TSTP Solution File: SYN084+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n002.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 19:25:30 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 96 ( 6 unt; 0 def)
% Number of atoms : 358 ( 5 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 424 ( 162 ~; 185 |; 51 &)
% ( 17 <=>; 6 =>; 0 <=; 3 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 15 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 53 ( 47 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f188,plain,
$false,
inference(avatar_sat_refutation,[],[f47,f51,f56,f61,f66,f75,f79,f83,f84,f89,f93,f97,f99,f129,f136,f155,f160,f187]) ).
fof(f187,plain,
( ~ spl7_3
| spl7_7
| ~ spl7_10
| spl7_11 ),
inference(avatar_contradiction_clause,[],[f186]) ).
fof(f186,plain,
( $false
| ~ spl7_3
| spl7_7
| ~ spl7_10
| spl7_11 ),
inference(subsumption_resolution,[],[f182,f70]) ).
fof(f70,plain,
( ~ big_p(sK2)
| spl7_7 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f68,plain,
( spl7_7
<=> big_p(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_7])]) ).
fof(f182,plain,
( big_p(sK2)
| ~ spl7_3
| ~ spl7_10
| spl7_11 ),
inference(resolution,[],[f180,f147]) ).
fof(f147,plain,
( ~ big_p(sF6(sK2))
| spl7_11 ),
inference(forward_demodulation,[],[f88,f37]) ).
fof(f37,plain,
! [X1] : f(f(X1)) = sF6(X1),
introduced(function_definition,[]) ).
fof(f88,plain,
( ~ big_p(f(f(sK2)))
| spl7_11 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f86,plain,
( spl7_11
<=> big_p(f(f(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_11])]) ).
fof(f180,plain,
( ! [X0] :
( big_p(sF6(X0))
| big_p(X0) )
| ~ spl7_3
| ~ spl7_10 ),
inference(forward_demodulation,[],[f179,f37]) ).
fof(f179,plain,
( ! [X0] :
( big_p(X0)
| big_p(f(f(X0))) )
| ~ spl7_3
| ~ spl7_10 ),
inference(subsumption_resolution,[],[f50,f82]) ).
fof(f82,plain,
( ! [X1] : sP0(X1)
| ~ spl7_10 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f81,plain,
( spl7_10
<=> ! [X1] : sP0(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_10])]) ).
fof(f50,plain,
( ! [X0] :
( big_p(f(f(X0)))
| big_p(X0)
| ~ sP0(X0) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f49,plain,
( spl7_3
<=> ! [X0] :
( big_p(X0)
| ~ sP0(X0)
| big_p(f(f(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
fof(f160,plain,
( ~ spl7_8
| spl7_11
| ~ spl7_13 ),
inference(avatar_split_clause,[],[f158,f95,f86,f72]) ).
fof(f72,plain,
( spl7_8
<=> big_p(f(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_8])]) ).
fof(f95,plain,
( spl7_13
<=> ! [X1] :
( big_p(sF6(X1))
| ~ big_p(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_13])]) ).
fof(f158,plain,
( ~ big_p(f(sK2))
| spl7_11
| ~ spl7_13 ),
inference(resolution,[],[f147,f96]) ).
fof(f96,plain,
( ! [X1] :
( big_p(sF6(X1))
| ~ big_p(f(X1)) )
| ~ spl7_13 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f155,plain,
( spl7_6
| ~ spl7_5
| ~ spl7_13 ),
inference(avatar_split_clause,[],[f154,f95,f58,f63]) ).
fof(f63,plain,
( spl7_6
<=> big_p(sF5) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).
fof(f58,plain,
( spl7_5
<=> big_p(sF4) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).
fof(f154,plain,
( big_p(sF5)
| ~ spl7_5
| ~ spl7_13 ),
inference(subsumption_resolution,[],[f153,f60]) ).
fof(f60,plain,
( big_p(sF4)
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f153,plain,
( big_p(sF5)
| ~ big_p(sF4)
| ~ spl7_13 ),
inference(forward_demodulation,[],[f138,f33]) ).
fof(f33,plain,
sF4 = f(sK3),
introduced(function_definition,[]) ).
