TSTP Solution File: SET792+4 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET792+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 : n008.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 18:25:39 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 6 unt; 0 def)
% Number of atoms : 230 ( 22 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 272 ( 90 ~; 82 |; 65 &)
% ( 6 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 148 ( 132 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f139,plain,
$false,
inference(subsumption_resolution,[],[f138,f53]) ).
fof(f53,plain,
member(sK3,sK1),
inference(resolution,[],[f51,f45]) ).
fof(f45,plain,
least(sK3,sK2,sK1),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
( ~ min(sK3,sK2,sK1)
& order(sK2,sK1)
& least(sK3,sK2,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f37,f38]) ).
fof(f38,plain,
( ? [X0,X1,X2] :
( ~ min(X2,X1,X0)
& order(X1,X0)
& least(X2,X1,X0) )
=> ( ~ min(sK3,sK2,sK1)
& order(sK2,sK1)
& least(sK3,sK2,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
? [X0,X1,X2] :
( ~ min(X2,X1,X0)
& order(X1,X0)
& least(X2,X1,X0) ),
inference(rectify,[],[f33]) ).
fof(f33,plain,
? [X1,X0,X2] :
( ~ min(X2,X0,X1)
& order(X0,X1)
& least(X2,X0,X1) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
? [X1,X2,X0] :
( ~ min(X2,X0,X1)
& order(X0,X1)
& least(X2,X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
~ ! [X1,X2,X0] :
( ( order(X0,X1)
& least(X2,X0,X1) )
=> min(X2,X0,X1) ),
inference(rectify,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X5] :
( ( least(X5,X0,X1)
& order(X0,X1) )
=> min(X5,X0,X1) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X0,X1,X5] :
( ( least(X5,X0,X1)
& order(X0,X1) )
=> min(X5,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV4) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ least(X2,X1,X0)
| member(X2,X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ least(X2,X1,X0)
| ( ! [X3] :
( apply(X1,X2,X3)
| ~ member(X3,X0) )
& member(X2,X0) ) ),
inference(rectify,[],[f29]) ).
fof(f29,plain,
! [X2,X1,X0] :
( ~ least(X0,X1,X2)
| ( ! [X3] :
( apply(X1,X0,X3)
| ~ member(X3,X2) )
& member(X0,X2) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X2,X0,X1] :
( least(X0,X1,X2)
=> ( member(X0,X2)
& ! [X3] :
( member(X3,X2)
=> apply(X1,X0,X3) ) ) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f15,plain,
! [X2,X0,X1] :
( least(X0,X1,X2)
<=> ( member(X0,X2)
& ! [X3] :
( member(X3,X2)
=> apply(X1,X0,X3) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X5,X0,X1] :
( ( ! [X2] :
( member(X2,X1)
=> apply(X0,X5,X2) )
& member(X5,X1) )
<=> least(X5,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',least) ).
fof(f138,plain,
~ member(sK3,sK1),
inference(subsumption_resolution,[],[f137,f47]) ).
fof(f47,plain,
~ min(sK3,sK2,sK1),
inference(cnf_transformation,[],[f39]) ).
fof(f137,plain,
( min(sK3,sK2,sK1)
| ~ member(sK3,sK1) ),
inference(duplicate_literal_removal,[],[f136]) ).
fof(f136,plain,
( ~ member(sK3,sK1)
| min(sK3,sK2,sK1)
| ~ member(sK3,sK1)
| min(sK3,sK2,sK1) ),
inference(resolution,[],[f133,f44]) ).
fof(f44,plain,
! [X2,X0,X1] :
( member(sK0(X0,X1,X2),X0)
| ~ member(X1,X0)
| min(X1,X2,X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ member(X1,X0)
| min(X1,X2,X0)
| ( member(sK0(X0,X1,X2),X0)
& sK0(X0,X1,X2) != X1
& apply(X2,sK0(X0,X1,X2),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f34,f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ? [X3] :
( member(X3,X0)
& X1 != X3
& apply(X2,X3,X1) )
=> ( member(sK0(X0,X1,X2),X0)
& sK0(X0,X1,X2) != X1
& apply(X2,sK0(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ member(X1,X0)
| min(X1,X2,X0)
| ? [X3] :
( member(X3,X0)
& X1 != X3
& apply(X2,X3,X1) ) ),
inference(rectify,[],[f31]) ).
