TSTP Solution File: KRS122+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : KRS122+1 : TPTP v8.1.0. Released v3.1.0.
% 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 : n025.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 17:30:52 EDT 2022
% Result : Unsatisfiable 0.21s 0.54s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 7 unt; 0 def)
% Number of atoms : 222 ( 10 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 246 ( 93 ~; 83 |; 47 &)
% ( 14 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 126 ( 102 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f252,plain,
$false,
inference(subsumption_resolution,[],[f251,f224]) ).
fof(f224,plain,
ca_Vx3(i2003_11_14_17_21_55116),
inference(resolution,[],[f223,f165]) ).
fof(f165,plain,
cUnsatisfiable(i2003_11_14_17_21_55116),
inference(cnf_transformation,[],[f31]) ).
fof(f31,axiom,
cUnsatisfiable(i2003_11_14_17_21_55116),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
fof(f223,plain,
! [X1] :
( ~ cUnsatisfiable(X1)
| ca_Vx3(X1) ),
inference(subsumption_resolution,[],[f222,f184]) ).
fof(f184,plain,
! [X0] :
( ca_Ax2(sK4(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0] :
( ( ( ca_Ax2(sK4(X0))
& rf(X0,sK4(X0)) )
| ~ cUnsatisfiable(X0) )
& ( cUnsatisfiable(X0)
| ! [X2] :
( ~ ca_Ax2(X2)
| ~ rf(X0,X2) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f139,f140]) ).
fof(f140,plain,
! [X0] :
( ? [X1] :
( ca_Ax2(X1)
& rf(X0,X1) )
=> ( ca_Ax2(sK4(X0))
& rf(X0,sK4(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f139,plain,
! [X0] :
( ( ? [X1] :
( ca_Ax2(X1)
& rf(X0,X1) )
| ~ cUnsatisfiable(X0) )
& ( cUnsatisfiable(X0)
| ! [X2] :
( ~ ca_Ax2(X2)
| ~ rf(X0,X2) ) ) ),
inference(rectify,[],[f138]) ).
fof(f138,plain,
! [X0] :
( ( ? [X1] :
( ca_Ax2(X1)
& rf(X0,X1) )
| ~ cUnsatisfiable(X0) )
& ( cUnsatisfiable(X0)
| ! [X1] :
( ~ ca_Ax2(X1)
| ~ rf(X0,X1) ) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ? [X1] :
( ca_Ax2(X1)
& rf(X0,X1) )
<=> cUnsatisfiable(X0) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X3] :
( ? [X4] :
( rf(X3,X4)
& ca_Ax2(X4) )
<=> cUnsatisfiable(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f222,plain,
! [X1] :
( ~ ca_Ax2(sK4(X1))
| ~ cUnsatisfiable(X1)
| ca_Vx3(X1) ),
inference(resolution,[],[f217,f183]) ).
fof(f183,plain,
! [X0] :
( rf(X0,sK4(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f217,plain,
! [X0,X1] :
( ~ rf(X0,X1)
| ~ ca_Ax2(X1)
| ca_Vx3(X0) ),
inference(resolution,[],[f177,f173]) ).
fof(f173,plain,
! [X0,X1] :
( rinvF(X0,X1)
| ~ rf(X1,X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( ( rf(X1,X0)
| ~ rinvF(X0,X1) )
& ( rinvF(X0,X1)
| ~ rf(X1,X0) ) ),
inference(rectify,[],[f128]) ).
fof(f128,plain,
! [X1,X0] :
( ( rf(X0,X1)
| ~ rinvF(X1,X0) )
& ( rinvF(X1,X0)
| ~ rf(X0,X1) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X1,X0] :
( rf(X0,X1)
<=> rinvF(X1,X0) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X4,X3] :
( rinvF(X3,X4)
<=> rf(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f177,plain,
! [X2,X0] :
( ~ rinvF(X0,X2)
| ca_Vx3(X2)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0] :
( ( ca_Ax2(X0)
| ( ~ ca_Vx3(sK3(X0))
& rinvF(X0,sK3(X0)) )
| ~ cp1(X0) )
& ( ( ! [X2] :
( ca_Vx3(X2)
| ~ rinvF(X0,X2) )
& cp1(X0) )
| ~ ca_Ax2(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f133,f134]) ).
