TSTP Solution File: SET930+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET930+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 : n020.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 15:14:02 EDT 2024
% Result : Theorem 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 125 ( 60 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 154 ( 67 ~; 41 |; 40 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 66 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f748,plain,
$false,
inference(subsumption_resolution,[],[f747,f31]) ).
fof(f31,plain,
set_difference(unordered_pair(sK1,sK2),sK3) != singleton(sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( unordered_pair(sK1,sK2) != set_difference(unordered_pair(sK1,sK2),sK3)
& set_difference(unordered_pair(sK1,sK2),sK3) != singleton(sK2)
& set_difference(unordered_pair(sK1,sK2),sK3) != singleton(sK1)
& empty_set != set_difference(unordered_pair(sK1,sK2),sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f11,f15]) ).
fof(f15,plain,
( ? [X0,X1,X2] :
( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2) )
=> ( unordered_pair(sK1,sK2) != set_difference(unordered_pair(sK1,sK2),sK3)
& set_difference(unordered_pair(sK1,sK2),sK3) != singleton(sK2)
& set_difference(unordered_pair(sK1,sK2),sK3) != singleton(sK1)
& empty_set != set_difference(unordered_pair(sK1,sK2),sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
? [X0,X1,X2] :
( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1,X2] :
~ ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).
fof(f747,plain,
set_difference(unordered_pair(sK1,sK2),sK3) = singleton(sK2),
inference(forward_demodulation,[],[f742,f34]) ).
fof(f34,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/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f742,plain,
singleton(sK2) = set_difference(unordered_pair(sK2,sK1),sK3),
inference(unit_resulting_resolution,[],[f689,f44]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ sP0(X1,X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f4,f13]) ).
fof(f13,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f689,plain,
sP0(sK1,sK2,sK3),
inference(unit_resulting_resolution,[],[f618,f622,f41]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ in(X0,X2)
| sP0(X0,X1,X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( X0 != X1
& ~ in(X0,X2) )
| in(X1,X2) )
& ( ( ( X0 = X1
| in(X0,X2) )
& ~ in(X1,X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2) )
& ( ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2) )
& ( ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f622,plain,
~ in(sK2,sK3),
inference(unit_resulting_resolution,[],[f29,f618,f38]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| empty_set = set_difference(unordered_pair(X0,X1),X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( empty_set = set_difference(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( empty_set = set_difference(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( empty_set = set_difference(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(f29,plain,
empty_set != set_difference(unordered_pair(sK1,sK2),sK3),
inference(cnf_transformation,[],[f16]) ).
fof(f618,plain,
in(sK1,sK3),
inference(subsumption_resolution,[],[f611,f32]) ).
fof(f32,plain,
unordered_pair(sK1,sK2) != set_difference(unordered_pair(sK1,sK2),sK3),
inference(cnf_transformation,[],[f16]) ).
fof(f611,plain,
( in(sK1,sK3)
| unordered_pair(sK1,sK2) = set_difference(unordered_pair(sK1,sK2),sK3) ),
inference(factoring,[],[f334]) ).
fof(f334,plain,
! [X0] :
( in(X0,sK3)
| in(sK1,sK3)
| unordered_pair(X0,sK2) = set_difference(unordered_pair(X0,sK2),sK3) ),
inference(resolution,[],[f77,f60]) ).
fof(f60,plain,
~ sP0(sK2,sK1,sK3),
inference(unit_resulting_resolution,[],[f30,f44]) ).
fof(f30,plain,
set_difference(unordered_pair(sK1,sK2),sK3) != singleton(sK1),
inference(cnf_transformation,[],[f16]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( sP0(X0,X3,X1)
| unordered_pair(X2,X0) = set_difference(unordered_pair(X2,X0),X1)
| in(X2,X1)
| in(X3,X1) ),
inference(resolution,[],[f47,f41]) ).
fof(f47,plain,
! [X2,X0,X1] :
( in(X1,X2)
| in(X0,X2)
| unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
| in(X1,X2)
| in(X0,X2) )
& ( ( ~ in(X1,X2)
& ~ in(X0,X2) )
| unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
| in(X1,X2)
| in(X0,X2) )
& ( ( ~ in(X1,X2)
& ~ in(X0,X2) )
| unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
<=> ( ~ in(X1,X2)
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.17 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37 % Computer : n020.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Tue Apr 30 01:06:02 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (20203)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (20206)WARNING: value z3 for option sas not known
% 0.15/0.39 % (20206)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)
% 0.15/0.39 % (20208)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)
% 0.15/0.39 % (20207)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (20205)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (20210)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)
% 0.15/0.39 % (20209)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)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (20204)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 TRYING [3]
% 0.15/0.40 TRYING [4]
% 0.15/0.40 TRYING [1]
% 0.15/0.40 TRYING [2]
% 0.19/0.41 TRYING [3]
% 0.19/0.41 TRYING [5]
% 0.19/0.42 % (20210)First to succeed.
% 0.19/0.42 % (20210)Refutation found. Thanks to Tanya!
% 0.19/0.42 % SZS status Theorem for theBenchmark
% 0.19/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.42 % (20210)------------------------------
% 0.19/0.42 % (20210)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.42 % (20210)Termination reason: Refutation
% 0.19/0.42
% 0.19/0.42 % (20210)Memory used [KB]: 931
% 0.19/0.42 % (20210)Time elapsed: 0.030 s
% 0.19/0.42 % (20210)Instructions burned: 59 (million)
% 0.19/0.42 % (20210)------------------------------
% 0.19/0.42 % (20210)------------------------------
% 0.19/0.42 % (20203)Success in time 0.044 s
%------------------------------------------------------------------------------