pair(sK1,sK1),unordered_pair(sK1,unordered_pair(sK0,sK0)))),
inference(resolution,[],[f391,f313]) ).
fof(f391,plain,
! [X6] :
( member(X6,universal_class)
| second(unordered_pair(unordered_pair(X6,X6),unordered_pair(X6,unordered_pair(sK0,sK0)))) = sK0 ),
inference(resolution,[],[f306,f347]) ).
fof(f306,plain,
! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1 ),
inference(consistent_polarity_flipping,[],[f273]) ).
fof(f273,plain,
! [X0,X1] :
( second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f223,f251]) ).
fof(f223,plain,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f137]) ).
fof(f166,plain,
( second(sK2) != sK0
| first(sK2) != sK1 ),
inference(cnf_transformation,[],[f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.06/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 12:58:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.49 % (3466)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.50 % (3485)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.51 % (3477)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.52 % (3485)First to succeed.
% 1.28/0.52 % (3467)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.28/0.53 % (3487)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.28/0.53 % (3468)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.28/0.53 % (3491)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.28/0.53 % (3490)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.28/0.53 % (3476)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.28/0.53 % (3488)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 1.28/0.53 % (3470)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.28/0.53 % (3480)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.28/0.53 % (3495)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.28/0.53 % (3469)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.28/0.53 % (3494)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.28/0.53 % (3493)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.28/0.54 % (3472)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.28/0.54 % (3471)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.28/0.54 % (3485)Refutation found. Thanks to Tanya!
% 1.28/0.54 % SZS status Theorem for theBenchmark
% 1.28/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 1.28/0.54 % (3485)------------------------------
% 1.28/0.54 % (3485)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.28/0.54 % (3485)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.28/0.54 % (3485)Termination reason: Refutation
% 1.28/0.54
% 1.28/0.54 % (3485)Memory used [KB]: 1279
% 1.28/0.54 % (3485)Time elapsed: 0.120 s
% 1.28/0.54 % (3485)Instructions burned: 15 (million)
% 1.28/0.54 % (3485)------------------------------
% 1.28/0.54 % (3485)------------------------------
% 1.28/0.54 % (3465)Success in time 0.19 s
%------------------------------------------------------------------------------