TSTP Solution File: SET909+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET909+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 : n015.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 18:22:43 EDT 2022
% Result : Theorem 0.20s 0.57s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 20 unt; 0 def)
% Number of atoms : 204 ( 93 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 249 ( 91 ~; 94 |; 51 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 119 ( 99 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f132,plain,
$false,
inference(resolution,[],[f131,f87]) ).
fof(f87,plain,
in(sK2,sF8),
inference(superposition,[],[f81,f84]) ).
fof(f84,plain,
sF8 = unordered_pair(sK2,sK1),
introduced(function_definition,[]) ).
fof(f81,plain,
! [X2,X3] : in(X3,unordered_pair(X3,X2)),
inference(equality_resolution,[],[f80]) ).
fof(f80,plain,
! [X2,X3,X0] :
( in(X3,X0)
| unordered_pair(X3,X2) != X0 ),
inference(equality_resolution,[],[f67]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| X1 != X3
| unordered_pair(X1,X2) != X0 ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ( X2 != X3
& X1 != X3 ) )
& ( X2 = X3
| X1 = X3
| ~ in(X3,X0) ) )
| unordered_pair(X1,X2) != X0 )
& ( unordered_pair(X1,X2) = X0
| ( ( ( sK5(X0,X1,X2) != X2
& sK5(X0,X1,X2) != X1 )
| ~ in(sK5(X0,X1,X2),X0) )
& ( sK5(X0,X1,X2) = X2
| sK5(X0,X1,X2) = X1
| in(sK5(X0,X1,X2),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f40,f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ( X2 != X4
& X1 != X4 )
| ~ in(X4,X0) )
& ( X2 = X4
| X1 = X4
| in(X4,X0) ) )
=> ( ( ( sK5(X0,X1,X2) != X2
& sK5(X0,X1,X2) != X1 )
| ~ in(sK5(X0,X1,X2),X0) )
& ( sK5(X0,X1,X2) = X2
| sK5(X0,X1,X2) = X1
| in(sK5(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ( X2 != X3
& X1 != X3 ) )
& ( X2 = X3
| X1 = X3
| ~ in(X3,X0) ) )
| unordered_pair(X1,X2) != X0 )
& ( unordered_pair(X1,X2) = X0
| ? [X4] :
( ( ( X2 != X4
& X1 != X4 )
| ~ in(X4,X0) )
& ( X2 = X4
| X1 = X4
| in(X4,X0) ) ) ) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| ( X2 != X3
& X0 != X3 ) )
& ( X2 = X3
| X0 = X3
| ~ in(X3,X1) ) )
| unordered_pair(X0,X2) != X1 )
& ( unordered_pair(X0,X2) = X1
| ? [X3] :
( ( ( X2 != X3
& X0 != X3 )
| ~ in(X3,X1) )
& ( X2 = X3
| X0 = X3
| in(X3,X1) ) ) ) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| ( X2 != X3
& X0 != X3 ) )
& ( X2 = X3
| X0 = X3
| ~ in(X3,X1) ) )
| unordered_pair(X0,X2) != X1 )
& ( unordered_pair(X0,X2) = X1
| ? [X3] :
( ( ( X2 != X3
& X0 != X3 )
| ~ in(X3,X1) )
& ( X2 = X3
| X0 = X3
| in(X3,X1) ) ) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X1,X0,X2] :
( ! [X3] :
( in(X3,X1)
<=> ( X2 = X3
| X0 = X3 ) )
<=> unordered_pair(X0,X2) = X1 ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X2,X1] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f131,plain,
! [X8] : ~ in(X8,sF8),
inference(subsumption_resolution,[],[f130,f83]) ).
fof(f83,plain,
! [X1] : ~ in(X1,empty_set),
inference(equality_resolution,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ~ in(X1,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| in(sK6(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f44,f45]) ).
fof(f45,plain,
! [X0] :
( ? [X2] : in(X2,X0)
=> in(sK6(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| ? [X2] : in(X2,X0) ) ),
inference(rectify,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| ? [X1] : in(X1,X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ! [X1] : ~ in(X1,X0)
<=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f130,plain,
! [X8] :
( ~ in(X8,sF8)
| in(X8,empty_set) ),
inference(superposition,[],[f75,f115]) ).
fof(f115,plain,
empty_set = set_union2(sK3,sF8),
inference(backward_demodulation,[],[f89,f55]) ).
fof(f55,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f89,plain,
empty_set = set_union2(sF8,sK3),
inference(forward_demodulation,[],[f85,f86]) ).
fof(f86,plain,
empty_set = sF9,
inference(definition_folding,[],[f52,f85,f84]) ).
fof(f52,plain,
empty_set = set_union2(unordered_pair(sK2,sK1),sK3),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
empty_set = set_union2(unordered_pair(sK2,sK1),sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f29,f30]) ).
