TSTP Solution File: GEO083+1 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : GEO083+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n024.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 : Mon Jun 24 06:25:07 EDT 2024
% Result : Theorem 0.17s 0.41s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 8 unt; 1 typ; 0 def)
% Number of atoms : 354 ( 13 equ)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 219 ( 77 ~; 74 |; 53 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 165 ( 165 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 7 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 114 ( 94 !; 19 ?; 39 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_8,type,
sQ10_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f686,plain,
$false,
inference(avatar_sat_refutation,[],[f235,f255,f685]) ).
tff(f685,plain,
~ spl11_12,
inference(avatar_contradiction_clause,[],[f684]) ).
tff(f684,plain,
( $false
| ~ spl11_12 ),
inference(subsumption_resolution,[],[f681,f234]) ).
tff(f234,plain,
( incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK1)
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f232]) ).
tff(f232,plain,
( spl11_12
<=> incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_12])]) ).
tff(f681,plain,
~ incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK1),
inference(resolution,[],[f249,f64]) ).
tff(f64,plain,
part_of(sK1,sK2),
inference(cnf_transformation,[],[f41]) ).
tff(f41,plain,
( ~ part_of(sum(sK0,sK1),sum(sK0,sK2))
& meet(sK3,sK0,sK2)
& meet(sK3,sK0,sK1)
& part_of(sK1,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f31,f40]) ).
tff(f40,plain,
( ? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),sum(X0,X2))
& meet(X3,X0,X2)
& meet(X3,X0,X1)
& part_of(X1,X2) )
=> ( ~ part_of(sum(sK0,sK1),sum(sK0,sK2))
& meet(sK3,sK0,sK2)
& meet(sK3,sK0,sK1)
& part_of(sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f31,plain,
? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),sum(X0,X2))
& meet(X3,X0,X2)
& meet(X3,X0,X1)
& part_of(X1,X2) ),
inference(flattening,[],[f30]) ).
tff(f30,plain,
? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),sum(X0,X2))
& meet(X3,X0,X2)
& meet(X3,X0,X1)
& part_of(X1,X2) ),
inference(ennf_transformation,[],[f19]) ).
tff(f19,plain,
~ ! [X0,X1,X2,X3] :
( ( meet(X3,X0,X2)
& meet(X3,X0,X1)
& part_of(X1,X2) )
=> part_of(sum(X0,X1),sum(X0,X2)) ),
inference(rectify,[],[f18]) ).
tff(f18,negated_conjecture,
~ ! [X1,X3,X5,X2] :
( ( meet(X2,X1,X5)
& meet(X2,X1,X3)
& part_of(X3,X5) )
=> part_of(sum(X1,X3),sum(X1,X5)) ),
inference(negated_conjecture,[],[f17]) ).
tff(f17,conjecture,
! [X1,X3,X5,X2] :
( ( meet(X2,X1,X5)
& meet(X2,X1,X3)
& part_of(X3,X5) )
=> part_of(sum(X1,X3),sum(X1,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f249,plain,
! [X0: $i] :
( ~ part_of(X0,sK2)
| ~ incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),X0) ),
inference(resolution,[],[f190,f76]) ).
tff(f76,plain,
! [X3: $i,X0: $i,X1: $i] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1)
| ~ part_of(X1,X0) ),
inference(cnf_transformation,[],[f53]) ).
tff(f53,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ( ~ incident_c(sK6(X0,X1),X0)
& incident_c(sK6(X0,X1),X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f51,f52]) ).
tff(f52,plain,
! [X0,X1] :
( ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) )
=> ( ~ incident_c(sK6(X0,X1),X0)
& incident_c(sK6(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
tff(f51,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(rectify,[],[f50]) ).
tff(f50,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) ) )
& ( ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) )
| ~ part_of(X1,X0) ) ),
inference(nnf_transformation,[],[f35]) ).
tff(f35,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X1)
=> incident_c(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f190,plain,
~ incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK2),
inference(resolution,[],[f111,f67]) ).
tff(f67,plain,
~ part_of(sum(sK0,sK1),sum(sK0,sK2)),
inference(cnf_transformation,[],[f41]) ).
tff(f111,plain,
! [X2: $i,X0: $i,X1: $i] :
( part_of(X2,sum(X0,X1))
| ~ incident_c(sK6(sum(X0,X1),X2),X1) ),
inference(resolution,[],[f94,f78]) ).