fof(f134,plain,
! [X0] :
( ? [X1] :
( ~ ca_Vx3(X1)
& rinvF(X0,X1) )
=> ( ~ ca_Vx3(sK3(X0))
& rinvF(X0,sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f133,plain,
! [X0] :
( ( ca_Ax2(X0)
| ? [X1] :
( ~ ca_Vx3(X1)
& rinvF(X0,X1) )
| ~ cp1(X0) )
& ( ( ! [X2] :
( ca_Vx3(X2)
| ~ rinvF(X0,X2) )
& cp1(X0) )
| ~ ca_Ax2(X0) ) ),
inference(rectify,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ( ca_Ax2(X0)
| ? [X1] :
( ~ ca_Vx3(X1)
& rinvF(X0,X1) )
| ~ cp1(X0) )
& ( ( ! [X1] :
( ca_Vx3(X1)
| ~ rinvF(X0,X1) )
& cp1(X0) )
| ~ ca_Ax2(X0) ) ),
inference(flattening,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ( ca_Ax2(X0)
| ? [X1] :
( ~ ca_Vx3(X1)
& rinvF(X0,X1) )
| ~ cp1(X0) )
& ( ( ! [X1] :
( ca_Vx3(X1)
| ~ rinvF(X0,X1) )
& cp1(X0) )
| ~ ca_Ax2(X0) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ca_Ax2(X0)
<=> ( ! [X1] :
( ca_Vx3(X1)
| ~ rinvF(X0,X1) )
& cp1(X0) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ( cp1(X0)
& ! [X1] :
( rinvF(X0,X1)
=> ca_Vx3(X1) ) )
<=> ca_Ax2(X0) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X3] :
( ca_Ax2(X3)
<=> ( cp1(X3)
& ! [X4] :
( rinvF(X3,X4)
=> ca_Vx3(X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f251,plain,
~ ca_Vx3(i2003_11_14_17_21_55116),
inference(resolution,[],[f249,f213]) ).
fof(f213,plain,
! [X0] :
( ~ ca_Ax2(sK0(X0))
| ~ ca_Vx3(X0) ),
inference(resolution,[],[f211,f176]) ).
fof(f176,plain,
! [X0] :
( cp1(X0)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f211,plain,
! [X0] :
( ~ cp1(sK0(X0))
| ~ ca_Vx3(X0) ),
inference(resolution,[],[f210,f158]) ).
fof(f158,plain,
! [X0] :
( cp1xcomp(sK0(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ( ( rf(X0,sK0(X0))
& cp1xcomp(sK0(X0)) )
| ~ ca_Vx3(X0) )
& ( ca_Vx3(X0)
| ! [X2] :
( ~ rf(X0,X2)
| ~ cp1xcomp(X2) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f112,f113]) ).
fof(f113,plain,
! [X0] :
( ? [X1] :
( rf(X0,X1)
& cp1xcomp(X1) )
=> ( rf(X0,sK0(X0))
& cp1xcomp(sK0(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
! [X0] :
( ( ? [X1] :
( rf(X0,X1)
& cp1xcomp(X1) )
| ~ ca_Vx3(X0) )
& ( ca_Vx3(X0)
| ! [X2] :
( ~ rf(X0,X2)
| ~ cp1xcomp(X2) ) ) ),
inference(rectify,[],[f111]) ).
fof(f111,plain,
! [X0] :
( ( ? [X1] :
( rf(X0,X1)
& cp1xcomp(X1) )
| ~ ca_Vx3(X0) )
& ( ca_Vx3(X0)
| ! [X1] :
( ~ rf(X0,X1)
| ~ cp1xcomp(X1) ) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ? [X1] :
( rf(X0,X1)
& cp1xcomp(X1) )
<=> ca_Vx3(X0) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X3] :
( ? [X4] :
( cp1xcomp(X4)
& rf(X3,X4) )
<=> ca_Vx3(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f210,plain,
! [X1] :
( ~ cp1xcomp(X1)
| ~ cp1(X1) ),
inference(resolution,[],[f170,f162]) ).
fof(f162,plain,
! [X2,X0] :
( ~ ra_Px1(X0,X2)
| ~ cp1(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ( cp1(X0)
| ra_Px1(X0,sK1(X0)) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ cp1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f117,f118]) ).
fof(f118,plain,
! [X0] :
( ? [X1] : ra_Px1(X0,X1)
=> ra_Px1(X0,sK1(X0)) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
! [X0] :
( ( cp1(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ cp1(X0) ) ),
inference(rectify,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ( cp1(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X1] : ~ ra_Px1(X0,X1)
| ~ cp1(X0) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] :
( cp1(X0)
<=> ! [X1] : ~ ra_Px1(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] :
( cp1(X0)
<=> ~ ? [X1] : ra_Px1(X0,X1) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X3] :
( ~ ? [X4] : ra_Px1(X3,X4)
<=> cp1(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f170,plain,
! [X0] :
( ra_Px1(X0,sK2(X0))
| ~ cp1xcomp(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ( ra_Px1(X0,sK2(X0))
| ~ cp1xcomp(X0) )
& ( cp1xcomp(X0)
| ! [X2] : ~ ra_Px1(X0,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f123,f124]) ).
