TSTP Solution File: SEU254+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU254+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.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 15:25:39 EDT 2024
% Result : Theorem 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 5 unt; 0 def)
% Number of atoms : 231 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 289 ( 117 ~; 121 |; 35 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 146 ( 131 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2915,plain,
$false,
inference(subsumption_resolution,[],[f2914,f79]) ).
fof(f79,plain,
transitive(sK1),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
( ~ transitive(relation_restriction(sK1,sK0))
& transitive(sK1)
& relation(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f40,f56]) ).
fof(f56,plain,
( ? [X0,X1] :
( ~ transitive(relation_restriction(X1,X0))
& transitive(X1)
& relation(X1) )
=> ( ~ transitive(relation_restriction(sK1,sK0))
& transitive(sK1)
& relation(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
? [X0,X1] :
( ~ transitive(relation_restriction(X1,X0))
& transitive(X1)
& relation(X1) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
? [X0,X1] :
( ~ transitive(relation_restriction(X1,X0))
& transitive(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( transitive(X1)
=> transitive(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X0,X1] :
( relation(X1)
=> ( transitive(X1)
=> transitive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_wellord1) ).
fof(f2914,plain,
~ transitive(sK1),
inference(subsumption_resolution,[],[f2912,f78]) ).
fof(f78,plain,
relation(sK1),
inference(cnf_transformation,[],[f57]) ).
fof(f2912,plain,
( ~ relation(sK1)
| ~ transitive(sK1) ),
inference(resolution,[],[f2906,f80]) ).
fof(f80,plain,
~ transitive(relation_restriction(sK1,sK0)),
inference(cnf_transformation,[],[f57]) ).
fof(f2906,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ transitive(X0) ),
inference(subsumption_resolution,[],[f2903,f163]) ).
fof(f163,plain,
! [X0,X1] :
( in(ordered_pair(sK2(relation_restriction(X0,X1)),sK3(relation_restriction(X0,X1))),X0)
| transitive(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(subsumption_resolution,[],[f162,f98]) ).
fof(f98,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f162,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1))
| in(ordered_pair(sK2(relation_restriction(X0,X1)),sK3(relation_restriction(X0,X1))),X0)
| ~ relation(X0) ),
inference(resolution,[],[f86,f104]) ).
fof(f104,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_restriction(X2,X1))
| in(X0,X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f86,plain,
! [X0] :
( in(ordered_pair(sK2(X0),sK3(X0)),X0)
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ( ( transitive(X0)
| ( ~ in(ordered_pair(sK2(X0),sK4(X0)),X0)
& in(ordered_pair(sK3(X0),sK4(X0)),X0)
& in(ordered_pair(sK2(X0),sK3(X0)),X0) ) )
& ( ! [X4,X5,X6] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f59,f60]) ).
fof(f60,plain,
! [X0] :
( ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> ( ~ in(ordered_pair(sK2(X0),sK4(X0)),X0)
& in(ordered_pair(sK3(X0),sK4(X0)),X0)
& in(ordered_pair(sK2(X0),sK3(X0)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0] :
( ( ( transitive(X0)
| ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X4,X5,X6] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ( ( transitive(X0)
| ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ( transitive(X0)
<=> ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ( transitive(X0)
<=> ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> in(ordered_pair(X1,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
fof(f2903,plain,
! [X0,X1] :
( ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| ~ in(ordered_pair(sK2(relation_restriction(X0,X1)),sK3(relation_restriction(X0,X1))),X0)
| ~ transitive(X0) ),
inference(duplicate_literal_removal,[],[f2891]) ).
fof(f2891,plain,
! [X0,X1] :
( ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| ~ in(ordered_pair(sK2(relation_restriction(X0,X1)),sK3(relation_restriction(X0,X1))),X0)
| ~ transitive(X0)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(resolution,[],[f506,f815]) ).
fof(f815,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK2(relation_restriction(X0,X1)),sK4(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(subsumption_resolution,[],[f814,f98]) ).
fof(f814,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK2(relation_restriction(X0,X1)),sK4(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(subsumption_resolution,[],[f813,f608]) ).
fof(f608,plain,
! [X0,X1] :
( in(sK2(relation_restriction(X0,X1)),X1)
| transitive(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(resolution,[],[f215,f107]) ).
fof(f107,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f215,plain,
! [X0,X1] :
( in(ordered_pair(sK2(relation_restriction(X0,X1)),sK3(relation_restriction(X0,X1))),cartesian_product2(X1,X1))
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(subsumption_resolution,[],[f212,f98]) ).
