TSTP Solution File: SET881+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET881+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 : 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 : Tue Apr 30 15:13:52 EDT 2024
% Result : Theorem 0.15s 0.33s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 112 ( 65 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 133 ( 50 ~; 49 |; 26 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 3 con; 0-3 aty)
% Number of variables : 73 ( 65 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f76,plain,
$false,
inference(trivial_inequality_removal,[],[f73]) ).
fof(f73,plain,
empty_set != empty_set,
inference(superposition,[],[f27,f66]) ).
fof(f66,plain,
! [X0,X1] : empty_set = set_difference(singleton(X0),unordered_pair(X0,X1)),
inference(resolution,[],[f32,f54]) ).
fof(f54,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(resolution,[],[f43,f49]) ).
fof(f49,plain,
! [X0,X1] : sP0(X1,X0,unordered_pair(X1,X0)),
inference(superposition,[],[f45,f29]) ).
fof(f29,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(f45,plain,
! [X0,X1] : sP0(X1,X0,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f39]) ).
fof(f39,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,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,[],[f13]) ).
fof(f13,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f3,f12]) ).
fof(f12,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(f3,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(f43,plain,
! [X2,X1,X4] :
( ~ sP0(X4,X1,X2)
| in(X4,X2) ),
inference(equality_resolution,[],[f35]) ).
fof(f35,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ( sK3(X0,X1,X2) != X0
& sK3(X0,X1,X2) != X1 )
| ~ in(sK3(X0,X1,X2),X2) )
& ( sK3(X0,X1,X2) = X0
| sK3(X0,X1,X2) = X1
| in(sK3(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,[sK3])],[f19,f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) )
=> ( ( ( sK3(X0,X1,X2) != X0
& sK3(X0,X1,X2) != X1 )
| ~ in(sK3(X0,X1,X2),X2) )
& ( sK3(X0,X1,X2) = X0
| sK3(X0,X1,X2) = X1
| in(sK3(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f19,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,[],[f18]) ).
fof(f18,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,[],[f17]) ).
fof(f17,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,[],[f12]) ).
fof(f32,plain,
! [X0,X1] :
( ~ in(X0,X1)
| empty_set = set_difference(singleton(X0),X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ( empty_set = set_difference(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| empty_set != set_difference(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( empty_set = set_difference(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f27,plain,
empty_set != set_difference(singleton(sK1),unordered_pair(sK1,sK2)),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
empty_set != set_difference(singleton(sK1),unordered_pair(sK1,sK2)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f10,f14]) ).
fof(f14,plain,
( ? [X0,X1] : empty_set != set_difference(singleton(X0),unordered_pair(X0,X1))
=> empty_set != set_difference(singleton(sK1),unordered_pair(sK1,sK2)) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
? [X0,X1] : empty_set != set_difference(singleton(X0),unordered_pair(X0,X1)),
inference(ennf_transformation,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] : empty_set = set_difference(singleton(X0),unordered_pair(X0,X1)),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X0,X1] : empty_set = set_difference(singleton(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n026.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Apr 30 01:42:19 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.15/0.31 % (18754)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.32 % (18757)WARNING: value z3 for option sas not known
% 0.15/0.33 % (18759)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)
% 0.15/0.33 % (18756)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.33 % (18760)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)
% 0.15/0.33 % (18758)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.33 % (18757)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)
% 0.15/0.33 % (18755)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.33 % (18761)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)
% 0.15/0.33 TRYING [1]
% 0.15/0.33 TRYING [2]
% 0.15/0.33 % (18760)First to succeed.
% 0.15/0.33 TRYING [3]
% 0.15/0.33 % (18761)Also succeeded, but the first one will report.
% 0.15/0.33 TRYING [1]
% 0.15/0.33 TRYING [2]
% 0.15/0.33 % (18757)Also succeeded, but the first one will report.
% 0.15/0.33 % (18760)Refutation found. Thanks to Tanya!
% 0.15/0.33 % SZS status Theorem for theBenchmark
% 0.15/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.33 % (18760)------------------------------
% 0.15/0.33 % (18760)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.33 % (18760)Termination reason: Refutation
% 0.15/0.33
% 0.15/0.33 % (18760)Memory used [KB]: 763
% 0.15/0.33 % (18760)Time elapsed: 0.004 s
% 0.15/0.33 % (18760)Instructions burned: 5 (million)
% 0.15/0.33 % (18760)------------------------------
% 0.15/0.33 % (18760)------------------------------
% 0.15/0.33 % (18754)Success in time 0.018 s
%------------------------------------------------------------------------------