TSTP Solution File: SET804+4 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET804+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n012.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 18:25:41 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 140 ( 27 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 143 ( 45 ~; 28 |; 49 &)
% ( 4 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 100 ( 69 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f76,plain,
$false,
inference(subsumption_resolution,[],[f75,f45]) ).
fof(f45,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
( least(sK4,sK1,sK0)
& min(sK3,sK1,sK0)
& min(sK2,sK1,sK0)
& sK2 != sK3
& order(sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f35,f38,f37,f36]) ).
fof(f36,plain,
( ? [X0,X1] :
( ? [X2,X3] :
( ? [X4] : least(X4,X1,X0)
& min(X3,X1,X0)
& min(X2,X1,X0)
& X2 != X3 )
& order(X1,X0) )
=> ( ? [X3,X2] :
( ? [X4] : least(X4,sK1,sK0)
& min(X3,sK1,sK0)
& min(X2,sK1,sK0)
& X2 != X3 )
& order(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
( ? [X3,X2] :
( ? [X4] : least(X4,sK1,sK0)
& min(X3,sK1,sK0)
& min(X2,sK1,sK0)
& X2 != X3 )
=> ( ? [X4] : least(X4,sK1,sK0)
& min(sK3,sK1,sK0)
& min(sK2,sK1,sK0)
& sK2 != sK3 ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
( ? [X4] : least(X4,sK1,sK0)
=> least(sK4,sK1,sK0) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4] : least(X4,X1,X0)
& min(X3,X1,X0)
& min(X2,X1,X0)
& X2 != X3 )
& order(X1,X0) ),
inference(rectify,[],[f29]) ).
fof(f29,plain,
? [X1,X0] :
( ? [X3,X2] :
( ? [X4] : least(X4,X0,X1)
& min(X2,X0,X1)
& min(X3,X0,X1)
& X2 != X3 )
& order(X0,X1) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
? [X0,X1] :
( ? [X3,X2] :
( ? [X4] : least(X4,X0,X1)
& min(X3,X0,X1)
& X2 != X3
& min(X2,X0,X1) )
& order(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X3,X2] :
( ( min(X3,X0,X1)
& X2 != X3
& min(X2,X0,X1) )
=> ~ ? [X4] : least(X4,X0,X1) ) ),
inference(rectify,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X8,X7] :
( ( min(X8,X0,X1)
& X7 != X8
& min(X7,X0,X1) )
=> ~ ? [X5] : least(X5,X0,X1) ) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X0,X1] :
( order(X0,X1)
=> ! [X8,X7] :
( ( min(X8,X0,X1)
& X7 != X8
& min(X7,X0,X1) )
=> ~ ? [X5] : least(X5,X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV16) ).
fof(f75,plain,
sK2 = sK3,
inference(forward_demodulation,[],[f74,f62]) ).
fof(f62,plain,
sK2 = sK4,
inference(subsumption_resolution,[],[f61,f55]) ).
fof(f55,plain,
member(sK4,sK0),
inference(resolution,[],[f52,f48]) ).
fof(f48,plain,
least(sK4,sK1,sK0),
inference(cnf_transformation,[],[f39]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ least(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ least(X2,X0,X1)
| ( member(X2,X1)
& ! [X3] :
( apply(X0,X2,X3)
| ~ member(X3,X1) ) ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X1,X2,X0] :
( ~ least(X0,X1,X2)
| ( member(X0,X2)
& ! [X3] :
( apply(X1,X0,X3)
| ~ member(X3,X2) ) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X1,X2,X0] :
( least(X0,X1,X2)
=> ( member(X0,X2)
& ! [X3] :
( member(X3,X2)
=> apply(X1,X0,X3) ) ) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f22,plain,
! [X1,X2,X0] :
( least(X0,X1,X2)
<=> ( member(X0,X2)
& ! [X3] :
( member(X3,X2)
=> apply(X1,X0,X3) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X5,X0,X1] :
( ( member(X5,X1)
& ! [X2] :
( member(X2,X1)
=> apply(X0,X5,X2) ) )
<=> least(X5,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',least) ).
