TSTP Solution File: SEU146+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU146+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n005.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 18:26:53 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 7 unt; 0 def)
% Number of atoms : 186 ( 56 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 191 ( 70 ~; 85 |; 20 &)
% ( 11 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 58 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f145,plain,
$false,
inference(avatar_sat_refutation,[],[f69,f74,f75,f78,f81,f144]) ).
fof(f144,plain,
( ~ spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_contradiction_clause,[],[f143]) ).
fof(f143,plain,
( $false
| ~ spl4_1
| spl4_2
| spl4_3 ),
inference(subsumption_resolution,[],[f142,f82]) ).
fof(f82,plain,
( ~ subset(sK3,empty_set)
| spl4_2 ),
inference(unit_resulting_resolution,[],[f68,f48]) ).
fof(f48,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f68,plain,
( empty_set != sK3
| spl4_2 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f66,plain,
( spl4_2
<=> empty_set = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f142,plain,
( subset(sK3,empty_set)
| ~ spl4_1
| spl4_3 ),
inference(forward_demodulation,[],[f135,f100]) ).
fof(f100,plain,
! [X0] : empty_set = set_difference(X0,X0),
inference(unit_resulting_resolution,[],[f53,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| empty_set = set_difference(X1,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( empty_set = set_difference(X1,X0)
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| empty_set != set_difference(X1,X0) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( empty_set = set_difference(X1,X0)
<=> subset(X1,X0) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X1,X0] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f53,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f135,plain,
( subset(sK3,set_difference(singleton(sK2),singleton(sK2)))
| ~ spl4_1
| spl4_3 ),
inference(unit_resulting_resolution,[],[f63,f128,f54]) ).
fof(f54,plain,
! [X2,X0,X1] :
( subset(X2,set_difference(X0,singleton(X1)))
| in(X1,X2)
| ~ subset(X2,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( in(X1,X2)
| subset(X2,set_difference(X0,singleton(X1)))
| ~ subset(X2,X0) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X2,X0,X1] :
( in(X0,X1)
| subset(X1,set_difference(X2,singleton(X0)))
| ~ subset(X1,X2) ),
inference(flattening,[],[f24]) ).
fof(f24,plain,
! [X1,X0,X2] :
( subset(X1,set_difference(X2,singleton(X0)))
| in(X0,X1)
| ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
! [X1,X0,X2] :
( subset(X1,X2)
=> ( subset(X1,set_difference(X2,singleton(X0)))
| in(X0,X1) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( subset(X0,X1)
=> ( in(X2,X0)
| subset(X0,set_difference(X1,singleton(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f128,plain,
( ~ in(sK2,sK3)
| ~ spl4_1
| spl4_3 ),
inference(unit_resulting_resolution,[],[f127,f47]) ).
fof(f47,plain,
! [X0,X1] :
( subset(singleton(X1),X0)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( ( subset(singleton(X1),X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ subset(singleton(X1),X0) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( subset(singleton(X1),X0)
<=> in(X1,X0) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f127,plain,
( ~ subset(singleton(sK2),sK3)
| ~ spl4_1
| spl4_3 ),
inference(unit_resulting_resolution,[],[f73,f63,f50]) ).
fof(f50,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
<=> X0 = X1 ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( ( subset(X0,X1)
& subset(X1,X0) )
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f73,plain,
( singleton(sK2) != sK3
| spl4_3 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f71,plain,
( spl4_3
<=> singleton(sK2) = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
fof(f63,plain,
( subset(sK3,singleton(sK2))
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f62,plain,
( spl4_1
<=> subset(sK3,singleton(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f81,plain,
( spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f80,plain,
( $false
| spl4_1
| ~ spl4_3 ),
inference(subsumption_resolution,[],[f79,f53]) ).
fof(f79,plain,
( ~ subset(sK3,sK3)
| spl4_1
| ~ spl4_3 ),
inference(backward_demodulation,[],[f64,f72]) ).
fof(f72,plain,
( singleton(sK2) = sK3
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f64,plain,
( ~ subset(sK3,singleton(sK2))
| spl4_1 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f78,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f77]) ).