fof(f138,plain,
( ~ big_p(f(sK3))
| big_p(sF5)
| ~ spl7_13 ),
inference(superposition,[],[f96,f119]) ).
fof(f119,plain,
sF6(sK3) = sF5,
inference(forward_demodulation,[],[f116,f35]) ).
fof(f35,plain,
f(sF4) = sF5,
introduced(function_definition,[]) ).
fof(f116,plain,
sF6(sK3) = f(sF4),
inference(superposition,[],[f37,f33]) ).
fof(f136,plain,
( spl7_13
| ~ spl7_12 ),
inference(avatar_split_clause,[],[f135,f91,f95]) ).
fof(f91,plain,
( spl7_12
<=> ! [X1] :
( big_p(f(f(X1)))
| ~ big_p(f(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_12])]) ).
fof(f135,plain,
( ! [X1] :
( big_p(sF6(X1))
| ~ big_p(f(X1)) )
| ~ spl7_12 ),
inference(forward_demodulation,[],[f92,f37]) ).
fof(f92,plain,
( ! [X1] :
( big_p(f(f(X1)))
| ~ big_p(f(X1)) )
| ~ spl7_12 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f129,plain,
( spl7_10
| ~ spl7_9 ),
inference(avatar_split_clause,[],[f128,f77,f81]) ).
fof(f77,plain,
( spl7_9
<=> ! [X1] :
( big_p(X1)
| big_p(f(f(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_9])]) ).
fof(f128,plain,
( ! [X0] : sP0(X0)
| ~ spl7_9 ),
inference(subsumption_resolution,[],[f123,f25]) ).
fof(f25,plain,
! [X0] :
( sP0(X0)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0] :
( ( sP0(X0)
| ( ~ big_p(f(f(X0)))
& big_p(a)
& ~ big_p(X0) ) )
& ( big_p(f(f(X0)))
| ~ big_p(a)
| big_p(X0)
| ~ sP0(X0) ) ),
inference(rectify,[],[f13]) ).
fof(f13,plain,
! [X1] :
( ( sP0(X1)
| ( ~ big_p(f(f(X1)))
& big_p(a)
& ~ big_p(X1) ) )
& ( big_p(f(f(X1)))
| ~ big_p(a)
| big_p(X1)
| ~ sP0(X1) ) ),
inference(flattening,[],[f12]) ).
fof(f12,plain,
! [X1] :
( ( sP0(X1)
| ( ~ big_p(f(f(X1)))
& big_p(a)
& ~ big_p(X1) ) )
& ( big_p(f(f(X1)))
| ~ big_p(a)
| big_p(X1)
| ~ sP0(X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,plain,
! [X1] :
( sP0(X1)
<=> ( big_p(f(f(X1)))
| ~ big_p(a)
| big_p(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f123,plain,
( ! [X0] :
( sP0(X0)
| big_p(X0) )
| ~ spl7_9 ),
inference(resolution,[],[f122,f115]) ).
fof(f115,plain,
! [X0] :
( ~ big_p(sF6(X0))
| sP0(X0) ),
inference(backward_demodulation,[],[f27,f37]) ).
fof(f27,plain,
! [X0] :
( ~ big_p(f(f(X0)))
| sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f122,plain,
( ! [X1] :
( big_p(sF6(X1))
| big_p(X1) )
| ~ spl7_9 ),
inference(forward_demodulation,[],[f78,f37]) ).
fof(f78,plain,
( ! [X1] :
( big_p(f(f(X1)))
| big_p(X1) )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f99,plain,
( spl7_4
| ~ spl7_10 ),
inference(avatar_contradiction_clause,[],[f98]) ).
fof(f98,plain,
( $false
| spl7_4
| ~ spl7_10 ),
inference(resolution,[],[f82,f55]) ).
fof(f55,plain,
( ~ sP0(sK3)
| spl7_4 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f53,plain,
( spl7_4
<=> sP0(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).
fof(f97,plain,
( ~ spl7_1
| spl7_13
| spl7_2 ),
inference(avatar_split_clause,[],[f38,f44,f95,f40]) ).
fof(f40,plain,
( spl7_1
<=> big_p(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f44,plain,
( spl7_2
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f38,plain,
! [X1] :
( sP1
| big_p(sF6(X1))
| ~ big_p(a)
| ~ big_p(f(X1)) ),
inference(definition_folding,[],[f29,f37]) ).
