TSTP Solution File: SET872+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET872+1 : 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_uns --cores 0 -t %d %s
% Computer : n026.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 18:22:38 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 176 ( 85 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 221 ( 81 ~; 84 |; 43 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 100 ( 86 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f82,plain,
$false,
inference(subsumption_resolution,[],[f80,f56]) ).
fof(f56,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X4] :
( in(X4,X0)
| unordered_pair(X4,X1) != X0 ),
inference(equality_resolution,[],[f41]) ).
fof(f41,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| X2 != X4
| unordered_pair(X2,X1) != X0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( unordered_pair(X2,X1) = X0
| ( ( ~ in(sK4(X0,X1,X2),X0)
| ( sK4(X0,X1,X2) != X1
& sK4(X0,X1,X2) != X2 ) )
& ( in(sK4(X0,X1,X2),X0)
| sK4(X0,X1,X2) = X1
| sK4(X0,X1,X2) = X2 ) ) )
& ( ! [X4] :
( ( X1 = X4
| X2 = X4
| ~ in(X4,X0) )
& ( in(X4,X0)
| ( X1 != X4
& X2 != X4 ) ) )
| unordered_pair(X2,X1) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f28,f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ( X1 != X3
& X2 != X3 ) )
& ( in(X3,X0)
| X1 = X3
| X2 = X3 ) )
=> ( ( ~ in(sK4(X0,X1,X2),X0)
| ( sK4(X0,X1,X2) != X1
& sK4(X0,X1,X2) != X2 ) )
& ( in(sK4(X0,X1,X2),X0)
| sK4(X0,X1,X2) = X1
| sK4(X0,X1,X2) = X2 ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( unordered_pair(X2,X1) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ( X1 != X3
& X2 != X3 ) )
& ( in(X3,X0)
| X1 = X3
| X2 = X3 ) ) )
& ( ! [X4] :
( ( X1 = X4
| X2 = X4
| ~ in(X4,X0) )
& ( in(X4,X0)
| ( X1 != X4
& X2 != X4 ) ) )
| unordered_pair(X2,X1) != X0 ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ( unordered_pair(X1,X0) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( in(X3,X2)
| X0 = X3
| X1 = X3 ) ) )
& ( ! [X3] :
( ( X0 = X3
| X1 = X3
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) ) )
| unordered_pair(X1,X0) != X2 ) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ( unordered_pair(X1,X0) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( in(X3,X2)
| X0 = X3
| X1 = X3 ) ) )
& ( ! [X3] :
( ( X0 = X3
| X1 = X3
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) ) )
| unordered_pair(X1,X0) != X2 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X2,X0,X1] :
( unordered_pair(X1,X0) = X2
<=> ! [X3] :
( ( X0 = X3
| X1 = X3 )
<=> in(X3,X2) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0,X2] :
( ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) )
<=> unordered_pair(X0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f80,plain,
~ in(sK0,unordered_pair(sK0,sK1)),
inference(resolution,[],[f77,f32]) ).
fof(f32,plain,
~ subset(singleton(sK0),unordered_pair(sK0,sK1)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
~ subset(singleton(sK0),unordered_pair(sK0,sK1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16]) ).
fof(f16,plain,
( ? [X0,X1] : ~ subset(singleton(X0),unordered_pair(X0,X1))
=> ~ subset(singleton(sK0),unordered_pair(sK0,sK1)) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
? [X0,X1] : ~ subset(singleton(X0),unordered_pair(X0,X1)),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : subset(singleton(X0),unordered_pair(X0,X1)),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1] : subset(singleton(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfmisc_1) ).
fof(f77,plain,
! [X4,X5] :
( subset(singleton(X5),X4)
| ~ in(X5,X4) ),
inference(duplicate_literal_removal,[],[f76]) ).
fof(f76,plain,
! [X4,X5] :
( subset(singleton(X5),X4)
| subset(singleton(X5),X4)
| ~ in(X5,X4) ),
inference(superposition,[],[f39,f71]) ).
fof(f71,plain,
! [X3,X4] :
( sK3(X4,singleton(X3)) = X3
| subset(singleton(X3),X4) ),
inference(resolution,[],[f40,f51]) ).
fof(f51,plain,
! [X3,X1] :
( ~ in(X3,singleton(X1))
| X1 = X3 ),
inference(equality_resolution,[],[f33]) ).