fof(f77,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f76,f49]) ).
fof(f49,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f76,plain,
( ~ subset(empty_set,singleton(sK2))
| spl4_1
| ~ spl4_2 ),
inference(backward_demodulation,[],[f64,f67]) ).
fof(f67,plain,
( empty_set = sK3
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f75,plain,
( spl4_2
| spl4_3
| spl4_1 ),
inference(avatar_split_clause,[],[f56,f62,f71,f66]) ).
fof(f56,plain,
( subset(sK3,singleton(sK2))
| singleton(sK2) = sK3
| empty_set = sK3 ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( ( ( singleton(sK2) != sK3
& empty_set != sK3 )
| ~ subset(sK3,singleton(sK2)) )
& ( singleton(sK2) = sK3
| empty_set = sK3
| subset(sK3,singleton(sK2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f38,f39]) ).
fof(f39,plain,
( ? [X0,X1] :
( ( ( singleton(X0) != X1
& empty_set != X1 )
| ~ subset(X1,singleton(X0)) )
& ( singleton(X0) = X1
| empty_set = X1
| subset(X1,singleton(X0)) ) )
=> ( ( ( singleton(sK2) != sK3
& empty_set != sK3 )
| ~ subset(sK3,singleton(sK2)) )
& ( singleton(sK2) = sK3
| empty_set = sK3
| subset(sK3,singleton(sK2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
? [X0,X1] :
( ( ( singleton(X0) != X1
& empty_set != X1 )
| ~ subset(X1,singleton(X0)) )
& ( singleton(X0) = X1
| empty_set = X1
| subset(X1,singleton(X0)) ) ),
inference(rectify,[],[f37]) ).
fof(f37,plain,
? [X1,X0] :
( ( ( singleton(X1) != X0
& empty_set != X0 )
| ~ subset(X0,singleton(X1)) )
& ( singleton(X1) = X0
| empty_set = X0
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
? [X1,X0] :
( ( ( singleton(X1) != X0
& empty_set != X0 )
| ~ subset(X0,singleton(X1)) )
& ( singleton(X1) = X0
| empty_set = X0
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
? [X1,X0] :
( subset(X0,singleton(X1))
<~> ( singleton(X1) = X0
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X1,X0] :
( ( singleton(X1) = X0
| empty_set = X0 )
<=> subset(X0,singleton(X1)) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X1,X0] :
( ( singleton(X1) = X0
| empty_set = X0 )
<=> subset(X0,singleton(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f74,plain,
( ~ spl4_3
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f58,f62,f71]) ).
fof(f58,plain,
( ~ subset(sK3,singleton(sK2))
| singleton(sK2) != sK3 ),
inference(cnf_transformation,[],[f40]) ).
fof(f69,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f57,f66,f62]) ).
fof(f57,plain,
( empty_set != sK3
| ~ subset(sK3,singleton(sK2)) ),
inference(cnf_transformation,[],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU146+1 : TPTP v8.1.0. Released v3.3.0.
% 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
% 0.13/0.35 % Computer : n005.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 Aug 30 14:44:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.47 % (9077)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.48 % (9085)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.48 % (9077)First to succeed.
% 0.20/0.48 % (9084)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.20/0.49 % (9093)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.20/0.49 % (9077)Refutation found. Thanks to Tanya!
% 0.20/0.49 % SZS status Theorem for theBenchmark
% 0.20/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49 % (9077)------------------------------
% 0.20/0.49 % (9077)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49 % (9077)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49 % (9077)Termination reason: Refutation
% 0.20/0.49
% 0.20/0.49 % (9077)Memory used [KB]: 6012
% 0.20/0.49 % (9077)Time elapsed: 0.094 s
% 0.20/0.49 % (9077)Instructions burned: 4 (million)
% 0.20/0.49 % (9077)------------------------------
% 0.20/0.49 % (9077)------------------------------
% 0.20/0.49 % (9063)Success in time 0.134 s
%------------------------------------------------------------------------------