TSTP Solution File: SYN084+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYN084+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 : n014.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 18:02:08 EDT 2024
% Result : Theorem 0.17s 0.36s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of formulae : 88 ( 1 unt; 0 def)
% Number of atoms : 337 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 395 ( 146 ~; 170 |; 52 &)
% ( 18 <=>; 6 =>; 0 <=; 3 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 18 ( 17 usr; 16 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 45 ( 39 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f118,plain,
$false,
inference(avatar_sat_refutation,[],[f49,f54,f59,f63,f67,f76,f85,f86,f87,f91,f92,f96,f97,f98,f100,f104,f109,f113,f115,f117]) ).
fof(f117,plain,
( spl5_12
| ~ spl5_7
| ~ spl5_13 ),
inference(avatar_split_clause,[],[f116,f94,f65,f89]) ).
fof(f89,plain,
( spl5_12
<=> ! [X1] :
( big_p(f(f(X1)))
| big_p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
fof(f65,plain,
( spl5_7
<=> ! [X1] : sP0(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
fof(f94,plain,
( spl5_13
<=> ! [X0] :
( big_p(f(f(X0)))
| ~ sP0(X0)
| big_p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).
fof(f116,plain,
( ! [X0] :
( big_p(f(f(X0)))
| big_p(X0) )
| ~ spl5_7
| ~ spl5_13 ),
inference(subsumption_resolution,[],[f95,f66]) ).
fof(f66,plain,
( ! [X1] : sP0(X1)
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f95,plain,
( ! [X0] :
( big_p(f(f(X0)))
| ~ sP0(X0)
| big_p(X0) )
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f115,plain,
( spl5_8
| spl5_10
| ~ spl5_12 ),
inference(avatar_contradiction_clause,[],[f114]) ).
fof(f114,plain,
( $false
| spl5_8
| spl5_10
| ~ spl5_12 ),
inference(subsumption_resolution,[],[f112,f80]) ).
fof(f80,plain,
( ~ big_p(sK4)
| spl5_10 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f78,plain,
( spl5_10
<=> big_p(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
fof(f112,plain,
( big_p(sK4)
| spl5_8
| ~ spl5_12 ),
inference(resolution,[],[f71,f90]) ).
fof(f90,plain,
( ! [X1] :
( big_p(f(f(X1)))
| big_p(X1) )
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f71,plain,
( ~ big_p(f(f(sK4)))
| spl5_8 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f69,plain,
( spl5_8
<=> big_p(f(f(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
fof(f113,plain,
( ~ spl5_11
| ~ spl5_6
| spl5_8 ),
inference(avatar_split_clause,[],[f111,f69,f61,f82]) ).
fof(f82,plain,
( spl5_11
<=> big_p(f(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
fof(f61,plain,
( spl5_6
<=> ! [X1] :
( big_p(f(f(X1)))
| ~ big_p(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
fof(f111,plain,
( ~ big_p(f(sK4))
| ~ spl5_6
| spl5_8 ),
inference(resolution,[],[f71,f62]) ).
fof(f62,plain,
( ! [X1] :
( big_p(f(f(X1)))
| ~ big_p(f(X1)) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f109,plain,
( spl5_2
| ~ spl5_4
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[],[f108]) ).
fof(f108,plain,
( $false
| spl5_2
| ~ spl5_4
| ~ spl5_6 ),
inference(subsumption_resolution,[],[f107,f53]) ).
fof(f53,plain,
( big_p(f(sK3))
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f51,plain,
( spl5_4
<=> big_p(f(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f107,plain,
( ~ big_p(f(sK3))
| spl5_2
| ~ spl5_6 ),
inference(resolution,[],[f62,f44]) ).
fof(f44,plain,
( ~ big_p(f(f(sK3)))
| spl5_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f42,plain,
( spl5_2
<=> big_p(f(f(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f104,plain,
( spl5_7
| ~ spl5_12 ),
inference(avatar_split_clause,[],[f103,f89,f65]) ).
fof(f103,plain,
( ! [X0] : sP0(X0)
| ~ spl5_12 ),
inference(subsumption_resolution,[],[f102,f33]) ).
fof(f33,plain,
! [X0] :
( sP0(X0)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0] :
( ( sP0(X0)
| ( ~ big_p(f(f(X0)))
& ~ big_p(X0)
& big_p(a) ) )
& ( big_p(f(f(X0)))
| big_p(X0)
| ~ big_p(a)
| ~ sP0(X0) ) ),
inference(rectify,[],[f18]) ).
fof(f18,plain,
! [X1] :
( ( sP0(X1)
| ( ~ big_p(f(f(X1)))
& ~ big_p(X1)
& big_p(a) ) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a)
| ~ sP0(X1) ) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
! [X1] :
( ( sP0(X1)
| ( ~ big_p(f(f(X1)))
& ~ big_p(X1)
& big_p(a) ) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a)
| ~ sP0(X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,plain,
! [X1] :
( sP0(X1)
<=> ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f102,plain,
( ! [X0] :
( big_p(X0)
| sP0(X0) )
| ~ spl5_12 ),
inference(resolution,[],[f90,f34]) ).
