TSTP Solution File: SYN417+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYN417+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 : n025.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 18:03:14 EDT 2024
% Result : Theorem 0.15s 0.33s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 78 ( 2 unt; 0 def)
% Number of atoms : 278 ( 165 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 350 ( 150 ~; 146 |; 36 &)
% ( 6 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 69 ( 47 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f108,plain,
$false,
inference(avatar_sat_refutation,[],[f33,f54,f91,f94,f98,f106]) ).
fof(f106,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f105]) ).
fof(f105,plain,
( $false
| ~ spl5_1 ),
inference(subsumption_resolution,[],[f104,f60]) ).
fof(f60,plain,
( g(sK2) != sK3(g(sK2))
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f57]) ).
fof(f57,plain,
( g(sK2) != g(sK2)
| g(sK2) != sK3(g(sK2))
| ~ spl5_1 ),
inference(superposition,[],[f56,f55]) ).
fof(f55,plain,
( sK2 = f(g(sK2))
| ~ spl5_1 ),
inference(subsumption_resolution,[],[f17,f28]) ).
fof(f28,plain,
( sP0
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f26,plain,
( spl5_1
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f17,plain,
( sK2 = f(g(sK2))
| ~ sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f11,plain,
( ( sP0
| ! [X0] :
( ( sK1(X0) != X0
& sK1(X0) = f(g(sK1(X0))) )
| f(g(X0)) != X0 ) )
& ( ( ! [X3] :
( sK2 = X3
| f(g(X3)) != X3 )
& sK2 = f(g(sK2)) )
| ~ sP0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f8,f10,f9]) ).
fof(f9,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& f(g(X1)) = X1 )
=> ( sK1(X0) != X0
& sK1(X0) = f(g(sK1(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
( ? [X2] :
( ! [X3] :
( X2 = X3
| f(g(X3)) != X3 )
& f(g(X2)) = X2 )
=> ( ! [X3] :
( sK2 = X3
| f(g(X3)) != X3 )
& sK2 = f(g(sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f8,plain,
( ( sP0
| ! [X0] :
( ? [X1] :
( X0 != X1
& f(g(X1)) = X1 )
| f(g(X0)) != X0 ) )
& ( ? [X2] :
( ! [X3] :
( X2 = X3
| f(g(X3)) != X3 )
& f(g(X2)) = X2 )
| ~ sP0 ) ),
inference(rectify,[],[f7]) ).
fof(f7,plain,
( ( sP0
| ! [X0] :
( ? [X1] :
( X0 != X1
& f(g(X1)) = X1 )
| f(g(X0)) != X0 ) )
& ( ? [X0] :
( ! [X1] :
( X0 = X1
| f(g(X1)) != X1 )
& f(g(X0)) = X0 )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,plain,
( sP0
<=> ? [X0] :
( ! [X1] :
( X0 = X1
| f(g(X1)) != X1 )
& f(g(X0)) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f56,plain,
( ! [X0] :
( g(f(X0)) != X0
| sK3(X0) != X0 )
| ~ spl5_1 ),
inference(subsumption_resolution,[],[f24,f28]) ).
fof(f24,plain,
! [X0] :
( sK3(X0) != X0
| g(f(X0)) != X0
| ~ sP0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ( ! [X0] :
( ( sK3(X0) != X0
& sK3(X0) = g(f(sK3(X0))) )
| g(f(X0)) != X0 )
| ~ sP0 )
& ( ( ! [X3] :
( sK4 = X3
| g(f(X3)) != X3 )
& sK4 = g(f(sK4)) )
| sP0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f13,f15,f14]) ).
fof(f14,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& g(f(X1)) = X1 )
=> ( sK3(X0) != X0
& sK3(X0) = g(f(sK3(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
( ? [X2] :
( ! [X3] :
( X2 = X3
| g(f(X3)) != X3 )
& g(f(X2)) = X2 )
=> ( ! [X3] :
( sK4 = X3
| g(f(X3)) != X3 )
& sK4 = g(f(sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
( ( ! [X0] :
( ? [X1] :
( X0 != X1
& g(f(X1)) = X1 )
| g(f(X0)) != X0 )
| ~ sP0 )
& ( ? [X2] :
( ! [X3] :
( X2 = X3
| g(f(X3)) != X3 )
& g(f(X2)) = X2 )
| sP0 ) ),
inference(rectify,[],[f12]) ).
fof(f12,plain,
( ( ! [X2] :
( ? [X3] :
( X2 != X3
& g(f(X3)) = X3 )
| g(f(X2)) != X2 )
| ~ sP0 )
& ( ? [X2] :
( ! [X3] :
( X2 = X3
| g(f(X3)) != X3 )
& g(f(X2)) = X2 )
| sP0 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,plain,
( sP0
<~> ? [X2] :
( ! [X3] :
( X2 = X3
| g(f(X3)) != X3 )
& g(f(X2)) = X2 ) ),
inference(definition_folding,[],[f4,f5]) ).