fof(f212,plain,
! [X0,X1] :
( in(ordered_pair(sK2(relation_restriction(X0,X1)),sK3(relation_restriction(X0,X1))),cartesian_product2(X1,X1))
| ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[],[f105,f86]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_restriction(X2,X1))
| in(X0,cartesian_product2(X1,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f813,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK2(relation_restriction(X0,X1)),sK4(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| ~ in(sK2(relation_restriction(X0,X1)),X1)
| transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(subsumption_resolution,[],[f802,f645]) ).
fof(f645,plain,
! [X0,X1] :
( in(sK4(relation_restriction(X0,X1)),X1)
| transitive(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(resolution,[],[f216,f108]) ).
fof(f108,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f67]) ).
fof(f216,plain,
! [X0,X1] :
( in(ordered_pair(sK3(relation_restriction(X0,X1)),sK4(relation_restriction(X0,X1))),cartesian_product2(X1,X1))
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(subsumption_resolution,[],[f213,f98]) ).
fof(f213,plain,
! [X0,X1] :
( in(ordered_pair(sK3(relation_restriction(X0,X1)),sK4(relation_restriction(X0,X1))),cartesian_product2(X1,X1))
| ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[],[f105,f87]) ).
fof(f87,plain,
! [X0] :
( in(ordered_pair(sK3(X0),sK4(X0)),X0)
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f802,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK2(relation_restriction(X0,X1)),sK4(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| ~ in(sK4(relation_restriction(X0,X1)),X1)
| ~ in(sK2(relation_restriction(X0,X1)),X1)
| transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[],[f297,f88]) ).
fof(f88,plain,
! [X0] :
( ~ in(ordered_pair(sK2(X0),sK4(X0)),X0)
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f297,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),relation_restriction(X2,X3))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(X0,X3) ),
inference(resolution,[],[f106,f109]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X1))
| in(X0,relation_restriction(X2,X1))
| ~ in(X0,X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f506,plain,
! [X2,X0,X1] :
( in(ordered_pair(X2,sK4(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| ~ in(ordered_pair(X2,sK3(relation_restriction(X0,X1))),X0)
| ~ transitive(X0) ),
inference(duplicate_literal_removal,[],[f498]) ).
fof(f498,plain,
! [X2,X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| in(ordered_pair(X2,sK4(relation_restriction(X0,X1))),X0)
| ~ in(ordered_pair(X2,sK3(relation_restriction(X0,X1))),X0)
| ~ transitive(X0)
| ~ relation(X0) ),
inference(resolution,[],[f198,f85]) ).
fof(f85,plain,
! [X0,X6,X4,X5] :
( ~ in(ordered_pair(X5,X6),X0)
| in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f198,plain,
! [X0,X1] :
( in(ordered_pair(sK3(relation_restriction(X0,X1)),sK4(relation_restriction(X0,X1))),X0)
| transitive(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(subsumption_resolution,[],[f197,f98]) ).
fof(f197,plain,
! [X0,X1] :
( transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1))
| in(ordered_pair(sK3(relation_restriction(X0,X1)),sK4(relation_restriction(X0,X1))),X0)
| ~ relation(X0) ),
inference(resolution,[],[f87,f104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.14 % Problem : SEU254+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.36 % Computer : n005.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Mon Apr 29 20:45:26 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % (20257)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38 % (20261)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38 % (20264)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)
% 0.13/0.38 % (20258)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38 % (20262)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)
% 0.13/0.38 % (20259)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 % (20263)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)
% 0.13/0.38 % (20260)WARNING: value z3 for option sas not known
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [2]
% 0.13/0.38 % (20260)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)
% 0.13/0.39 TRYING [3]
% 0.13/0.39 TRYING [1]
% 0.13/0.39 TRYING [2]
% 0.13/0.40 TRYING [3]
% 0.13/0.40 TRYING [4]
% 0.13/0.42 TRYING [4]
% 0.19/0.43 TRYING [1]
% 0.19/0.43 TRYING [2]
% 0.19/0.43 TRYING [3]
% 0.19/0.44 TRYING [4]
% 0.19/0.46 TRYING [5]
% 0.19/0.48 TRYING [5]
% 0.19/0.49 % (20260)First to succeed.
% 0.19/0.50 % (20260)Refutation found. Thanks to Tanya!
% 0.19/0.50 % SZS status Theorem for theBenchmark
% 0.19/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50 % (20260)------------------------------
% 0.19/0.50 % (20260)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.50 % (20260)Termination reason: Refutation
% 0.19/0.50
% 0.19/0.50 % (20260)Memory used [KB]: 2012
% 0.19/0.50 % (20260)Time elapsed: 0.112 s
% 0.19/0.50 % (20260)Instructions burned: 226 (million)
% 0.19/0.50 % (20260)------------------------------
% 0.19/0.50 % (20260)------------------------------
% 0.19/0.50 % (20257)Success in time 0.128 s
%------------------------------------------------------------------------------