fof(f34,plain,
! [X0] :
( ~ big_p(f(f(X0)))
| sP0(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f100,plain,
( spl5_1
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[],[f99]) ).
fof(f99,plain,
( $false
| spl5_1
| ~ spl5_7 ),
inference(resolution,[],[f66,f40]) ).
fof(f40,plain,
( ~ sP0(sK3)
| spl5_1 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f38,plain,
( spl5_1
<=> sP0(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f98,plain,
( spl5_9
| spl5_3 ),
inference(avatar_split_clause,[],[f35,f46,f73]) ).
fof(f73,plain,
( spl5_9
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).
fof(f46,plain,
( spl5_3
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f35,plain,
( sP2
| sP1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
( ( ~ sP2
| ~ sP1 )
& ( sP2
| sP1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,plain,
( sP1
<~> sP2 ),
inference(definition_folding,[],[f4,f7,f6,f5]) ).
fof(f6,plain,
( sP1
<=> ! [X0] :
( big_p(f(f(X0)))
| ( ~ big_p(f(X0))
& big_p(X0) )
| ~ big_p(a) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f7,plain,
( sP2
<=> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& sP0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f4,plain,
( ! [X0] :
( big_p(f(f(X0)))
| ( ~ big_p(f(X0))
& big_p(X0) )
| ~ big_p(a) )
<~> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(flattening,[],[f3]) ).
fof(f3,plain,
( ! [X0] :
( big_p(f(f(X0)))
| ( ~ big_p(f(X0))
& big_p(X0) )
| ~ big_p(a) )
<~> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( ( ( big_p(X0)
=> big_p(f(X0)) )
& big_p(a) )
=> big_p(f(f(X0))) )
<=> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
( ! [X0] :
( ( ( big_p(X0)
=> big_p(f(X0)) )
& big_p(a) )
=> big_p(f(f(X0))) )
<=> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel62) ).
fof(f97,plain,
( ~ spl5_9
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f36,f46,f73]) ).
fof(f36,plain,
( ~ sP2
| ~ sP1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f96,plain,
( ~ spl5_5
| spl5_13 ),
inference(avatar_split_clause,[],[f31,f94,f56]) ).
fof(f56,plain,
( spl5_5
<=> big_p(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f31,plain,
! [X0] :
( big_p(f(f(X0)))
| big_p(X0)
| ~ big_p(a)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f92,plain,
( spl5_5
| spl5_7 ),
inference(avatar_split_clause,[],[f32,f65,f56]) ).
fof(f32,plain,
! [X0] :
( sP0(X0)
| big_p(a) ),
inference(cnf_transformation,[],[f19]) ).
fof(f91,plain,
( ~ spl5_9
| ~ spl5_5
| spl5_12 ),
inference(avatar_split_clause,[],[f26,f89,f56,f73]) ).
fof(f26,plain,
! [X1] :
( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a)
| ~ sP1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ( sP1
| ( ~ big_p(f(f(sK4)))
& ( big_p(f(sK4))
| ~ big_p(sK4) )
& big_p(a) ) )
& ( ! [X1] :
( big_p(f(f(X1)))
| ( ~ big_p(f(X1))
& big_p(X1) )
| ~ big_p(a) )
| ~ sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f14,f15]) ).
fof(f15,plain,
( ? [X0] :
( ~ big_p(f(f(X0)))
& ( big_p(f(X0))
| ~ big_p(X0) )
& big_p(a) )
=> ( ~ big_p(f(f(sK4)))
& ( big_p(f(sK4))
| ~ big_p(sK4) )
& big_p(a) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
( ( sP1
| ? [X0] :
( ~ big_p(f(f(X0)))
& ( big_p(f(X0))
| ~ big_p(X0) )
& big_p(a) ) )
& ( ! [X1] :
( big_p(f(f(X1)))
| ( ~ big_p(f(X1))
& big_p(X1) )
| ~ big_p(a) )
| ~ sP1 ) ),
inference(rectify,[],[f13]) ).
fof(f13,plain,
( ( sP1
| ? [X0] :
( ~ big_p(f(f(X0)))
& ( big_p(f(X0))
| ~ big_p(X0) )
& big_p(a) ) )
& ( ! [X0] :
( big_p(f(f(X0)))
| ( ~ big_p(f(X0))
& big_p(X0) )
| ~ big_p(a) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f87,plain,
( ~ spl5_9
| ~ spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f27,f61,f56,f73]) ).
fof(f27,plain,
! [X1] :
( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a)
| ~ sP1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f86,plain,
( spl5_5
| spl5_9 ),
inference(avatar_split_clause,[],[f28,f73,f56]) ).