fof(f4,plain,
( ? [X0] :
( ! [X1] :
( X0 = X1
| f(g(X1)) != X1 )
& f(g(X0)) = X0 )
<~> ? [X2] :
( ! [X3] :
( X2 = X3
| g(f(X3)) != X3 )
& g(f(X2)) = X2 ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,plain,
~ ( ? [X0] :
( ! [X1] :
( f(g(X1)) = X1
=> X0 = X1 )
& f(g(X0)) = X0 )
<=> ? [X2] :
( ! [X3] :
( g(f(X3)) = X3
=> X2 = X3 )
& g(f(X2)) = X2 ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
( ! [X1] :
( f(g(X1)) = X1
=> X0 = X1 )
& f(g(X0)) = X0 )
<=> ? [X0] :
( ! [X1] :
( g(f(X1)) = X1
=> X0 = X1 )
& g(f(X0)) = X0 ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
( ? [X0] :
( ! [X1] :
( f(g(X1)) = X1
=> X0 = X1 )
& f(g(X0)) = X0 )
<=> ? [X0] :
( ! [X1] :
( g(f(X1)) = X1
=> X0 = X1 )
& g(f(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cute) ).
fof(f104,plain,
( g(sK2) = sK3(g(sK2))
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f100]) ).
fof(f100,plain,
( g(sK2) != g(sK2)
| g(sK2) = sK3(g(sK2))
| ~ spl5_1 ),
inference(superposition,[],[f77,f55]) ).
fof(f77,plain,
( ! [X0] :
( g(f(X0)) != X0
| g(sK2) = sK3(X0) )
| ~ spl5_1 ),
inference(duplicate_literal_removal,[],[f75]) ).
fof(f75,plain,
( ! [X0] :
( g(sK2) = sK3(X0)
| g(f(X0)) != X0
| g(f(X0)) != X0 )
| ~ spl5_1 ),
inference(superposition,[],[f70,f73]) ).
fof(f73,plain,
( ! [X0] :
( sK2 = f(sK3(X0))
| g(f(X0)) != X0 )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f72]) ).
fof(f72,plain,
( ! [X0] :
( f(sK3(X0)) != f(sK3(X0))
| sK2 = f(sK3(X0))
| g(f(X0)) != X0 )
| ~ spl5_1 ),
inference(superposition,[],[f61,f70]) ).
fof(f61,plain,
( ! [X3] :
( f(g(X3)) != X3
| sK2 = X3 )
| ~ spl5_1 ),
inference(subsumption_resolution,[],[f18,f28]) ).
fof(f18,plain,
! [X3] :
( sK2 = X3
| f(g(X3)) != X3
| ~ sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f70,plain,
( ! [X0] :
( sK3(X0) = g(f(sK3(X0)))
| g(f(X0)) != X0 )
| ~ spl5_1 ),
inference(subsumption_resolution,[],[f23,f28]) ).
fof(f23,plain,
! [X0] :
( sK3(X0) = g(f(sK3(X0)))
| g(f(X0)) != X0
| ~ sP0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f98,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f97]) ).
fof(f97,plain,
( $false
| ~ spl5_1
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f87,f59]) ).
fof(f59,plain,
( sK4 != sK3(sK4)
| ~ spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f58]) ).
fof(f58,plain,
( sK4 != sK4
| sK4 != sK3(sK4)
| ~ spl5_1
| ~ spl5_2 ),
inference(superposition,[],[f56,f32]) ).
fof(f32,plain,
( sK4 = g(f(sK4))
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f30,plain,
( spl5_2
<=> sK4 = g(f(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f87,plain,
( sK4 = sK3(sK4)
| ~ spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f84]) ).
fof(f84,plain,
( sK4 != sK4
| sK4 = sK3(sK4)
| ~ spl5_1
| ~ spl5_2 ),
inference(superposition,[],[f78,f32]) ).
fof(f78,plain,
( ! [X0] :
( g(f(X0)) != X0
| sK3(X0) = sK4 )
| ~ spl5_1
| ~ spl5_2 ),
inference(forward_demodulation,[],[f77,f65]) ).
fof(f65,plain,
( g(sK2) = sK4
| ~ spl5_1
| ~ spl5_2 ),
inference(superposition,[],[f32,f64]) ).
fof(f64,plain,
( sK2 = f(sK4)
| ~ spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f62]) ).
fof(f62,plain,
( f(sK4) != f(sK4)
| sK2 = f(sK4)
| ~ spl5_1
| ~ spl5_2 ),
inference(superposition,[],[f61,f32]) ).
fof(f94,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f93]) ).
fof(f93,plain,
( $false
| ~ spl5_1
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f92,f59]) ).
fof(f92,plain,
( sK4 = sK3(sK4)
| ~ spl5_1
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f82,f65]) ).
fof(f82,plain,
( g(sK2) != sK4
| sK4 = sK3(sK4)
| ~ spl5_1
| ~ spl5_2 ),
inference(superposition,[],[f78,f64]) ).
fof(f91,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f90]) ).
fof(f90,plain,
( $false
| ~ spl5_1
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f89,f59]) ).
