TSTP Solution File: SET983+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET983+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 : n011.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 15:14:11 EDT 2024
% Result : Theorem 0.15s 0.38s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 9 unt; 0 def)
% Number of atoms : 123 ( 7 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 148 ( 53 ~; 47 |; 39 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 82 ( 63 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f94,plain,
$false,
inference(resolution,[],[f93,f28]) ).
fof(f28,plain,
in(sK1,cartesian_product2(sK2,sK3)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
( ~ in(sK1,cartesian_product2(set_intersection2(sK2,sK4),set_intersection2(sK3,sK5)))
& in(sK1,cartesian_product2(sK4,sK5))
& in(sK1,cartesian_product2(sK2,sK3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f12,f16]) ).
fof(f16,plain,
( ? [X0,X1,X2,X3,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4)))
& in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2)) )
=> ( ~ in(sK1,cartesian_product2(set_intersection2(sK2,sK4),set_intersection2(sK3,sK5)))
& in(sK1,cartesian_product2(sK4,sK5))
& in(sK1,cartesian_product2(sK2,sK3)) ) ),
introduced(choice_axiom,[]) ).
fof(f12,plain,
? [X0,X1,X2,X3,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4)))
& in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2)) ),
inference(flattening,[],[f11]) ).
fof(f11,plain,
? [X0,X1,X2,X3,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4)))
& in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2)) )
=> in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4))) ),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X0,X1,X2,X3,X4] :
( ( in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2)) )
=> in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).
fof(f93,plain,
~ in(sK1,cartesian_product2(sK2,sK3)),
inference(resolution,[],[f77,f29]) ).
fof(f29,plain,
in(sK1,cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f17]) ).
fof(f77,plain,
( ~ in(sK1,cartesian_product2(sK4,sK5))
| ~ in(sK1,cartesian_product2(sK2,sK3)) ),
inference(resolution,[],[f73,f46]) ).
fof(f46,plain,
~ in(sK1,set_intersection2(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5))),
inference(backward_demodulation,[],[f30,f42]) ).
fof(f42,plain,
! [X2,X3,X0,X1] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(f30,plain,
~ in(sK1,cartesian_product2(set_intersection2(sK2,sK4),set_intersection2(sK3,sK5))),
inference(cnf_transformation,[],[f17]) ).
fof(f73,plain,
! [X2,X0,X1] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[],[f36,f45]) ).
fof(f45,plain,
! [X0,X1] : sP0(X1,X0,set_intersection2(X0,X1)),
inference(equality_resolution,[],[f40]) ).
fof(f40,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f3,f14]) ).
fof(f14,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f36,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( sP0(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) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f20,f21]) ).
fof(f21,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(f20,plain,
! [X0,X1,X2] :
( ( sP0(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) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X1,X0,X2] :
( ( sP0(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) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X1,X0,X2] :
( ( sP0(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) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET983+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 01:29:16 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (10316)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (10318)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (10319)WARNING: value z3 for option sas not known
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 % (10317)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (10320)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (10319)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)
% 0.15/0.38 % (10321)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)
% 0.15/0.38 % (10322)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)
% 0.15/0.38 % (10323)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)
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 % (10322)First to succeed.
% 0.15/0.38 % (10319)Also succeeded, but the first one will report.
% 0.15/0.38 TRYING [3]
% 0.15/0.38 % (10322)Refutation found. Thanks to Tanya!
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38 % (10322)------------------------------
% 0.15/0.38 % (10322)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38 % (10322)Termination reason: Refutation
% 0.15/0.38
% 0.15/0.38 % (10322)Memory used [KB]: 841
% 0.15/0.38 % (10322)Time elapsed: 0.006 s
% 0.15/0.38 % (10322)Instructions burned: 6 (million)
% 0.15/0.38 % (10322)------------------------------
% 0.15/0.38 % (10322)------------------------------
% 0.15/0.38 % (10316)Success in time 0.022 s
%------------------------------------------------------------------------------