fof(f29,plain,
! [X1] :
( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1)))
| sP1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( ( ( big_p(a)
& big_p(f(sK3))
& ~ big_p(f(f(sK3))) )
| ~ sP0(sK3)
| ~ sP1 )
& ( ! [X1] :
( ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) )
& sP0(X1) )
| sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f16,f17]) ).
fof(f17,plain,
( ? [X0] :
( ( big_p(a)
& big_p(f(X0))
& ~ big_p(f(f(X0))) )
| ~ sP0(X0) )
=> ( ( big_p(a)
& big_p(f(sK3))
& ~ big_p(f(f(sK3))) )
| ~ sP0(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
( ( ? [X0] :
( ( big_p(a)
& big_p(f(X0))
& ~ big_p(f(f(X0))) )
| ~ sP0(X0) )
| ~ sP1 )
& ( ! [X1] :
( ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) )
& sP0(X1) )
| sP1 ) ),
inference(rectify,[],[f15]) ).
fof(f15,plain,
( ( ? [X1] :
( ( big_p(a)
& big_p(f(X1))
& ~ big_p(f(f(X1))) )
| ~ sP0(X1) )
| ~ sP1 )
& ( ! [X1] :
( ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) )
& sP0(X1) )
| sP1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,plain,
( sP1
<~> ! [X1] :
( ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) )
& sP0(X1) ) ),
inference(definition_folding,[],[f4,f6,f5]) ).
fof(f6,plain,
( sP1
<=> ! [X0] :
( ( ~ big_p(f(X0))
& big_p(X0) )
| ~ big_p(a)
| big_p(f(f(X0))) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f4,plain,
( ! [X0] :
( ( ~ big_p(f(X0))
& big_p(X0) )
| ~ big_p(a)
| big_p(f(f(X0))) )
<~> ! [X1] :
( ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) )
& ( big_p(f(f(X1)))
| ~ big_p(a)
| big_p(X1) ) ) ),
inference(flattening,[],[f3]) ).
fof(f3,plain,
( ! [X1] :
( ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) )
& ( big_p(f(f(X1)))
| ~ big_p(a)
| big_p(X1) ) )
<~> ! [X0] :
( big_p(f(f(X0)))
| ~ big_p(a)
| ( ~ big_p(f(X0))
& big_p(X0) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ( ! [X1] :
( ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) )
& ( big_p(f(f(X1)))
| ~ big_p(a)
| big_p(X1) ) )
<=> ! [X0] :
( ( big_p(a)
& ( big_p(X0)
=> big_p(f(X0)) ) )
=> big_p(f(f(X0))) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
( ! [X1] :
( ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) )
& ( big_p(f(f(X1)))
| ~ big_p(a)
| big_p(X1) ) )
<=> ! [X0] :
( ( big_p(a)
& ( big_p(X0)
=> big_p(f(X0)) ) )
=> big_p(f(f(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel62) ).
fof(f93,plain,
( ~ spl7_1
| spl7_12
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f20,f44,f91,f40]) ).
fof(f20,plain,
! [X1] :
( ~ sP1
| big_p(f(f(X1)))
| ~ big_p(a)
| ~ big_p(f(X1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f11,plain,
( ( sP1
| ( ( big_p(f(sK2))
| ~ big_p(sK2) )
& big_p(a)
& ~ big_p(f(f(sK2))) ) )
& ( ! [X1] :
( ( ~ big_p(f(X1))
& big_p(X1) )
| ~ big_p(a)
| big_p(f(f(X1))) )
| ~ sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f9,f10]) ).
fof(f10,plain,
( ? [X0] :
( ( big_p(f(X0))
| ~ big_p(X0) )
& big_p(a)
& ~ big_p(f(f(X0))) )
=> ( ( big_p(f(sK2))
| ~ big_p(sK2) )
& big_p(a)
& ~ big_p(f(f(sK2))) ) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
( ( sP1
| ? [X0] :
( ( big_p(f(X0))
| ~ big_p(X0) )
& big_p(a)
& ~ big_p(f(f(X0))) ) )
& ( ! [X1] :
( ( ~ big_p(f(X1))
& big_p(X1) )
| ~ big_p(a)
| big_p(f(f(X1))) )
| ~ sP1 ) ),
inference(rectify,[],[f8]) ).