tff(f78,plain,
! [X0: $i,X1: $i] :
( ~ incident_c(sK6(X0,X1),X0)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f53]) ).
tff(f94,plain,
! [X2: $i,X1: $i,X4: $i] :
( incident_c(X4,sum(X1,X2))
| ~ incident_c(X4,X2) ),
inference(equality_resolution,[],[f70]) ).
tff(f70,plain,
! [X2: $i,X0: $i,X1: $i,X4: $i] :
( incident_c(X4,X0)
| ~ incident_c(X4,X2)
| ( sum(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f46]) ).
tff(f46,plain,
! [X0,X1,X2] :
( ( ( sum(X1,X2) = X0 )
| ( ( ( ~ incident_c(sK4(X0,X1,X2),X2)
& ~ incident_c(sK4(X0,X1,X2),X1) )
| ~ incident_c(sK4(X0,X1,X2),X0) )
& ( incident_c(sK4(X0,X1,X2),X2)
| incident_c(sK4(X0,X1,X2),X1)
| incident_c(sK4(X0,X1,X2),X0) ) ) )
& ( ! [X4] :
( ( incident_c(X4,X0)
| ( ~ incident_c(X4,X2)
& ~ incident_c(X4,X1) ) )
& ( incident_c(X4,X2)
| incident_c(X4,X1)
| ~ incident_c(X4,X0) ) )
| ( sum(X1,X2) != X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f44,f45]) ).
tff(f45,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) )
=> ( ( ( ~ incident_c(sK4(X0,X1,X2),X2)
& ~ incident_c(sK4(X0,X1,X2),X1) )
| ~ incident_c(sK4(X0,X1,X2),X0) )
& ( incident_c(sK4(X0,X1,X2),X2)
| incident_c(sK4(X0,X1,X2),X1)
| incident_c(sK4(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f44,plain,
! [X0,X1,X2] :
( ( ( sum(X1,X2) = X0 )
| ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) ) )
& ( ! [X4] :
( ( incident_c(X4,X0)
| ( ~ incident_c(X4,X2)
& ~ incident_c(X4,X1) ) )
& ( incident_c(X4,X2)
| incident_c(X4,X1)
| ~ incident_c(X4,X0) ) )
| ( sum(X1,X2) != X0 ) ) ),
inference(rectify,[],[f43]) ).
tff(f43,plain,
! [X0,X1,X2] :
( ( ( sum(X1,X2) = X0 )
| ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) ) )
& ( ! [X3] :
( ( incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| ~ incident_c(X3,X0) ) )
| ( sum(X1,X2) != X0 ) ) ),
inference(flattening,[],[f42]) ).
tff(f42,plain,
! [X0,X1,X2] :
( ( ( sum(X1,X2) = X0 )
| ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) ) )
& ( ! [X3] :
( ( incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| ~ incident_c(X3,X0) ) )
| ( sum(X1,X2) != X0 ) ) ),
inference(nnf_transformation,[],[f21]) ).
tff(f21,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) = X0 )
<=> ! [X3] :
( incident_c(X3,X0)
<=> ( incident_c(X3,X2)
| incident_c(X3,X1) ) ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X0,X1,X3] :
( ( sum(X1,X3) = X0 )
<=> ! [X4] :
( incident_c(X4,X0)
<=> ( incident_c(X4,X3)
| incident_c(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f255,plain,
~ spl11_11,
inference(avatar_split_clause,[],[f195,f228]) ).
tff(f228,plain,
( spl11_11
<=> incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_11])]) ).
tff(f195,plain,
~ incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK0),
inference(resolution,[],[f112,f67]) ).
tff(f112,plain,
! [X2: $i,X0: $i,X1: $i] :
( part_of(X2,sum(X0,X1))
| ~ incident_c(sK6(sum(X0,X1),X2),X0) ),
inference(resolution,[],[f95,f78]) ).
tff(f95,plain,
! [X2: $i,X1: $i,X4: $i] :
( incident_c(X4,sum(X1,X2))
| ~ incident_c(X4,X1) ),
inference(equality_resolution,[],[f69]) ).
tff(f69,plain,
! [X2: $i,X0: $i,X1: $i,X4: $i] :
( incident_c(X4,X0)
| ~ incident_c(X4,X1)
| ( sum(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f46]) ).
tff(f235,plain,
( spl11_11
| spl11_12 ),
inference(avatar_split_clause,[],[f225,f232,f228]) ).
