TSTP Solution File: SWV381+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SWV381+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 : n018.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 18:45:23 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 7 unt; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 112 ( 45 ~; 34 |; 17 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 109 ( 95 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f186,plain,
$false,
inference(subsumption_resolution,[],[f185,f132]) ).
fof(f132,plain,
phi(findmin_cpq_eff(triple(sK1,sK0,sK2))),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
( phi(findmin_cpq_eff(triple(sK1,sK0,sK2)))
& ~ issmallestelement_pq(i(triple(sK1,sK0,sK2)),findmin_cpq_res(triple(sK1,sK0,sK2))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f102,f103]) ).
fof(f103,plain,
( ? [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X1,X0,X2)))
& ~ issmallestelement_pq(i(triple(X1,X0,X2)),findmin_cpq_res(triple(X1,X0,X2))) )
=> ( phi(findmin_cpq_eff(triple(sK1,sK0,sK2)))
& ~ issmallestelement_pq(i(triple(sK1,sK0,sK2)),findmin_cpq_res(triple(sK1,sK0,sK2))) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
? [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X1,X0,X2)))
& ~ issmallestelement_pq(i(triple(X1,X0,X2)),findmin_cpq_res(triple(X1,X0,X2))) ),
inference(rectify,[],[f89]) ).
fof(f89,plain,
? [X1,X2,X0] :
( phi(findmin_cpq_eff(triple(X2,X1,X0)))
& ~ issmallestelement_pq(i(triple(X2,X1,X0)),findmin_cpq_res(triple(X2,X1,X0))) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,plain,
~ ! [X2,X0,X1] :
( phi(findmin_cpq_eff(triple(X2,X1,X0)))
=> issmallestelement_pq(i(triple(X2,X1,X0)),findmin_cpq_res(triple(X2,X1,X0))) ),
inference(rectify,[],[f66]) ).
fof(f66,negated_conjecture,
~ ! [X2,X1,X0] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
inference(negated_conjecture,[],[f65]) ).
fof(f65,conjecture,
! [X2,X1,X0] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_co) ).
fof(f185,plain,
~ phi(findmin_cpq_eff(triple(sK1,sK0,sK2))),
inference(subsumption_resolution,[],[f183,f166]) ).
fof(f166,plain,
~ less_than(findmin_cpq_res(triple(sK1,sK0,sK2)),sK3(findmin_cpq_res(triple(sK1,sK0,sK2)),i(triple(sK1,sK0,sK2)))),
inference(resolution,[],[f131,f145]) ).
fof(f145,plain,
! [X0,X1] :
( issmallestelement_pq(X1,X0)
| ~ less_than(X0,sK3(X0,X1)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ( contains_pq(X1,sK3(X0,X1))
& ~ less_than(X0,sK3(X0,X1)) )
| issmallestelement_pq(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f114,f115]) ).
fof(f115,plain,
! [X0,X1] :
( ? [X2] :
( contains_pq(X1,X2)
& ~ less_than(X0,X2) )
=> ( contains_pq(X1,sK3(X0,X1))
& ~ less_than(X0,sK3(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
! [X0,X1] :
( ? [X2] :
( contains_pq(X1,X2)
& ~ less_than(X0,X2) )
| issmallestelement_pq(X1,X0) ),
inference(rectify,[],[f93]) ).
fof(f93,plain,
! [X1,X0] :
( ? [X2] :
( contains_pq(X0,X2)
& ~ less_than(X1,X2) )
| issmallestelement_pq(X0,X1) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,plain,
! [X1,X0] :
( ! [X2] :
( contains_pq(X0,X2)
=> less_than(X1,X2) )
=> issmallestelement_pq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f10,axiom,
! [X1,X0] :
( issmallestelement_pq(X0,X1)
<=> ! [X2] :
( contains_pq(X0,X2)
=> less_than(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
fof(f131,plain,
~ issmallestelement_pq(i(triple(sK1,sK0,sK2)),findmin_cpq_res(triple(sK1,sK0,sK2))),
inference(cnf_transformation,[],[f104]) ).
fof(f183,plain,
( less_than(findmin_cpq_res(triple(sK1,sK0,sK2)),sK3(findmin_cpq_res(triple(sK1,sK0,sK2)),i(triple(sK1,sK0,sK2))))
| ~ phi(findmin_cpq_eff(triple(sK1,sK0,sK2))) ),
inference(resolution,[],[f178,f174]) ).
fof(f174,plain,
! [X2,X3,X0,X1] :
( ~ contains_cpq(triple(X0,X1,X2),X3)
| less_than(findmin_cpq_res(triple(X0,X1,X2)),X3)
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(subsumption_resolution,[],[f172,f144]) ).
fof(f144,plain,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(rectify,[],[f74]) ).
fof(f74,plain,
! [X1,X0] :
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( less_than(X0,X1)
| less_than(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
fof(f172,plain,
! [X2,X3,X0,X1] :
( less_than(findmin_cpq_res(triple(X0,X1,X2)),X3)
| ~ contains_cpq(triple(X0,X1,X2),X3)
| ~ less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(resolution,[],[f141,f140]) ).