fof(f61,plain,
( ~ member(sK4,sK0)
| sK2 = sK4 ),
inference(subsumption_resolution,[],[f59,f53]) ).
fof(f53,plain,
member(sK2,sK0),
inference(resolution,[],[f50,f46]) ).
fof(f46,plain,
min(sK2,sK1,sK0),
inference(cnf_transformation,[],[f39]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ min(X0,X2,X1)
| member(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( member(X0,X1)
& ! [X3] :
( ~ member(X3,X1)
| ~ apply(X2,X3,X0)
| X0 = X3 ) )
| ~ min(X0,X2,X1) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X1,X2,X0] :
( ( ! [X3] :
( X0 = X3
| ~ apply(X2,X3,X0)
| ~ member(X3,X1) )
& member(X0,X1) )
| ~ min(X0,X2,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X1,X2,X0] :
( min(X0,X2,X1)
=> ( ! [X3] :
( ( apply(X2,X3,X0)
& member(X3,X1) )
=> X0 = X3 )
& member(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f20,plain,
! [X1,X2,X0] :
( ( ! [X3] :
( ( apply(X2,X3,X0)
& member(X3,X1) )
=> X0 = X3 )
& member(X0,X1) )
<=> min(X0,X2,X1) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X5,X1,X0] :
( ( ! [X2] :
( ( apply(X0,X2,X5)
& member(X2,X1) )
=> X2 = X5 )
& member(X5,X1) )
<=> min(X5,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',min) ).
fof(f59,plain,
( sK2 = sK4
| ~ member(sK2,sK0)
| ~ member(sK4,sK0) ),
inference(resolution,[],[f57,f56]) ).
fof(f56,plain,
! [X0] :
( apply(sK1,sK4,X0)
| ~ member(X0,sK0) ),
inference(resolution,[],[f51,f48]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( ~ least(X2,X0,X1)
| apply(X0,X2,X3)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f57,plain,
! [X0] :
( ~ apply(sK1,X0,sK2)
| ~ member(X0,sK0)
| sK2 = X0 ),
inference(resolution,[],[f49,f46]) ).
fof(f49,plain,
! [X2,X3,X0,X1] :
( ~ min(X0,X2,X1)
| X0 = X3
| ~ apply(X2,X3,X0)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f74,plain,
sK3 = sK4,
inference(subsumption_resolution,[],[f73,f54]) ).
fof(f54,plain,
member(sK3,sK0),
inference(resolution,[],[f50,f47]) ).
fof(f47,plain,
min(sK3,sK1,sK0),
inference(cnf_transformation,[],[f39]) ).
fof(f73,plain,
( ~ member(sK3,sK0)
| sK3 = sK4 ),
inference(subsumption_resolution,[],[f70,f55]) ).
fof(f70,plain,
( sK3 = sK4
| ~ member(sK4,sK0)
| ~ member(sK3,sK0) ),
inference(resolution,[],[f58,f56]) ).
fof(f58,plain,
! [X1] :
( ~ apply(sK1,X1,sK3)
| sK3 = X1
| ~ member(X1,sK0) ),
inference(resolution,[],[f49,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET804+4 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n012.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 14:20:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50 % (4918)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.50 % (4925)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.50 % (4925)First to succeed.
% 0.19/0.51 % (4925)Refutation found. Thanks to Tanya!
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51 % (4925)------------------------------
% 0.19/0.51 % (4925)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (4925)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (4925)Termination reason: Refutation
% 0.19/0.51
% 0.19/0.51 % (4925)Memory used [KB]: 5500
% 0.19/0.51 % (4925)Time elapsed: 0.095 s
% 0.19/0.51 % (4925)Instructions burned: 2 (million)
% 0.19/0.51 % (4925)------------------------------
% 0.19/0.51 % (4925)------------------------------
% 0.19/0.51 % (4912)Success in time 0.155 s
%------------------------------------------------------------------------------