fof(f89,plain,
( sK4 = sK3(sK4)
| ~ spl5_1
| ~ spl5_2 ),
inference(forward_demodulation,[],[f88,f65]) ).
fof(f88,plain,
( sK4 = sK3(g(sK2))
| ~ spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f81]) ).
fof(f81,plain,
( g(sK2) != g(sK2)
| sK4 = sK3(g(sK2))
| ~ spl5_1
| ~ spl5_2 ),
inference(superposition,[],[f78,f55]) ).
fof(f54,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f53]) ).
fof(f53,plain,
( $false
| spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f52]) ).
fof(f52,plain,
( f(sK4) != f(sK4)
| spl5_1
| ~ spl5_2 ),
inference(forward_demodulation,[],[f51,f32]) ).
fof(f51,plain,
( f(sK4) != f(g(f(sK4)))
| spl5_1
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f48,f38]) ).
fof(f38,plain,
( f(sK4) != sK1(f(sK4))
| spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f37]) ).
fof(f37,plain,
( f(sK4) != f(sK4)
| f(sK4) != sK1(f(sK4))
| spl5_1
| ~ spl5_2 ),
inference(superposition,[],[f36,f32]) ).
fof(f36,plain,
( ! [X0] :
( f(g(X0)) != X0
| sK1(X0) != X0 )
| spl5_1 ),
inference(subsumption_resolution,[],[f20,f27]) ).
fof(f27,plain,
( ~ sP0
| spl5_1 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f20,plain,
! [X0] :
( sP0
| sK1(X0) != X0
| f(g(X0)) != X0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f48,plain,
( f(sK4) = sK1(f(sK4))
| f(sK4) != f(g(f(sK4)))
| spl5_1
| ~ spl5_2 ),
inference(superposition,[],[f39,f47]) ).
fof(f47,plain,
( sK4 = g(sK1(f(sK4)))
| spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f44]) ).
fof(f44,plain,
( f(sK4) != f(sK4)
| sK4 = g(sK1(f(sK4)))
| spl5_1
| ~ spl5_2 ),
inference(superposition,[],[f42,f32]) ).
fof(f42,plain,
( ! [X0] :
( f(g(X0)) != X0
| g(sK1(X0)) = sK4 )
| spl5_1 ),
inference(trivial_inequality_removal,[],[f41]) ).
fof(f41,plain,
( ! [X0] :
( g(sK1(X0)) != g(sK1(X0))
| g(sK1(X0)) = sK4
| f(g(X0)) != X0 )
| spl5_1 ),
inference(superposition,[],[f34,f39]) ).
fof(f34,plain,
( ! [X3] :
( g(f(X3)) != X3
| sK4 = X3 )
| spl5_1 ),
inference(subsumption_resolution,[],[f22,f27]) ).
fof(f22,plain,
! [X3] :
( sK4 = X3
| g(f(X3)) != X3
| sP0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f39,plain,
( ! [X0] :
( sK1(X0) = f(g(sK1(X0)))
| f(g(X0)) != X0 )
| spl5_1 ),
inference(subsumption_resolution,[],[f19,f27]) ).
fof(f19,plain,
! [X0] :
( sP0
| sK1(X0) = f(g(sK1(X0)))
| f(g(X0)) != X0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f33,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f21,f30,f26]) ).
fof(f21,plain,
( sK4 = g(f(sK4))
| sP0 ),
inference(cnf_transformation,[],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : SYN417+1 : TPTP v8.1.2. Released v2.0.0.
% 0.08/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n025.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Apr 30 02:09:26 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.15/0.31 % (3512)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.33 % (3515)WARNING: value z3 for option sas not known
% 0.15/0.33 % (3516)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.33 % (3517)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)
% 0.15/0.33 % (3513)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.33 % (3514)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.33 % (3518)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)
% 0.15/0.33 % (3515)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)
% 0.15/0.33 % (3519)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)
% 0.15/0.33 TRYING [1]
% 0.15/0.33 TRYING [1]
% 0.15/0.33 TRYING [2]
% 0.15/0.33 TRYING [2]
% 0.15/0.33 TRYING [3]
% 0.15/0.33 TRYING [3]
% 0.15/0.33 % (3515)First to succeed.
% 0.15/0.33 TRYING [4]
% 0.15/0.33 TRYING [4]
% 0.15/0.33 % (3515)Refutation found. Thanks to Tanya!
% 0.15/0.33 % SZS status Theorem for theBenchmark
% 0.15/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.34 % (3515)------------------------------
% 0.15/0.34 % (3515)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.34 % (3515)Termination reason: Refutation
% 0.15/0.34
% 0.15/0.34 % (3515)Memory used [KB]: 779
% 0.15/0.34 % (3515)Time elapsed: 0.006 s
% 0.15/0.34 % (3515)Instructions burned: 8 (million)
% 0.15/0.34 % (3515)------------------------------
% 0.15/0.34 % (3515)------------------------------
% 0.15/0.34 % (3512)Success in time 0.021 s
%------------------------------------------------------------------------------