tff(f225,plain,
( incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK1)
| incident_c(sK6(sum(sK0,sK2),sum(sK0,sK1)),sK0) ),
inference(resolution,[],[f118,f67]) ).
tff(f118,plain,
! [X2: $i,X0: $i,X1: $i] :
( part_of(sum(X1,X2),X0)
| incident_c(sK6(X0,sum(X1,X2)),X2)
| incident_c(sK6(X0,sum(X1,X2)),X1) ),
inference(resolution,[],[f96,f77]) ).
tff(f77,plain,
! [X0: $i,X1: $i] :
( incident_c(sK6(X0,X1),X1)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f53]) ).
tff(f96,plain,
! [X2: $i,X1: $i,X4: $i] :
( ~ incident_c(X4,sum(X1,X2))
| incident_c(X4,X1)
| incident_c(X4,X2) ),
inference(equality_resolution,[],[f68]) ).
tff(f68,plain,
! [X2: $i,X0: $i,X1: $i,X4: $i] :
( incident_c(X4,X2)
| incident_c(X4,X1)
| ~ incident_c(X4,X0)
| ( sum(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GEO083+1 : TPTP v8.2.0. Released v2.4.0.
% 0.00/0.10 % Command : run_vampire %s %d THM
% 0.10/0.30 % Computer : n024.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % 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 : Fri Jun 21 10:45:09 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.17/0.32 This is a FOF_THM_RFO_SEQ problem
% 0.17/0.32 Running first-order theorem proving
% 0.17/0.32 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.37 % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.37 % (20241)lrs+1002_74:59_drc=off:tgt=full:sos=all:cond=fast:i=124987:kws=inv_frequency:afp=300:afq=2.0744697298148953:rawr=on:urr=full:sil=128000:si=on:rtra=on:random_seed=3250543_0 on theBenchmark for (2999ds/124987Mi)
% 0.17/0.37 % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.37 % (20242)lrs+11_1:16_to=lpo:drc=off:bsd=on:sp=frequency:i=172350:bs=on:av=off:fsd=on:sil=256000:fdi=50_0 on theBenchmark for (2999ds/172350Mi)
% 0.17/0.38 % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.38 % (20240)lrs+2_5:39_bsr=unit_only:to=lpo:drc=off:sil=128000:plsq=on:plsqr=2,19:sp=frequency:lcm=reverse:fd=preordered:s2a=on:i=38749:s2at=-1.0:fsr=off:uhcvi=on:rawr=on:aer=off:lwlo=on:add=off:bce=on:acc=model:afr=on_0 on theBenchmark for (2999ds/38749Mi)
% 0.17/0.38 % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.38 % (20244)lrs+1011_1:1_sil=32000:rnwc=on:nwc=10.0:lwlo=on:i=121:bd=off:av=off_0 on theBenchmark for (2999ds/121Mi)
% 0.17/0.38 % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.38 % (20245)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=113:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2999ds/113Mi)
% 0.17/0.38 % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.38 % (20243)lrs+1011_1:1_sil=2000:i=103:ep=RS:nm=32:ss=axioms:sos=on_0 on theBenchmark for (2999ds/103Mi)
% 0.17/0.38 % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.38 % (20246)lrs+1010_1:1_to=lpo:sil=2000:plsq=on:plsqr=32,1:sp=reverse_arity:sos=on:spb=goal_then_units:i=128:ss=axioms:sgt=50:bd=off:sd=3_0 on theBenchmark for (2999ds/128Mi)
% 0.17/0.40 % (20245)First to succeed.
% 0.17/0.40 % (20245)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20239"
% 0.17/0.41 % (20239)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.41 % (20245)Refutation found. Thanks to Tanya!
% 0.17/0.41 % SZS status Theorem for theBenchmark
% 0.17/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.41 % (20245)------------------------------
% 0.17/0.41 % (20245)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.17/0.41 % (20245)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.17/0.41 % (20245)Termination reason: Refutation
% 0.17/0.41
% 0.17/0.41 % (20245)Memory used [KB]: 1511
% 0.17/0.41 % (20245)Time elapsed: 0.025 s
% 0.17/0.41 % (20245)Instructions burned: 49 (million)
% 0.17/0.41 % (20245)------------------------------
% 0.17/0.41 % (20245)------------------------------
% 0.17/0.41 % (20239)Success in time 0.078 s
%------------------------------------------------------------------------------