fof(f28,plain,
( sP1
| big_p(a) ),
inference(cnf_transformation,[],[f16]) ).
fof(f85,plain,
( ~ spl5_10
| spl5_11
| spl5_9 ),
inference(avatar_split_clause,[],[f29,f73,f82,f78]) ).
fof(f29,plain,
( sP1
| big_p(f(sK4))
| ~ big_p(sK4) ),
inference(cnf_transformation,[],[f16]) ).
fof(f76,plain,
( ~ spl5_8
| spl5_9 ),
inference(avatar_split_clause,[],[f30,f73,f69]) ).
fof(f30,plain,
( sP1
| ~ big_p(f(f(sK4))) ),
inference(cnf_transformation,[],[f16]) ).
fof(f67,plain,
( ~ spl5_3
| spl5_7 ),
inference(avatar_split_clause,[],[f21,f65,f46]) ).
fof(f21,plain,
! [X1] :
( sP0(X1)
| ~ sP2 ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
( ( sP2
| ( ~ big_p(f(f(sK3)))
& big_p(f(sK3))
& big_p(a) )
| ~ sP0(sK3) )
& ( ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& sP0(X1) )
| ~ sP2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f10,f11]) ).
fof(f11,plain,
( ? [X0] :
( ( ~ big_p(f(f(X0)))
& big_p(f(X0))
& big_p(a) )
| ~ sP0(X0) )
=> ( ( ~ big_p(f(f(sK3)))
& big_p(f(sK3))
& big_p(a) )
| ~ sP0(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
( ( sP2
| ? [X0] :
( ( ~ big_p(f(f(X0)))
& big_p(f(X0))
& big_p(a) )
| ~ sP0(X0) ) )
& ( ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& sP0(X1) )
| ~ sP2 ) ),
inference(rectify,[],[f9]) ).
fof(f9,plain,
( ( sP2
| ? [X1] :
( ( ~ big_p(f(f(X1)))
& big_p(f(X1))
& big_p(a) )
| ~ sP0(X1) ) )
& ( ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& sP0(X1) )
| ~ sP2 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f63,plain,
( ~ spl5_3
| ~ spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f22,f61,f56,f46]) ).
fof(f22,plain,
! [X1] :
( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a)
| ~ sP2 ),
inference(cnf_transformation,[],[f12]) ).
fof(f59,plain,
( ~ spl5_1
| spl5_5
| spl5_3 ),
inference(avatar_split_clause,[],[f23,f46,f56,f38]) ).
fof(f23,plain,
( sP2
| big_p(a)
| ~ sP0(sK3) ),
inference(cnf_transformation,[],[f12]) ).
fof(f54,plain,
( ~ spl5_1
| spl5_4
| spl5_3 ),
inference(avatar_split_clause,[],[f24,f46,f51,f38]) ).
fof(f24,plain,
( sP2
| big_p(f(sK3))
| ~ sP0(sK3) ),
inference(cnf_transformation,[],[f12]) ).
fof(f49,plain,
( ~ spl5_1
| ~ spl5_2
| spl5_3 ),
inference(avatar_split_clause,[],[f25,f46,f42,f38]) ).
fof(f25,plain,
( sP2
| ~ big_p(f(f(sK3)))
| ~ sP0(sK3) ),
inference(cnf_transformation,[],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN084+1 : TPTP v8.1.2. Released v2.0.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Apr 30 01:38:19 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.34 % (27788)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35 % (27790)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.35 % (27792)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.11/0.35 % (27793)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.35 % (27795)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.35 % (27791)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.11/0.35 % (27794)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.11/0.35 TRYING [1]
% 0.11/0.35 TRYING [1]
% 0.11/0.35 TRYING [1]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 % (27789)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.35 TRYING [2]
% 0.11/0.35 % (27794)First to succeed.
% 0.11/0.35 TRYING [3]
% 0.11/0.35 TRYING [3]
% 0.11/0.35 TRYING [3]
% 0.11/0.35 % (27791)Also succeeded, but the first one will report.
% 0.11/0.35 TRYING [1]
% 0.11/0.36 TRYING [2]
% 0.11/0.36 TRYING [4]
% 0.11/0.36 % (27793)Also succeeded, but the first one will report.
% 0.17/0.36 % (27794)Refutation found. Thanks to Tanya!
% 0.17/0.36 % SZS status Theorem for theBenchmark
% 0.17/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.36 % (27794)------------------------------
% 0.17/0.36 % (27794)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.17/0.36 % (27794)Termination reason: Refutation
% 0.17/0.36
% 0.17/0.36 % (27794)Memory used [KB]: 778
% 0.17/0.36 % (27794)Time elapsed: 0.004 s
% 0.17/0.36 % (27794)Instructions burned: 5 (million)
% 0.17/0.36 % (27794)------------------------------
% 0.17/0.36 % (27794)------------------------------
% 0.17/0.36 % (27788)Success in time 0.019 s
%------------------------------------------------------------------------------