TSTP Solution File: SYN077+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYN077+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.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 18:02:06 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 8 unt; 0 def)
% Number of atoms : 165 ( 12 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 191 ( 71 ~; 64 |; 39 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 104 ( 71 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f91,plain,
$false,
inference(subsumption_resolution,[],[f89,f55]) ).
fof(f55,plain,
big_f(sK3,sK3),
inference(duplicate_literal_removal,[],[f48]) ).
fof(f48,plain,
( big_f(sK3,sK3)
| big_f(sK3,sK3) ),
inference(resolution,[],[f46,f42]) ).
fof(f42,plain,
! [X0] :
( ~ big_f(sK1(sK4(X0),X0),sK3)
| big_f(X0,sK3) ),
inference(subsumption_resolution,[],[f40,f28]) ).
fof(f28,plain,
! [X1] :
( ~ sP0(sK4(X1))
| big_f(X1,sK3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X1] :
( ( big_f(X1,sK3)
| ( ~ sP0(sK4(X1))
& big_f(X1,sK4(X1)) ) )
& ( ! [X3] :
( sP0(X3)
| ~ big_f(X1,X3) )
| ~ big_f(X1,sK3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f15,f17,f16]) ).
fof(f16,plain,
( ? [X0] :
! [X1] :
( ( big_f(X1,X0)
| ? [X2] :
( ~ sP0(X2)
& big_f(X1,X2) ) )
& ( ! [X3] :
( sP0(X3)
| ~ big_f(X1,X3) )
| ~ big_f(X1,X0) ) )
=> ! [X1] :
( ( big_f(X1,sK3)
| ? [X2] :
( ~ sP0(X2)
& big_f(X1,X2) ) )
& ( ! [X3] :
( sP0(X3)
| ~ big_f(X1,X3) )
| ~ big_f(X1,sK3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X1] :
( ? [X2] :
( ~ sP0(X2)
& big_f(X1,X2) )
=> ( ~ sP0(sK4(X1))
& big_f(X1,sK4(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
? [X0] :
! [X1] :
( ( big_f(X1,X0)
| ? [X2] :
( ~ sP0(X2)
& big_f(X1,X2) ) )
& ( ! [X3] :
( sP0(X3)
| ~ big_f(X1,X3) )
| ~ big_f(X1,X0) ) ),
inference(rectify,[],[f14]) ).
fof(f14,plain,
? [X0] :
! [X1] :
( ( big_f(X1,X0)
| ? [X2] :
( ~ sP0(X2)
& big_f(X1,X2) ) )
& ( ! [X2] :
( sP0(X2)
| ~ big_f(X1,X2) )
| ~ big_f(X1,X0) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,plain,
? [X0] :
! [X1] :
( big_f(X1,X0)
<=> ! [X2] :
( sP0(X2)
| ~ big_f(X1,X2) ) ),
inference(definition_folding,[],[f6,f7]) ).
fof(f7,plain,
! [X2] :
( sP0(X2)
<=> ? [X3] :
( ! [X4] :
( ~ big_f(X4,X3)
| ~ big_f(X4,X2) )
& big_f(X3,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f6,plain,
? [X0] :
! [X1] :
( big_f(X1,X0)
<=> ! [X2] :
( ? [X3] :
( ! [X4] :
( ~ big_f(X4,X3)
| ~ big_f(X4,X2) )
& big_f(X3,X2) )
| ~ big_f(X1,X2) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,plain,
? [X0] :
! [X1] :
( big_f(X1,X0)
<=> ! [X2] :
( big_f(X1,X2)
=> ? [X3] :
( ~ ? [X4] :
( big_f(X4,X3)
& big_f(X4,X2) )
& big_f(X3,X2) ) ) ),
inference(flattening,[],[f4]) ).
fof(f4,plain,
~ ~ ? [X0] :
! [X1] :
( big_f(X1,X0)
<=> ! [X2] :
( big_f(X1,X2)
=> ? [X3] :
( ~ ? [X4] :
( big_f(X4,X3)
& big_f(X4,X2) )
& big_f(X3,X2) ) ) ),
inference(rectify,[],[f3]) ).
fof(f3,negated_conjecture,
~ ~ ? [X3] :
! [X2] :
( big_f(X2,X3)
<=> ! [X4] :
( big_f(X2,X4)
=> ? [X0] :
( ~ ? [X1] :
( big_f(X1,X0)
& big_f(X1,X4) )
& big_f(X0,X4) ) ) ),
inference(negated_conjecture,[],[f2]) ).
fof(f2,conjecture,
~ ? [X3] :
! [X2] :
( big_f(X2,X3)
<=> ! [X4] :
( big_f(X2,X4)
=> ? [X0] :
( ~ ? [X1] :
( big_f(X1,X0)
& big_f(X1,X4) )
& big_f(X0,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel54) ).
fof(f40,plain,
! [X0] :
( big_f(X0,sK3)
| sP0(sK4(X0))
| ~ big_f(sK1(sK4(X0),X0),sK3) ),
inference(resolution,[],[f38,f26]) ).
fof(f26,plain,
! [X3,X1] :
( ~ big_f(X1,X3)
| sP0(X3)
| ~ big_f(X1,sK3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X0] :
( big_f(sK1(sK4(X0),X0),sK4(X0))
| big_f(X0,sK3) ),
inference(subsumption_resolution,[],[f37,f28]) ).
