TSTP Solution File: SWV408+2 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SWV408+2 : 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 : n014.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 18:45:29 EDT 2022
% Result : Theorem 0.22s 0.51s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 7 unt; 0 def)
% Number of atoms : 153 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 169 ( 67 ~; 53 |; 36 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 130 ( 106 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f291,plain,
$false,
inference(subsumption_resolution,[],[f290,f172]) ).
fof(f172,plain,
contains_slb(sK2,sK0),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
( contains_slb(sK2,sK0)
& ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK0,findmin_pqp_res(sK1))
& strictly_less_than(sK0,findmin_cpq_res(triple(sK1,sK2,sK3)))
& ! [X4] :
( ~ less_than(findmin_pqp_res(sK1),X4)
| ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK0,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f125,f126]) ).
fof(f126,plain,
( ? [X0,X1,X2,X3] :
( contains_slb(X2,X0)
& ~ pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X0,findmin_pqp_res(X1))
& strictly_less_than(X0,findmin_cpq_res(triple(X1,X2,X3)))
& ! [X4] :
( ~ less_than(findmin_pqp_res(X1),X4)
| ~ pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X0,X4) ) )
=> ( contains_slb(sK2,sK0)
& ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK0,findmin_pqp_res(sK1))
& strictly_less_than(sK0,findmin_cpq_res(triple(sK1,sK2,sK3)))
& ! [X4] :
( ~ less_than(findmin_pqp_res(sK1),X4)
| ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK0,X4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
? [X0,X1,X2,X3] :
( contains_slb(X2,X0)
& ~ pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X0,findmin_pqp_res(X1))
& strictly_less_than(X0,findmin_cpq_res(triple(X1,X2,X3)))
& ! [X4] :
( ~ less_than(findmin_pqp_res(X1),X4)
| ~ pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X0,X4) ) ),
inference(rectify,[],[f101]) ).
fof(f101,plain,
? [X3,X0,X2,X1] :
( contains_slb(X2,X3)
& ~ pair_in_list(update_slb(X2,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X2,X1)))
& ! [X4] :
( ~ less_than(findmin_pqp_res(X0),X4)
| ~ pair_in_list(update_slb(X2,findmin_pqp_res(X0)),X3,X4) ) ),
inference(flattening,[],[f100]) ).
fof(f100,plain,
? [X1,X3,X2,X0] :
( ~ pair_in_list(update_slb(X2,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
& ! [X4] :
( ~ less_than(findmin_pqp_res(X0),X4)
| ~ pair_in_list(update_slb(X2,findmin_pqp_res(X0)),X3,X4) )
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X2,X1)))
& contains_slb(X2,X3) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,plain,
~ ! [X1,X3,X2,X0] :
( ( strictly_less_than(X3,findmin_cpq_res(triple(X0,X2,X1)))
& contains_slb(X2,X3) )
=> ( pair_in_list(update_slb(X2,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
| ? [X4] :
( pair_in_list(update_slb(X2,findmin_pqp_res(X0)),X3,X4)
& less_than(findmin_pqp_res(X0),X4) ) ) ),
inference(rectify,[],[f46]) ).
fof(f46,negated_conjecture,
~ ! [X0,X2,X1,X3] :
( ( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_slb(X1,X3) )
=> ( ? [X4] :
( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
& less_than(findmin_pqp_res(X0),X4) )
| pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ) ),
inference(negated_conjecture,[],[f45]) ).
fof(f45,conjecture,
! [X0,X2,X1,X3] :
( ( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_slb(X1,X3) )
=> ( ? [X4] :
( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
& less_than(findmin_pqp_res(X0),X4) )
| pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l44_co) ).
fof(f290,plain,
~ contains_slb(sK2,sK0),
inference(subsumption_resolution,[],[f287,f171]) ).
fof(f171,plain,
~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK0,findmin_pqp_res(sK1)),
inference(cnf_transformation,[],[f127]) ).