fof(f140,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( less_than(X1,X0)
| strictly_less_than(X0,X1)
| ~ less_than(X0,X1) ),
inference(rectify,[],[f99]) ).
fof(f99,plain,
! [X1,X0] :
( less_than(X0,X1)
| strictly_less_than(X1,X0)
| ~ less_than(X1,X0) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
! [X1,X0] :
( strictly_less_than(X1,X0)
| ~ less_than(X1,X0)
| less_than(X0,X1) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,plain,
! [X1,X0] :
( ( less_than(X1,X0)
& ~ less_than(X0,X1) )
=> strictly_less_than(X1,X0) ),
inference(unused_predicate_definition_removal,[],[f72]) ).
fof(f72,plain,
! [X1,X0] :
( ( less_than(X1,X0)
& ~ less_than(X0,X1) )
<=> strictly_less_than(X1,X0) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( strictly_less_than(X0,X1)
<=> ( less_than(X0,X1)
& ~ less_than(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X2,X1)))
| ~ phi(findmin_cpq_eff(triple(X0,X2,X1)))
| ~ contains_cpq(triple(X0,X2,X1),X3) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ~ phi(findmin_cpq_eff(triple(X0,X2,X1)))
| ! [X3] :
( ~ contains_cpq(triple(X0,X2,X1),X3)
| ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X2,X1))) ) ),
inference(rectify,[],[f95]) ).
fof(f95,plain,
! [X1,X0,X2] :
( ~ phi(findmin_cpq_eff(triple(X1,X2,X0)))
| ! [X3] :
( ~ contains_cpq(triple(X1,X2,X0),X3)
| ~ strictly_less_than(X3,findmin_cpq_res(triple(X1,X2,X0))) ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ? [X3] :
( strictly_less_than(X3,findmin_cpq_res(triple(X1,X2,X0)))
& contains_cpq(triple(X1,X2,X0),X3) )
=> ~ phi(findmin_cpq_eff(triple(X1,X2,X0))) ),
inference(rectify,[],[f64]) ).
fof(f64,axiom,
! [X2,X0,X1] :
( ? [X3] :
( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_cpq(triple(X0,X1,X2),X3) )
=> ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_l18) ).
fof(f178,plain,
contains_cpq(triple(sK1,sK0,sK2),sK3(findmin_cpq_res(triple(sK1,sK0,sK2)),i(triple(sK1,sK0,sK2)))),
inference(resolution,[],[f165,f159]) ).
fof(f159,plain,
! [X2,X3,X0,X1] :
( ~ contains_pq(i(triple(X0,X3,X2)),X1)
| contains_cpq(triple(X0,X3,X2),X1) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( ( contains_pq(i(triple(X0,X3,X2)),X1)
| ~ contains_cpq(triple(X0,X3,X2),X1) )
& ( contains_cpq(triple(X0,X3,X2),X1)
| ~ contains_pq(i(triple(X0,X3,X2)),X1) ) ),
inference(rectify,[],[f127]) ).
fof(f127,plain,
! [X0,X2,X3,X1] :
( ( contains_pq(i(triple(X0,X1,X3)),X2)
| ~ contains_cpq(triple(X0,X1,X3),X2) )
& ( contains_cpq(triple(X0,X1,X3),X2)
| ~ contains_pq(i(triple(X0,X1,X3)),X2) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X2,X3,X1] :
( contains_pq(i(triple(X0,X1,X3)),X2)
<=> contains_cpq(triple(X0,X1,X3),X2) ),
inference(rectify,[],[f63]) ).
fof(f63,axiom,
! [X0,X1,X3,X2] :
( contains_pq(i(triple(X0,X1,X2)),X3)
<=> contains_cpq(triple(X0,X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_li56) ).
fof(f165,plain,
contains_pq(i(triple(sK1,sK0,sK2)),sK3(findmin_cpq_res(triple(sK1,sK0,sK2)),i(triple(sK1,sK0,sK2)))),
inference(resolution,[],[f131,f146]) ).
fof(f146,plain,
! [X0,X1] :
( issmallestelement_pq(X1,X0)
| contains_pq(X1,sK3(X0,X1)) ),
inference(cnf_transformation,[],[f116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV381+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % 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 : n018.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 19:24:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.47 % (25565)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.47 % (25544)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.48 % (25557)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.48 % (25544)First to succeed.
% 0.19/0.49 % (25544)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (25544)------------------------------
% 0.19/0.49 % (25544)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49 % (25544)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49 % (25544)Termination reason: Refutation
% 0.19/0.49
% 0.19/0.49 % (25544)Memory used [KB]: 1535
% 0.19/0.49 % (25544)Time elapsed: 0.101 s
% 0.19/0.49 % (25544)Instructions burned: 3 (million)
% 0.19/0.49 % (25544)------------------------------
% 0.19/0.49 % (25544)------------------------------
% 0.19/0.49 % (25538)Success in time 0.145 s
%------------------------------------------------------------------------------