fof(f37,plain,
! [X0] :
( big_f(sK1(sK4(X0),X0),sK4(X0))
| sP0(sK4(X0))
| big_f(X0,sK3) ),
inference(resolution,[],[f24,f27]) ).
fof(f27,plain,
! [X1] :
( big_f(X1,sK4(X1))
| big_f(X1,sK3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f24,plain,
! [X0,X1] :
( ~ big_f(X1,X0)
| big_f(sK1(X0,X1),X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0] :
( ( sP0(X0)
| ! [X1] :
( ( big_f(sK1(X0,X1),X1)
& big_f(sK1(X0,X1),X0) )
| ~ big_f(X1,X0) ) )
& ( ( ! [X4] :
( ~ big_f(X4,sK2(X0))
| ~ big_f(X4,X0) )
& big_f(sK2(X0),X0) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f10,f12,f11]) ).
fof(f11,plain,
! [X0,X1] :
( ? [X2] :
( big_f(X2,X1)
& big_f(X2,X0) )
=> ( big_f(sK1(X0,X1),X1)
& big_f(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f12,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( ~ big_f(X4,X3)
| ~ big_f(X4,X0) )
& big_f(X3,X0) )
=> ( ! [X4] :
( ~ big_f(X4,sK2(X0))
| ~ big_f(X4,X0) )
& big_f(sK2(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
! [X0] :
( ( sP0(X0)
| ! [X1] :
( ? [X2] :
( big_f(X2,X1)
& big_f(X2,X0) )
| ~ big_f(X1,X0) ) )
& ( ? [X3] :
( ! [X4] :
( ~ big_f(X4,X3)
| ~ big_f(X4,X0) )
& big_f(X3,X0) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f9]) ).
fof(f9,plain,
! [X2] :
( ( sP0(X2)
| ! [X3] :
( ? [X4] :
( big_f(X4,X3)
& big_f(X4,X2) )
| ~ big_f(X3,X2) ) )
& ( ? [X3] :
( ! [X4] :
( ~ big_f(X4,X3)
| ~ big_f(X4,X2) )
& big_f(X3,X2) )
| ~ sP0(X2) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f46,plain,
! [X0] :
( big_f(sK1(sK4(X0),X0),X0)
| big_f(X0,sK3) ),
inference(subsumption_resolution,[],[f44,f28]) ).
fof(f44,plain,
! [X0] :
( big_f(sK1(sK4(X0),X0),X0)
| sP0(sK4(X0))
| big_f(X0,sK3) ),
inference(resolution,[],[f25,f27]) ).
fof(f25,plain,
! [X0,X1] :
( ~ big_f(X1,X0)
| big_f(sK1(X0,X1),X1)
| sP0(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f89,plain,
~ big_f(sK3,sK3),
inference(superposition,[],[f67,f82]) ).
fof(f82,plain,
sK3 = sK2(sK5(sK3)),
inference(unit_resulting_resolution,[],[f68,f29]) ).
fof(f29,plain,
! [X2,X0] :
( ~ big_f(X2,sK5(X0))
| X0 = X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X2] :
( ( big_f(X2,sK5(X0))
| X0 != X2 )
& ( X0 = X2
| ~ big_f(X2,sK5(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f19,f20]) ).
fof(f20,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( big_f(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ big_f(X2,X1) ) )
=> ! [X2] :
( ( big_f(X2,sK5(X0))
| X0 != X2 )
& ( X0 = X2
| ~ big_f(X2,sK5(X0)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0] :
? [X1] :
! [X2] :
( ( big_f(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ big_f(X2,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
? [X1] :
! [X2] :
( big_f(X2,X1)
<=> X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel54_1) ).
fof(f68,plain,
big_f(sK2(sK5(sK3)),sK5(sK3)),
inference(unit_resulting_resolution,[],[f58,f22]) ).
fof(f22,plain,
! [X0] :
( ~ sP0(X0)
| big_f(sK2(X0),X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f58,plain,
sP0(sK5(sK3)),
inference(unit_resulting_resolution,[],[f31,f55,f26]) ).
fof(f31,plain,
! [X2] : big_f(X2,sK5(X2)),
inference(equality_resolution,[],[f30]) ).
fof(f30,plain,
! [X2,X0] :
( big_f(X2,sK5(X0))
| X0 != X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f67,plain,
~ big_f(sK3,sK2(sK5(sK3))),
inference(unit_resulting_resolution,[],[f31,f58,f23]) ).
fof(f23,plain,
! [X0,X4] :
( ~ big_f(X4,sK2(X0))
| ~ big_f(X4,X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN077+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 30 01:49:41 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (13331)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (13338)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)
% 0.13/0.36 % (13338)First to succeed.
% 0.13/0.37 % (13338)Refutation found. Thanks to Tanya!
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37 % (13338)------------------------------
% 0.13/0.37 % (13338)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.37 % (13338)Termination reason: Refutation
% 0.13/0.37
% 0.13/0.37 % (13338)Memory used [KB]: 826
% 0.13/0.37 % (13338)Time elapsed: 0.004 s
% 0.13/0.37 % (13338)Instructions burned: 6 (million)
% 0.13/0.37 % (13338)------------------------------
% 0.13/0.37 % (13338)------------------------------
% 0.13/0.37 % (13331)Success in time 0.013 s
%------------------------------------------------------------------------------