fof(f287,plain,
( pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK0,findmin_pqp_res(sK1))
| ~ contains_slb(sK2,sK0) ),
inference(resolution,[],[f284,f272]) ).
fof(f272,plain,
! [X10,X11,X12] :
( ~ strictly_less_than(sK4(X10,X12),X11)
| ~ contains_slb(X10,X12)
| pair_in_list(update_slb(X10,X11),X12,X11) ),
inference(resolution,[],[f193,f173]) ).
fof(f173,plain,
! [X0,X1] :
( pair_in_list(X0,X1,sK4(X0,X1))
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1] :
( ~ contains_slb(X0,X1)
| pair_in_list(X0,X1,sK4(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f128,f129]) ).
fof(f129,plain,
! [X0,X1] :
( ? [X2] : pair_in_list(X0,X1,X2)
=> pair_in_list(X0,X1,sK4(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f128,plain,
! [X0,X1] :
( ~ contains_slb(X0,X1)
| ? [X2] : pair_in_list(X0,X1,X2) ),
inference(rectify,[],[f115]) ).
fof(f115,plain,
! [X1,X0] :
( ~ contains_slb(X1,X0)
| ? [X2] : pair_in_list(X1,X0,X2) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,plain,
! [X1,X0] :
( contains_slb(X1,X0)
=> ? [X2] : pair_in_list(X1,X0,X2) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X1,X0] :
( contains_slb(X0,X1)
=> ? [X2] : pair_in_list(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_li4647) ).
fof(f193,plain,
! [X2,X3,X0,X1] :
( ~ pair_in_list(X1,X0,X2)
| pair_in_list(update_slb(X1,X3),X0,X3)
| ~ strictly_less_than(X2,X3) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0,X1,X2,X3] :
( ~ pair_in_list(X1,X0,X2)
| pair_in_list(update_slb(X1,X3),X0,X3)
| ~ strictly_less_than(X2,X3) ),
inference(rectify,[],[f92]) ).
fof(f92,plain,
! [X0,X3,X2,X1] :
( ~ pair_in_list(X3,X0,X2)
| pair_in_list(update_slb(X3,X1),X0,X1)
| ~ strictly_less_than(X2,X1) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( pair_in_list(update_slb(X3,X1),X0,X1)
| ~ strictly_less_than(X2,X1)
| ~ pair_in_list(X3,X0,X2) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( ( strictly_less_than(X2,X1)
& pair_in_list(X3,X0,X2) )
=> pair_in_list(update_slb(X3,X1),X0,X1) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X1,X3,X2,X0] :
( ( strictly_less_than(X2,X3)
& pair_in_list(X0,X1,X2) )
=> pair_in_list(update_slb(X0,X3),X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l48_li3839) ).
fof(f284,plain,
strictly_less_than(sK4(sK2,sK0),findmin_pqp_res(sK1)),
inference(subsumption_resolution,[],[f283,f278]) ).
fof(f278,plain,
~ less_than(findmin_pqp_res(sK1),sK4(sK2,sK0)),
inference(subsumption_resolution,[],[f277,f172]) ).
fof(f277,plain,
( ~ contains_slb(sK2,sK0)
| ~ less_than(findmin_pqp_res(sK1),sK4(sK2,sK0)) ),
inference(resolution,[],[f276,f173]) ).
fof(f276,plain,
! [X0] :
( ~ pair_in_list(sK2,sK0,X0)
| ~ less_than(findmin_pqp_res(sK1),X0) ),
inference(duplicate_literal_removal,[],[f274]) ).
fof(f274,plain,
! [X0] :
( ~ less_than(findmin_pqp_res(sK1),X0)
| ~ pair_in_list(sK2,sK0,X0)
| ~ less_than(findmin_pqp_res(sK1),X0) ),
inference(resolution,[],[f195,f169]) ).
fof(f169,plain,
! [X4] :
( ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK0,X4)
| ~ less_than(findmin_pqp_res(sK1),X4) ),
inference(cnf_transformation,[],[f127]) ).