fof(f33,plain,
! [X3,X0,X1] :
( X1 = X3
| ~ in(X3,X0)
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ( ( sK2(X0,X1) != X1
| ~ in(sK2(X0,X1),X0) )
& ( sK2(X0,X1) = X1
| in(sK2(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( in(X3,X0)
| X1 != X3 )
& ( X1 = X3
| ~ in(X3,X0) ) )
| singleton(X1) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f19,f20]) ).
fof(f20,plain,
! [X0,X1] :
( ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) )
=> ( ( sK2(X0,X1) != X1
| ~ in(sK2(X0,X1),X0) )
& ( sK2(X0,X1) = X1
| in(sK2(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) ) )
& ( ! [X3] :
( ( in(X3,X0)
| X1 != X3 )
& ( X1 = X3
| ~ in(X3,X0) ) )
| singleton(X1) != X0 ) ),
inference(rectify,[],[f18]) ).
fof(f18,plain,
! [X1,X0] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f40,plain,
! [X0,X1] :
( in(sK3(X0,X1),X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(X1,X0)
| ( in(sK3(X0,X1),X1)
& ~ in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| in(X3,X0) )
| ~ subset(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X1)
& ~ in(X2,X0) )
=> ( in(sK3(X0,X1),X1)
& ~ in(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1] :
( ( subset(X1,X0)
| ? [X2] :
( in(X2,X1)
& ~ in(X2,X0) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| in(X3,X0) )
| ~ subset(X1,X0) ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X1,X0] :
( ( subset(X0,X1)
| ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) ) )
& ( ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f39,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X0)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET872+1 : 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_uns --cores 0 -t %d %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 14:41:51 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.50 % (10320)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.51 % (10325)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.51 % (10320)Refutation not found, incomplete strategy% (10320)------------------------------
% 0.20/0.51 % (10320)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (10320)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (10320)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51
% 0.20/0.51 % (10320)Memory used [KB]: 5884
% 0.20/0.51 % (10320)Time elapsed: 0.061 s
% 0.20/0.51 % (10320)Instructions burned: 2 (million)
% 0.20/0.51 % (10320)------------------------------
% 0.20/0.51 % (10320)------------------------------
% 0.20/0.51 % (10340)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.20/0.52 % (10344)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)
% 0.20/0.52 % (10330)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)
% 0.20/0.52 % (10324)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.52 % (10330)Refutation not found, incomplete strategy% (10330)------------------------------
% 0.20/0.52 % (10330)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (10330)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (10330)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.52
% 0.20/0.52 % (10330)Memory used [KB]: 1407
% 0.20/0.52 % (10330)Time elapsed: 0.102 s
% 0.20/0.52 % (10330)Instructions burned: 3 (million)
% 0.20/0.52 % (10330)------------------------------
% 0.20/0.52 % (10330)------------------------------
% 0.20/0.52 % (10336)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)
% 0.20/0.52 % (10336)Instruction limit reached!
% 0.20/0.52 % (10336)------------------------------
% 0.20/0.52 % (10336)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (10336)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (10336)Termination reason: Unknown
% 0.20/0.52 % (10336)Termination phase: Preprocessing 3
% 0.20/0.52
% 0.20/0.52 % (10336)Memory used [KB]: 1407
% 0.20/0.52 % (10336)Time elapsed: 0.002 s
% 0.20/0.52 % (10336)Instructions burned: 2 (million)
% 0.20/0.52 % (10336)------------------------------
% 0.20/0.52 % (10336)------------------------------
% 0.20/0.52 % (10319)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)
% 0.20/0.52 % (10324)First to succeed.
% 0.20/0.52 % (10322)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.52 % (10340)Also succeeded, but the first one will report.
% 0.20/0.53 % (10324)Refutation found. Thanks to Tanya!
% 0.20/0.53 % SZS status Theorem for theBenchmark
% 0.20/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53 % (10324)------------------------------
% 0.20/0.53 % (10324)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (10324)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (10324)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (10324)Memory used [KB]: 6012
% 0.20/0.53 % (10324)Time elapsed: 0.089 s
% 0.20/0.53 % (10324)Instructions burned: 3 (million)
% 0.20/0.53 % (10324)------------------------------
% 0.20/0.53 % (10324)------------------------------
% 0.20/0.53 % (10317)Success in time 0.18 s
%------------------------------------------------------------------------------