TSTP Solution File: SYN063+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYN063+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 : n032.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 12:08:43 EDT 2024
% Result : Theorem 0.11s 0.35s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 7 unt; 0 def)
% Number of atoms : 242 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 280 ( 97 ~; 120 |; 48 &)
% ( 6 <=>; 6 =>; 0 <=; 3 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 43 ( 37 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f127,plain,
$false,
inference(subsumption_resolution,[],[f125,f89]) ).
fof(f89,plain,
~ sP2,
inference(resolution,[],[f86,f41]) ).
fof(f41,plain,
( ~ sP3
| ~ sP2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
( ( ~ sP3
| ~ sP2 )
& ( sP3
| sP2 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,plain,
( sP2
<~> sP3 ),
inference(definition_folding,[],[f4,f8,f7,f6,f5]) ).
fof(f5,plain,
! [X1] :
( sP0(X1)
<=> ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f6,plain,
( sP1
<=> ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f7,plain,
( sP2
<=> ! [X0] :
( big_p(c)
| ( ~ big_p(b)
& big_p(X0) )
| ~ big_p(a) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f8,plain,
( sP3
<=> ! [X1] :
( sP1
& sP0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f4,plain,
( ! [X0] :
( big_p(c)
| ( ~ big_p(b)
& big_p(X0) )
| ~ big_p(a) )
<~> ! [X1] :
( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(flattening,[],[f3]) ).
fof(f3,plain,
( ! [X0] :
( big_p(c)
| ( ~ big_p(b)
& big_p(X0) )
| ~ big_p(a) )
<~> ! [X1] :
( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( ( ( big_p(X0)
=> big_p(b) )
& big_p(a) )
=> big_p(c) )
<=> ! [X1] :
( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
( ! [X0] :
( ( ( big_p(X0)
=> big_p(b) )
& big_p(a) )
=> big_p(c) )
<=> ! [X1] :
( ( big_p(c)
| ~ big_p(b)
| ~ big_p(a) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel33) ).
fof(f86,plain,
sP3,
inference(subsumption_resolution,[],[f85,f65]) ).
fof(f65,plain,
sP1,
inference(duplicate_literal_removal,[],[f62]) ).
fof(f62,plain,
( sP1
| sP1 ),
inference(resolution,[],[f58,f35]) ).
fof(f35,plain,
( ~ big_p(c)
| sP1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
( ( sP1
| ( ~ big_p(c)
& big_p(b)
& big_p(a) ) )
& ( big_p(c)
| ~ big_p(b)
| ~ big_p(a)
| ~ sP1 ) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
( ( sP1
| ( ~ big_p(c)
& big_p(b)
& big_p(a) ) )
& ( big_p(c)
| ~ big_p(b)
| ~ big_p(a)
| ~ sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f58,plain,
! [X0] :
( big_p(X0)
| sP1 ),
inference(subsumption_resolution,[],[f57,f43]) ).
fof(f43,plain,
( sP2
| sP1 ),
inference(resolution,[],[f25,f40]) ).
fof(f40,plain,
( sP3
| sP2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f25,plain,
( ~ sP3
| sP1 ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
( ( sP3
| ~ sP1
| ~ sP0(sK4) )
& ( ! [X1] :
( sP1
& sP0(X1) )
| ~ sP3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f11,f12]) ).
fof(f12,plain,
( ? [X0] :
( ~ sP1
| ~ sP0(X0) )
=> ( ~ sP1
| ~ sP0(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
( ( sP3
| ? [X0] :
( ~ sP1
| ~ sP0(X0) ) )
& ( ! [X1] :
( sP1
& sP0(X1) )
| ~ sP3 ) ),
inference(rectify,[],[f10]) ).
fof(f10,plain,
( ( sP3
| ? [X1] :
( ~ sP1
| ~ sP0(X1) ) )
& ( ! [X1] :
( sP1
& sP0(X1) )
| ~ sP3 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f57,plain,
! [X0] :
( big_p(X0)
| ~ sP2
| sP1 ),
inference(subsumption_resolution,[],[f54,f35]) ).
fof(f54,plain,
! [X0] :
( big_p(X0)
| big_p(c)
| ~ sP2
| sP1 ),
inference(resolution,[],[f27,f33]) ).
fof(f33,plain,
( big_p(a)
| sP1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
! [X1] :
( ~ big_p(a)
| big_p(X1)
| big_p(c)
| ~ sP2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
( ( sP2
| ( ~ big_p(c)
& ( big_p(b)
| ~ big_p(sK5) )
& big_p(a) ) )
& ( ! [X1] :
( big_p(c)
| ( ~ big_p(b)
& big_p(X1) )
| ~ big_p(a) )
| ~ sP2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f15,f16]) ).