fof(f195,plain,
! [X2,X3,X0,X1] :
( pair_in_list(update_slb(X2,X0),X1,X3)
| ~ pair_in_list(X2,X1,X3)
| ~ less_than(X0,X3) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0,X1,X2,X3] :
( ~ less_than(X0,X3)
| ~ pair_in_list(X2,X1,X3)
| pair_in_list(update_slb(X2,X0),X1,X3) ),
inference(rectify,[],[f106]) ).
fof(f106,plain,
! [X1,X2,X0,X3] :
( ~ less_than(X1,X3)
| ~ pair_in_list(X0,X2,X3)
| pair_in_list(update_slb(X0,X1),X2,X3) ),
inference(flattening,[],[f105]) ).
fof(f105,plain,
! [X1,X3,X0,X2] :
( pair_in_list(update_slb(X0,X1),X2,X3)
| ~ pair_in_list(X0,X2,X3)
| ~ less_than(X1,X3) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,plain,
! [X1,X3,X0,X2] :
( ( pair_in_list(X0,X2,X3)
& less_than(X1,X3) )
=> pair_in_list(update_slb(X0,X1),X2,X3) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X0,X3,X1,X2] :
( ( pair_in_list(X0,X1,X2)
& less_than(X3,X2) )
=> pair_in_list(update_slb(X0,X3),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l49_li3637) ).
fof(f283,plain,
( less_than(findmin_pqp_res(sK1),sK4(sK2,sK0))
| strictly_less_than(sK4(sK2,sK0),findmin_pqp_res(sK1)) ),
inference(resolution,[],[f279,f167]) ).
fof(f167,plain,
! [X0,X1] :
( ~ less_than(X0,X1)
| less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1] :
( ( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) )
& ( ( less_than(X0,X1)
& ~ less_than(X1,X0) )
| ~ strictly_less_than(X0,X1) ) ),
inference(rectify,[],[f122]) ).
fof(f122,plain,
! [X1,X0] :
( ( strictly_less_than(X1,X0)
| ~ less_than(X1,X0)
| less_than(X0,X1) )
& ( ( less_than(X1,X0)
& ~ less_than(X0,X1) )
| ~ strictly_less_than(X1,X0) ) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X1,X0] :
( ( strictly_less_than(X1,X0)
| ~ less_than(X1,X0)
| less_than(X0,X1) )
& ( ( less_than(X1,X0)
& ~ less_than(X0,X1) )
| ~ strictly_less_than(X1,X0) ) ),
inference(nnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X1,X0] :
( strictly_less_than(X1,X0)
<=> ( less_than(X1,X0)
& ~ less_than(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
<=> strictly_less_than(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f279,plain,
less_than(sK4(sK2,sK0),findmin_pqp_res(sK1)),
inference(resolution,[],[f278,f202]) ).
fof(f202,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(rectify,[],[f80]) ).
fof(f80,plain,
! [X1,X0] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( less_than(X1,X0)
| less_than(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV408+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 30 19:23:48 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.22/0.48 % (24465)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.50 % (24481)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.22/0.50 % (24465)First to succeed.
% 0.22/0.50 % (24473)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)
% 0.22/0.51 % (24481)Instruction limit reached!
% 0.22/0.51 % (24481)------------------------------
% 0.22/0.51 % (24481)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.51 % (24454)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.22/0.51 % (24465)Refutation found. Thanks to Tanya!
% 0.22/0.51 % SZS status Theorem for theBenchmark
% 0.22/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.51 % (24465)------------------------------
% 0.22/0.51 % (24465)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.51 % (24465)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.51 % (24465)Termination reason: Refutation
% 0.22/0.51
% 0.22/0.51 % (24465)Memory used [KB]: 1663
% 0.22/0.51 % (24465)Time elapsed: 0.091 s
% 0.22/0.51 % (24465)Instructions burned: 7 (million)
% 0.22/0.51 % (24465)------------------------------
% 0.22/0.51 % (24465)------------------------------
% 0.22/0.51 % (24452)Success in time 0.154 s
%------------------------------------------------------------------------------