TSTP Solution File: SET906+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET906+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.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 : Tue Apr 30 15:13:56 EDT 2024
% Result : Theorem 0.07s 0.28s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 15 unt; 0 def)
% Number of atoms : 219 ( 59 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 265 ( 95 ~; 97 |; 54 &)
% ( 11 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 137 ( 123 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f209,plain,
$false,
inference(resolution,[],[f204,f99]) ).
fof(f99,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(resolution,[],[f73,f83]) ).
fof(f83,plain,
! [X0,X1] : sP0(X1,X0,unordered_pair(X1,X0)),
inference(superposition,[],[f75,f49]) ).
fof(f49,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f75,plain,
! [X0,X1] : sP0(X1,X0,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f61]) ).
fof(f61,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f4,f23]) ).
fof(f23,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f73,plain,
! [X2,X1,X4] :
( ~ sP0(X4,X1,X2)
| in(X4,X2) ),
inference(equality_resolution,[],[f57]) ).
fof(f57,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ( sK5(X0,X1,X2) != X0
& sK5(X0,X1,X2) != X1 )
| ~ in(sK5(X0,X1,X2),X2) )
& ( sK5(X0,X1,X2) = X0
| sK5(X0,X1,X2) = X1
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f31,f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) )
=> ( ( ( sK5(X0,X1,X2) != X0
& sK5(X0,X1,X2) != X1 )
| ~ in(sK5(X0,X1,X2),X2) )
& ( sK5(X0,X1,X2) = X0
| sK5(X0,X1,X2) = X1
| in(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f30]) ).
fof(f30,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f204,plain,
~ in(sK2,unordered_pair(sK2,sK3)),
inference(resolution,[],[f138,f117]) ).
fof(f117,plain,
~ in(sK2,set_union2(sK4,unordered_pair(sK2,sK3))),
inference(forward_demodulation,[],[f115,f50]) ).
fof(f50,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f115,plain,
~ in(sK2,set_union2(unordered_pair(sK2,sK3),sK4)),
inference(resolution,[],[f110,f45]) ).
fof(f45,plain,
subset(set_union2(unordered_pair(sK2,sK3),sK4),sK4),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
( ~ in(sK2,sK4)
& subset(set_union2(unordered_pair(sK2,sK3),sK4),sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f18,f27]) ).
fof(f27,plain,
( ? [X0,X1,X2] :
( ~ in(X0,X2)
& subset(set_union2(unordered_pair(X0,X1),X2),X2) )
=> ( ~ in(sK2,sK4)
& subset(set_union2(unordered_pair(sK2,sK3),sK4),sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ~ in(X0,X2)
& subset(set_union2(unordered_pair(X0,X1),X2),X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(set_union2(unordered_pair(X0,X1),X2),X2)
=> in(X0,X2) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( subset(set_union2(unordered_pair(X0,X1),X2),X2)
=> in(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_zfmisc_1) ).
fof(f110,plain,
! [X0] :
( ~ subset(X0,sK4)
| ~ in(sK2,X0) ),
inference(resolution,[],[f54,f46]) ).
fof(f46,plain,
~ in(sK2,sK4),
inference(cnf_transformation,[],[f28]) ).
fof(f54,plain,
! [X2,X0,X1] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f138,plain,
! [X2,X0,X1] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(resolution,[],[f64,f88]) ).
fof(f88,plain,
! [X0,X1] : sP1(X1,X0,set_union2(X1,X0)),
inference(superposition,[],[f76,f50]) ).
fof(f76,plain,
! [X0,X1] : sP1(X1,X0,set_union2(X0,X1)),
inference(equality_resolution,[],[f69]) ).
fof(f69,plain,
! [X2,X0,X1] :
( sP1(X1,X0,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP1(X1,X0,X2) )
& ( sP1(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP1(X1,X0,X2) ),
inference(definition_folding,[],[f5,f25]) ).
fof(f25,plain,
! [X1,X0,X2] :
( sP1(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f64,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ( ( ~ in(sK6(X0,X1,X2),X0)
& ~ in(sK6(X0,X1,X2),X1) )
| ~ in(sK6(X0,X1,X2),X2) )
& ( in(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f37,f38]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK6(X0,X1,X2),X0)
& ~ in(sK6(X0,X1,X2),X1) )
| ~ in(sK6(X0,X1,X2),X2) )
& ( in(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP1(X1,X0,X2) ) ),
inference(flattening,[],[f35]) ).
fof(f35,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP1(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.07 % Problem : SET906+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.08 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.26 % Computer : n023.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue Apr 30 01:47:55 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % (20226)Running in auto input_syntax mode. Trying TPTP
% 0.07/0.28 % (20229)WARNING: value z3 for option sas not known
% 0.07/0.28 % (20230)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.07/0.28 % (20227)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.07/0.28 % (20228)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.07/0.28 % (20229)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.07/0.28 % (20231)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.07/0.28 % (20232)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.07/0.28 % (20233)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.07/0.28 TRYING [1]
% 0.07/0.28 TRYING [2]
% 0.07/0.28 TRYING [3]
% 0.07/0.28 % (20232)First to succeed.
% 0.07/0.28 % (20229)Also succeeded, but the first one will report.
% 0.07/0.28 % (20232)Refutation found. Thanks to Tanya!
% 0.07/0.28 % SZS status Theorem for theBenchmark
% 0.07/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.28 % (20232)------------------------------
% 0.07/0.28 % (20232)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.07/0.28 % (20232)Termination reason: Refutation
% 0.07/0.28
% 0.07/0.28 % (20232)Memory used [KB]: 841
% 0.07/0.28 % (20232)Time elapsed: 0.004 s
% 0.07/0.28 % (20232)Instructions burned: 11 (million)
% 0.07/0.28 % (20232)------------------------------
% 0.07/0.28 % (20232)------------------------------
% 0.07/0.28 % (20226)Success in time 0.013 s
%------------------------------------------------------------------------------