fof(f30,plain,
( ? [X0,X1,X2] : empty_set = set_union2(unordered_pair(X1,X0),X2)
=> empty_set = set_union2(unordered_pair(sK2,sK1),sK3) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
? [X0,X1,X2] : empty_set = set_union2(unordered_pair(X1,X0),X2),
inference(rectify,[],[f26]) ).
fof(f26,plain,
? [X2,X0,X1] : empty_set = set_union2(unordered_pair(X0,X2),X1),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0,X1,X2] : empty_set != set_union2(unordered_pair(X0,X2),X1),
inference(rectify,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X2,X1] : empty_set != set_union2(unordered_pair(X0,X1),X2),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X2,X1] : empty_set != set_union2(unordered_pair(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_zfmisc_1) ).
fof(f85,plain,
sF9 = set_union2(sF8,sK3),
introduced(function_definition,[]) ).
fof(f75,plain,
! [X2,X3,X0] :
( in(X3,set_union2(X0,X2))
| ~ in(X3,X2) ),
inference(equality_resolution,[],[f62]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X2)
| set_union2(X0,X2) != X1 ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| ( ~ in(X3,X2)
& ~ in(X3,X0) ) )
& ( in(X3,X2)
| in(X3,X0)
| ~ in(X3,X1) ) )
| set_union2(X0,X2) != X1 )
& ( set_union2(X0,X2) = X1
| ( ( ( ~ in(sK4(X0,X1,X2),X2)
& ~ in(sK4(X0,X1,X2),X0) )
| ~ in(sK4(X0,X1,X2),X1) )
& ( in(sK4(X0,X1,X2),X2)
| in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X1) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f35,f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ( ~ in(X4,X2)
& ~ in(X4,X0) )
| ~ in(X4,X1) )
& ( in(X4,X2)
| in(X4,X0)
| in(X4,X1) ) )
=> ( ( ( ~ in(sK4(X0,X1,X2),X2)
& ~ in(sK4(X0,X1,X2),X0) )
| ~ in(sK4(X0,X1,X2),X1) )
& ( in(sK4(X0,X1,X2),X2)
| in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| ( ~ in(X3,X2)
& ~ in(X3,X0) ) )
& ( in(X3,X2)
| in(X3,X0)
| ~ in(X3,X1) ) )
| set_union2(X0,X2) != X1 )
& ( set_union2(X0,X2) = X1
| ? [X4] :
( ( ( ~ in(X4,X2)
& ~ in(X4,X0) )
| ~ in(X4,X1) )
& ( in(X4,X2)
| in(X4,X0)
| in(X4,X1) ) ) ) ),
inference(rectify,[],[f34]) ).
fof(f34,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ( ~ in(X3,X2)
& ~ in(X3,X1) ) )
& ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| set_union2(X1,X2) != X0 )
& ( set_union2(X1,X2) = X0
| ? [X3] :
( ( ( ~ in(X3,X2)
& ~ in(X3,X1) )
| ~ in(X3,X0) )
& ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) ) ) ) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ( ~ in(X3,X2)
& ~ in(X3,X1) ) )
& ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| set_union2(X1,X2) != X0 )
& ( set_union2(X1,X2) = X0
| ? [X3] :
( ( ( ~ in(X3,X2)
& ~ in(X3,X1) )
| ~ in(X3,X0) )
& ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) ) ) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X1,X0,X2] :
( ! [X3] :
( in(X3,X0)
<=> ( in(X3,X2)
| in(X3,X1) ) )
<=> set_union2(X1,X2) = X0 ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) )
<=> set_union2(X0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 15:07:06 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.54 % (31678)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.54 % (31686)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.54 % (31670)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.56 % (31678)Refutation not found, incomplete strategy% (31678)------------------------------
% 0.20/0.56 % (31678)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56 % (31678)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56 % (31678)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.56
% 0.20/0.56 % (31678)Memory used [KB]: 6012
% 0.20/0.56 % (31678)Time elapsed: 0.131 s
% 0.20/0.56 % (31678)Instructions burned: 3 (million)
% 0.20/0.56 % (31678)------------------------------
% 0.20/0.56 % (31678)------------------------------
% 0.20/0.56 % (31662)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.56 % (31662)First to succeed.
% 0.20/0.57 % (31683)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.57 % (31670)Also succeeded, but the first one will report.
% 0.20/0.57 % (31662)Refutation found. Thanks to Tanya!
% 0.20/0.57 % SZS status Theorem for theBenchmark
% 0.20/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.58 % (31662)------------------------------
% 0.20/0.58 % (31662)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.58 % (31662)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.58 % (31662)Termination reason: Refutation
% 0.20/0.58
% 0.20/0.58 % (31662)Memory used [KB]: 6012
% 0.20/0.58 % (31662)Time elapsed: 0.138 s
% 0.20/0.58 % (31662)Instructions burned: 4 (million)
% 0.20/0.58 % (31662)------------------------------
% 0.20/0.58 % (31662)------------------------------
% 0.20/0.58 % (31661)Success in time 0.213 s
%------------------------------------------------------------------------------