fof(f31,plain,
! [X2,X1,X0] :
( ~ member(X1,X2)
| min(X1,X0,X2)
| ? [X3] :
( member(X3,X2)
& X1 != X3
& apply(X0,X3,X1) ) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X2,X1,X0] :
( min(X1,X0,X2)
| ? [X3] :
( X1 != X3
& member(X3,X2)
& apply(X0,X3,X1) )
| ~ member(X1,X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X2,X1,X0] :
( ( ! [X3] :
( ( member(X3,X2)
& apply(X0,X3,X1) )
=> X1 = X3 )
& member(X1,X2) )
=> min(X1,X0,X2) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f14,plain,
! [X2,X1,X0] :
( min(X1,X0,X2)
<=> ( ! [X3] :
( ( member(X3,X2)
& apply(X0,X3,X1) )
=> X1 = X3 )
& member(X1,X2) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X0,X5,X1] :
( ( member(X5,X1)
& ! [X2] :
( ( apply(X0,X2,X5)
& member(X2,X1) )
=> X2 = X5 ) )
<=> min(X5,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',min) ).
fof(f133,plain,
! [X3] :
( ~ member(sK0(X3,sK3,sK2),sK1)
| ~ member(sK3,X3)
| min(sK3,sK2,X3) ),
inference(subsumption_resolution,[],[f130,f43]) ).
fof(f43,plain,
! [X2,X0,X1] :
( min(X1,X2,X0)
| ~ member(X1,X0)
| sK0(X0,X1,X2) != X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f130,plain,
! [X3] :
( sK3 = sK0(X3,sK3,sK2)
| ~ member(sK0(X3,sK3,sK2),sK1)
| ~ member(sK3,X3)
| min(sK3,sK2,X3) ),
inference(resolution,[],[f120,f42]) ).
fof(f42,plain,
! [X2,X0,X1] :
( apply(X2,sK0(X0,X1,X2),X1)
| min(X1,X2,X0)
| ~ member(X1,X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f120,plain,
! [X1] :
( ~ apply(sK2,X1,sK3)
| sK3 = X1
| ~ member(X1,sK1) ),
inference(subsumption_resolution,[],[f117,f53]) ).
fof(f117,plain,
! [X1] :
( sK3 = X1
| ~ apply(sK2,X1,sK3)
| ~ member(X1,sK1)
| ~ member(sK3,sK1) ),
inference(duplicate_literal_removal,[],[f95]) ).
fof(f95,plain,
! [X1] :
( ~ member(sK3,sK1)
| ~ member(X1,sK1)
| ~ apply(sK2,X1,sK3)
| ~ member(X1,sK1)
| sK3 = X1 ),
inference(resolution,[],[f79,f57]) ).
fof(f57,plain,
! [X0] :
( apply(sK2,sK3,X0)
| ~ member(X0,sK1) ),
inference(resolution,[],[f52,f45]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,X0)
| apply(X1,X2,X3)
| ~ least(X2,X1,X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f79,plain,
! [X0,X1] :
( ~ apply(sK2,X1,X0)
| ~ apply(sK2,X0,X1)
| ~ member(X0,sK1)
| X0 = X1
| ~ member(X1,sK1) ),
inference(resolution,[],[f49,f46]) ).
fof(f46,plain,
order(sK2,sK1),
inference(cnf_transformation,[],[f39]) ).