fof(f8,plain,
( ( sP1
| ? [X0] :
( ( big_p(f(X0))
| ~ big_p(X0) )
& big_p(a)
& ~ big_p(f(f(X0))) ) )
& ( ! [X0] :
( ( ~ big_p(f(X0))
& big_p(X0) )
| ~ big_p(a)
| big_p(f(f(X0))) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f89,plain,
( spl7_2
| ~ spl7_11 ),
inference(avatar_split_clause,[],[f21,f86,f44]) ).
fof(f21,plain,
( ~ big_p(f(f(sK2)))
| sP1 ),
inference(cnf_transformation,[],[f11]) ).
fof(f84,plain,
( spl7_1
| spl7_10 ),
inference(avatar_split_clause,[],[f26,f81,f40]) ).
fof(f26,plain,
! [X0] :
( sP0(X0)
| big_p(a) ),
inference(cnf_transformation,[],[f14]) ).
fof(f83,plain,
( spl7_2
| spl7_10 ),
inference(avatar_split_clause,[],[f28,f81,f44]) ).
fof(f28,plain,
! [X1] :
( sP0(X1)
| sP1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f79,plain,
( ~ spl7_1
| ~ spl7_2
| spl7_9 ),
inference(avatar_split_clause,[],[f19,f77,f44,f40]) ).
fof(f19,plain,
! [X1] :
( big_p(X1)
| big_p(f(f(X1)))
| ~ sP1
| ~ big_p(a) ),
inference(cnf_transformation,[],[f11]) ).
fof(f75,plain,
( ~ spl7_7
| spl7_8
| spl7_2 ),
inference(avatar_split_clause,[],[f23,f44,f72,f68]) ).
fof(f23,plain,
( sP1
| big_p(f(sK2))
| ~ big_p(sK2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f66,plain,
( ~ spl7_2
| ~ spl7_4
| ~ spl7_6 ),
inference(avatar_split_clause,[],[f36,f63,f53,f44]) ).
fof(f36,plain,
( ~ big_p(sF5)
| ~ sP0(sK3)
| ~ sP1 ),
inference(definition_folding,[],[f30,f35,f33]) ).
fof(f30,plain,
( ~ big_p(f(f(sK3)))
| ~ sP0(sK3)
| ~ sP1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f61,plain,
( ~ spl7_4
| spl7_5
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f34,f44,f58,f53]) ).
fof(f34,plain,
( ~ sP1
| big_p(sF4)
| ~ sP0(sK3) ),
inference(definition_folding,[],[f31,f33]) ).
fof(f31,plain,
( big_p(f(sK3))
| ~ sP0(sK3)
| ~ sP1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f56,plain,
( ~ spl7_2
| ~ spl7_4
| spl7_1 ),
inference(avatar_split_clause,[],[f32,f40,f53,f44]) ).
fof(f32,plain,
( big_p(a)
| ~ sP0(sK3)
| ~ sP1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f51,plain,
( ~ spl7_1
| spl7_3 ),
inference(avatar_split_clause,[],[f24,f49,f40]) ).
fof(f24,plain,
! [X0] :
( big_p(X0)
| big_p(f(f(X0)))
| ~ big_p(a)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f47,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f22,f44,f40]) ).
fof(f22,plain,
( sP1
| big_p(a) ),
inference(cnf_transformation,[],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n002.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 21:42:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.51 % (10628)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.52 % (10621)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.52 % (10621)First to succeed.
% 0.19/0.52 % (10637)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.52 % (10621)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Theorem for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (10621)------------------------------
% 0.19/0.52 % (10621)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (10621)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (10621)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (10621)Memory used [KB]: 6012
% 0.19/0.52 % (10621)Time elapsed: 0.111 s
% 0.19/0.52 % (10621)Instructions burned: 3 (million)
% 0.19/0.52 % (10621)------------------------------
% 0.19/0.52 % (10621)------------------------------
% 0.19/0.52 % (10620)Success in time 0.174 s
%------------------------------------------------------------------------------