fof(f16,plain,
( ? [X0] :
( ~ big_p(c)
& ( big_p(b)
| ~ big_p(X0) )
& big_p(a) )
=> ( ~ big_p(c)
& ( big_p(b)
| ~ big_p(sK5) )
& big_p(a) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
( ( sP2
| ? [X0] :
( ~ big_p(c)
& ( big_p(b)
| ~ big_p(X0) )
& big_p(a) ) )
& ( ! [X1] :
( big_p(c)
| ( ~ big_p(b)
& big_p(X1) )
| ~ big_p(a) )
| ~ sP2 ) ),
inference(rectify,[],[f14]) ).
fof(f14,plain,
( ( sP2
| ? [X0] :
( ~ big_p(c)
& ( big_p(b)
| ~ big_p(X0) )
& big_p(a) ) )
& ( ! [X0] :
( big_p(c)
| ( ~ big_p(b)
& big_p(X0) )
| ~ big_p(a) )
| ~ sP2 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f85,plain,
( ~ sP1
| sP3 ),
inference(resolution,[],[f80,f26]) ).
fof(f26,plain,
( ~ sP0(sK4)
| ~ sP1
| sP3 ),
inference(cnf_transformation,[],[f13]) ).
fof(f80,plain,
! [X0] : sP0(X0),
inference(subsumption_resolution,[],[f79,f24]) ).
fof(f24,plain,
! [X1] :
( ~ sP3
| sP0(X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f79,plain,
! [X0] :
( sP3
| sP0(X0) ),
inference(subsumption_resolution,[],[f67,f39]) ).
fof(f39,plain,
! [X0] :
( ~ big_p(c)
| sP0(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] :
( ( sP0(X0)
| ( ~ big_p(c)
& ~ big_p(X0)
& big_p(a) ) )
& ( big_p(c)
| big_p(X0)
| ~ big_p(a)
| ~ sP0(X0) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X1] :
( ( sP0(X1)
| ( ~ big_p(c)
& ~ big_p(X1)
& big_p(a) ) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a)
| ~ sP0(X1) ) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
! [X1] :
( ( sP0(X1)
| ( ~ big_p(c)
& ~ big_p(X1)
& big_p(a) ) )
& ( big_p(c)
| big_p(X1)
| ~ big_p(a)
| ~ sP0(X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f67,plain,
! [X0] :
( big_p(c)
| sP3
| sP0(X0) ),
inference(resolution,[],[f56,f38]) ).
fof(f38,plain,
! [X0] :
( ~ big_p(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f56,plain,
! [X0] :
( big_p(X0)
| big_p(c)
| sP3 ),
inference(subsumption_resolution,[],[f53,f40]) ).
fof(f53,plain,
! [X0] :
( big_p(X0)
| big_p(c)
| ~ sP2
| sP3 ),
inference(resolution,[],[f27,f47]) ).
fof(f47,plain,
( big_p(a)
| sP3 ),
inference(subsumption_resolution,[],[f46,f33]) ).
fof(f46,plain,
( big_p(a)
| ~ sP1
| sP3 ),
inference(resolution,[],[f37,f26]) ).
fof(f37,plain,
! [X0] :
( sP0(X0)
| big_p(a) ),
inference(cnf_transformation,[],[f22]) ).
fof(f125,plain,
sP2,
inference(resolution,[],[f116,f31]) ).
fof(f31,plain,
( ~ big_p(c)
| sP2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f116,plain,
big_p(c),
inference(factoring,[],[f103]) ).
fof(f103,plain,
! [X0] :
( big_p(X0)
| big_p(c) ),
inference(subsumption_resolution,[],[f99,f89]) ).
fof(f99,plain,
! [X0] :
( big_p(X0)
| big_p(c)
| sP2 ),
inference(resolution,[],[f96,f29]) ).
fof(f29,plain,
( big_p(a)
| sP2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f96,plain,
! [X0] :
( ~ big_p(a)
| big_p(X0)
| big_p(c) ),
inference(subsumption_resolution,[],[f36,f80]) ).
fof(f36,plain,
! [X0] :
( big_p(c)
| big_p(X0)
| ~ big_p(a)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN063+1 : TPTP v8.1.2. Released v2.0.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.34 % Computer : n032.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Fri May 3 17:38:38 EDT 2024
% 0.11/0.34 % CPUTime :
% 0.11/0.34 % (9372)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35 % (9377)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.35 % (9377)First to succeed.
% 0.11/0.35 % (9377)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9372"
% 0.11/0.35 % (9377)Refutation found. Thanks to Tanya!
% 0.11/0.35 % SZS status Theorem for theBenchmark
% 0.11/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.35 % (9377)------------------------------
% 0.11/0.35 % (9377)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.35 % (9377)Termination reason: Refutation
% 0.11/0.35
% 0.11/0.35 % (9377)Memory used [KB]: 753
% 0.11/0.35 % (9377)Time elapsed: 0.003 s
% 0.11/0.35 % (9377)Instructions burned: 4 (million)
% 0.11/0.35 % (9372)Success in time 0.001 s
%------------------------------------------------------------------------------