TSTP Solution File: SET893+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET893+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n017.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 May 21 03:24:43 EDT 2024
% Result : Theorem 0.19s 0.37s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 6 unt; 0 def)
% Number of atoms : 150 ( 77 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 179 ( 71 ~; 71 |; 29 &)
% ( 5 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 57 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f125,plain,
$false,
inference(resolution,[],[f124,f44]) ).
fof(f44,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f43]) ).
fof(f43,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f35]) ).
fof(f35,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f18,f19]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( 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,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f124,plain,
~ in(sK0,singleton(sK0)),
inference(resolution,[],[f118,f44]) ).
fof(f118,plain,
( ~ in(sK1,singleton(sK1))
| ~ in(sK0,singleton(sK0)) ),
inference(resolution,[],[f40,f90]) ).
fof(f90,plain,
~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),singleton(sK1))),
inference(trivial_inequality_removal,[],[f89]) ).
fof(f89,plain,
( sK1 != sK1
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),singleton(sK1))) ),
inference(backward_demodulation,[],[f80,f88]) ).
fof(f88,plain,
sK1 = sK3,
inference(duplicate_literal_removal,[],[f85]) ).
fof(f85,plain,
( sK1 = sK3
| sK1 = sK3 ),
inference(resolution,[],[f84,f45]) ).
fof(f45,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f34]) ).
fof(f34,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f84,plain,
( in(sK1,singleton(sK3))
| sK1 = sK3 ),
inference(resolution,[],[f39,f77]) ).
fof(f77,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),singleton(sK3)))
| sK1 = sK3 ),
inference(backward_demodulation,[],[f28,f76]) ).
fof(f76,plain,
sK0 = sK2,
inference(duplicate_literal_removal,[],[f73]) ).
fof(f73,plain,
( sK0 = sK2
| sK0 = sK2 ),
inference(resolution,[],[f65,f45]) ).
fof(f65,plain,
( in(sK0,singleton(sK2))
| sK0 = sK2 ),
inference(resolution,[],[f38,f27]) ).
fof(f27,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),singleton(sK3)))
| sK0 = sK2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ( sK1 != sK3
| sK0 != sK2
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),singleton(sK3))) )
& ( ( sK1 = sK3
& sK0 = sK2 )
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),singleton(sK3))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f15]) ).
fof(f15,plain,
( ? [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3))) )
& ( ( X1 = X3
& X0 = X2 )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3))) ) )
=> ( ( sK1 != sK3
| sK0 != sK2
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),singleton(sK3))) )
& ( ( sK1 = sK3
& sK0 = sK2 )
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),singleton(sK3))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3))) )
& ( ( X1 = X3
& X0 = X2 )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3))) ) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
? [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3))) )
& ( ( X1 = X3
& X0 = X2 )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3))) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3)))
<~> ( X1 = X3
& X0 = X2 ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3)))
<=> ( X1 = X3
& X0 = X2 ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3)))
<=> ( X1 = X3
& X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_zfmisc_1) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f28,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),singleton(sK3)))
| sK1 = sK3 ),
inference(cnf_transformation,[],[f16]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f80,plain,
( sK1 != sK3
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),singleton(sK1))) ),
inference(trivial_inequality_removal,[],[f78]) ).
fof(f78,plain,
( sK0 != sK0
| sK1 != sK3
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),singleton(sK1))) ),
inference(backward_demodulation,[],[f47,f76]) ).
fof(f47,plain,
( sK1 != sK3
| sK0 != sK2
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),singleton(sK1))) ),
inference(inner_rewriting,[],[f46]) ).
fof(f46,plain,
( sK1 != sK3
| sK0 != sK2
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),singleton(sK1))) ),
inference(inner_rewriting,[],[f29]) ).
fof(f29,plain,
( sK1 != sK3
| sK0 != sK2
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),singleton(sK3))) ),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET893+1 : TPTP v8.2.0. Released v3.2.0.
% 0.12/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 13:08:52 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.34 % (16534)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.36 % (16535)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.36 % (16538)WARNING: value z3 for option sas not known
% 0.19/0.36 % (16537)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.36 % (16539)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.36 % (16538)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)
% 0.19/0.36 % (16540)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)
% 0.19/0.36 % (16542)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)
% 0.19/0.36 % (16541)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)
% 0.19/0.36 TRYING [1]
% 0.19/0.36 TRYING [2]
% 0.19/0.36 TRYING [1]
% 0.19/0.36 TRYING [1]
% 0.19/0.36 TRYING [2]
% 0.19/0.36 TRYING [2]
% 0.19/0.37 TRYING [3]
% 0.19/0.37 % (16541)First to succeed.
% 0.19/0.37 TRYING [3]
% 0.19/0.37 % (16538)Also succeeded, but the first one will report.
% 0.19/0.37 % (16541)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16534"
% 0.19/0.37 % (16541)Refutation found. Thanks to Tanya!
% 0.19/0.37 % SZS status Theorem for theBenchmark
% 0.19/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.37 % (16541)------------------------------
% 0.19/0.37 % (16541)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.37 % (16541)Termination reason: Refutation
% 0.19/0.37
% 0.19/0.37 % (16541)Memory used [KB]: 845
% 0.19/0.37 % (16541)Time elapsed: 0.007 s
% 0.19/0.37 % (16541)Instructions burned: 9 (million)
% 0.19/0.37 % (16534)Success in time 0.024 s
%------------------------------------------------------------------------------