fof(f124,plain,
! [X0] :
( ? [X1] : ra_Px1(X0,X1)
=> ra_Px1(X0,sK2(X0)) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
! [X0] :
( ( ? [X1] : ra_Px1(X0,X1)
| ~ cp1xcomp(X0) )
& ( cp1xcomp(X0)
| ! [X2] : ~ ra_Px1(X0,X2) ) ),
inference(rectify,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ( ? [X1] : ra_Px1(X0,X1)
| ~ cp1xcomp(X0) )
& ( cp1xcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ? [X1] : ra_Px1(X0,X1)
<=> cp1xcomp(X0) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X3] :
( cp1xcomp(X3)
<=> ? [X5] : ra_Px1(X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f249,plain,
ca_Ax2(sK0(i2003_11_14_17_21_55116)),
inference(subsumption_resolution,[],[f248,f165]) ).
fof(f248,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_55116)
| ca_Ax2(sK0(i2003_11_14_17_21_55116)) ),
inference(superposition,[],[f184,f245]) ).
fof(f245,plain,
sK4(i2003_11_14_17_21_55116) = sK0(i2003_11_14_17_21_55116),
inference(resolution,[],[f244,f165]) ).
fof(f244,plain,
! [X1] :
( ~ cUnsatisfiable(X1)
| sK4(X1) = sK0(X1) ),
inference(subsumption_resolution,[],[f241,f223]) ).
fof(f241,plain,
! [X1] :
( sK4(X1) = sK0(X1)
| ~ cUnsatisfiable(X1)
| ~ ca_Vx3(X1) ),
inference(resolution,[],[f234,f183]) ).
fof(f234,plain,
! [X0,X1] :
( ~ rf(X0,X1)
| sK0(X0) = X1
| ~ ca_Vx3(X0) ),
inference(resolution,[],[f155,f159]) ).
fof(f159,plain,
! [X0] :
( rf(X0,sK0(X0))
| ~ ca_Vx3(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ rf(X2,X0)
| ~ rf(X2,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ~ rf(X2,X0)
| X0 = X1
| ~ rf(X2,X1) ),
inference(rectify,[],[f98]) ).
fof(f98,plain,
! [X2,X1,X0] :
( ~ rf(X0,X2)
| X1 = X2
| ~ rf(X0,X1) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X2,X1,X0] :
( X1 = X2
| ~ rf(X0,X2)
| ~ rf(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,plain,
! [X2,X1,X0] :
( ( rf(X0,X2)
& rf(X0,X1) )
=> X1 = X2 ),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X3,X6,X4] :
( ( rf(X3,X4)
& rf(X3,X6) )
=> X4 = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS122+1 : TPTP v8.1.0. Released v3.1.0.
% 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
% 0.13/0.34 % Computer : n025.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 00:43:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.51 % (29743)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)
% 0.21/0.52 % (29745)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.52 % (29761)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)
% 0.21/0.52 % (29743)First to succeed.
% 0.21/0.52 % (29760)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.52 % (29752)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)
% 0.21/0.53 % (29741)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.53 % (29740)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)
% 0.21/0.53 % (29768)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.21/0.53 % (29742)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.53 % (29767)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.21/0.53 % (29753)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)
% 0.21/0.53 % (29745)Also succeeded, but the first one will report.
% 0.21/0.53 % (29747)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.53 % (29762)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.21/0.53 % (29744)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)
% 0.21/0.54 % (29751)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.54 % (29743)Refutation found. Thanks to Tanya!
% 0.21/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.54 % (29743)------------------------------
% 0.21/0.54 % (29743)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54 % (29743)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54 % (29743)Termination reason: Refutation
% 0.21/0.54
% 0.21/0.54 % (29743)Memory used [KB]: 5500
% 0.21/0.54 % (29743)Time elapsed: 0.125 s
% 0.21/0.54 % (29743)Instructions burned: 4 (million)
% 0.21/0.54 % (29743)------------------------------
% 0.21/0.54 % (29743)------------------------------
% 0.21/0.54 % (29737)Success in time 0.185 s
%------------------------------------------------------------------------------