fof(f49,plain,
! [X0,X1,X6,X5] :
( ~ apply(X1,X5,X6)
| ~ apply(X1,X6,X5)
| ~ order(X1,X0)
| ~ member(X5,X0)
| ~ member(X6,X0)
| X5 = X6 ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( ~ order(X1,X0)
| ( ! [X2,X3,X4] :
( apply(X1,X2,X3)
| ~ member(X4,X0)
| ~ member(X2,X0)
| ~ apply(X1,X4,X3)
| ~ apply(X1,X2,X4)
| ~ member(X3,X0) )
& ! [X5,X6] :
( ~ member(X5,X0)
| X5 = X6
| ~ member(X6,X0)
| ~ apply(X1,X6,X5)
| ~ apply(X1,X5,X6) )
& ! [X7] :
( ~ member(X7,X0)
| apply(X1,X7,X7) ) ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X1,X0] :
( ~ order(X0,X1)
| ( ! [X2,X4,X3] :
( apply(X0,X2,X4)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1) )
& ! [X7,X6] :
( ~ member(X7,X1)
| X6 = X7
| ~ member(X6,X1)
| ~ apply(X0,X6,X7)
| ~ apply(X0,X7,X6) )
& ! [X5] :
( ~ member(X5,X1)
| apply(X0,X5,X5) ) ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X1,X0] :
( ( ! [X7,X6] :
( X6 = X7
| ~ apply(X0,X6,X7)
| ~ apply(X0,X7,X6)
| ~ member(X6,X1)
| ~ member(X7,X1) )
& ! [X2,X3,X4] :
( apply(X0,X2,X4)
| ~ apply(X0,X2,X3)
| ~ apply(X0,X3,X4)
| ~ member(X4,X1)
| ~ member(X2,X1)
| ~ member(X3,X1) )
& ! [X5] :
( ~ member(X5,X1)
| apply(X0,X5,X5) ) )
| ~ order(X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
! [X1,X0] :
( order(X0,X1)
=> ( ! [X7,X6] :
( ( member(X6,X1)
& member(X7,X1) )
=> ( ( apply(X0,X6,X7)
& apply(X0,X7,X6) )
=> X6 = X7 ) )
& ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X2,X1)
& member(X3,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X4) )
=> apply(X0,X2,X4) ) )
& ! [X5] :
( member(X5,X1)
=> apply(X0,X5,X5) ) ) ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f21,plain,
! [X1,X0] :
( order(X0,X1)
<=> ( ! [X7,X6] :
( ( member(X6,X1)
& member(X7,X1) )
=> ( ( apply(X0,X6,X7)
& apply(X0,X7,X6) )
=> X6 = X7 ) )
& ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X2,X1)
& member(X3,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X4) )
=> apply(X0,X2,X4) ) )
& ! [X5] :
( member(X5,X1)
=> apply(X0,X5,X5) ) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X2,X1)
& member(X3,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X4) )
=> apply(X0,X2,X4) ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X3,X2] :
( ( member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X2)
& apply(X0,X2,X3) )
=> X2 = X3 ) ) )
<=> order(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET792+4 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 14:23:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.49 % (16998)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.49 % (17002)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)
% 0.20/0.49 % (16998)Refutation not found, incomplete strategy% (16998)------------------------------
% 0.20/0.49 % (16998)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49 % (16998)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49 % (16998)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.49
% 0.20/0.49 % (16998)Memory used [KB]: 5500
% 0.20/0.49 % (16998)Time elapsed: 0.098 s
% 0.20/0.49 % (16998)Instructions burned: 2 (million)
% 0.20/0.49 % (16998)------------------------------
% 0.20/0.49 % (16998)------------------------------
% 0.20/0.50 % (17023)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.50 % (16999)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.50 % (17018)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.50 % (17028)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.50 % (17012)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.50 % (17020)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.50 % (17015)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.50 % (17003)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50 % (17013)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.50 % (17002)First to succeed.
% 0.20/0.50 TRYING [1]
% 0.20/0.50 TRYING [2]
% 0.20/0.50 % (17001)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51 % (17002)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (17002)------------------------------
% 0.20/0.51 % (17002)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (17002)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (17002)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (17002)Memory used [KB]: 5500
% 0.20/0.51 % (17002)Time elapsed: 0.108 s
% 0.20/0.51 % (17002)Instructions burned: 4 (million)
% 0.20/0.51 % (17002)------------------------------
% 0.20/0.51 % (17002)------------------------------
% 0.20/0.51 % (16993)Success in time 0.159 s
%------------------------------------------------------------------------------