%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HWV052-1.002.001 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:35:08 AM UTC 2026
% Result : Unsatisfiable 0.18s 1.03s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 74 ( 18 unt; 5 def)
% Number of atoms : 159 ( 89 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 134 ( 49 ~; 80 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 65 ( 0 sgn 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( X0 = o
| X0 = i ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bit_domain) ).
fof(f2,plain,
! [X0] :
( i = X0
| o = X0 ),
inference(reorient_equations,[],[f1]) ).
fof(f3,axiom,
! [X0] : inv(X0) != X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bit_inverse) ).
fof(f4,axiom,
! [X0,X1] : unpack1(X0,X1,pack1(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack1) ).
fof(f5,axiom,
! [X0,X1] : unpack1(inv(X0),X1,pack1(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack1_01) ).
fof(f7,axiom,
! [X0,X1] : unpack1(X0,X1,inv(pack1(X0,X1))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack1_03) ).
fof(f8,axiom,
! [X0,X1] : unpack2(X0,X1,pack1(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack2) ).
fof(f10,axiom,
! [X0,X1] : unpack2(X0,inv(X1),pack1(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack2_05) ).
fof(f11,axiom,
! [X0,X1] : unpack2(X0,X1,inv(pack1(X0,X1))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unpack2_06) ).
fof(f12,plain,
! [X0,X1] :
( o = X1
| X0 = X1
| o = X0 ),
inference(superposition,[],[f2,f2]) ).
fof(f13,plain,
! [X0] :
( o = inv(X0)
| i != X0 ),
inference(superposition,[],[f3,f2]) ).
fof(f19,definition,
( spl0_2
<=> o = i ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f21,plain,
( o != i
| spl0_2 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f24,plain,
! [X0,X1] :
( unpack1(X0,X1,i) = X0
| o = pack1(X0,X1) ),
inference(superposition,[],[f4,f2]) ).
fof(f28,plain,
! [X0] :
( o != X0
| i != X0 ),
inference(superposition,[],[f3,f13]) ).
fof(f32,plain,
o != i,
inference(equality_resolution,[],[f28]) ).
fof(f33,plain,
! [X0,X1] :
( i != X0
| unpack1(o,X1,pack1(X0,X1)) = X0 ),
inference(superposition,[],[f5,f13]) ).
fof(f34,plain,
! [X0,X1] :
( unpack1(i,X1,pack1(X0,X1)) = X0
| o = inv(X0) ),
inference(superposition,[],[f5,f2]) ).
fof(f44,plain,
! [X0,X1] :
( i != pack1(X0,X1)
| unpack1(X0,X1,o) = X0 ),
inference(superposition,[],[f7,f13]) ).
fof(f53,plain,
! [X0,X1] :
( i != X1
| unpack2(X0,o,pack1(X0,X1)) = X1 ),
inference(superposition,[],[f10,f13]) ).
fof(f59,plain,
! [X0,X1] :
( i != pack1(X0,X1)
| unpack2(X0,X1,o) = X1 ),
inference(superposition,[],[f11,f13]) ).
fof(f71,plain,
! [X0,X1] :
( o != X0
| inv(X0) = X1
| o = X1 ),
inference(superposition,[],[f3,f12]) ).
fof(f74,plain,
! [X2,X0,X1] :
( unpack1(X0,X1,o) = X0
| pack1(X0,X1) = X2
| o = X2 ),
inference(superposition,[],[f4,f12]) ).
fof(f78,plain,
! [X2,X0,X1] :
( unpack2(X0,X1,o) = X1
| pack1(X0,X1) = X2
| o = X2 ),
inference(superposition,[],[f8,f12]) ).
fof(f105,plain,
! [X0] :
( o = X0
| inv(o) = X0 ),
inference(equality_resolution,[],[f71]) ).
fof(f116,plain,
( o != o
| i = inv(o)
| spl0_2 ),
inference(superposition,[],[f21,f105]) ).
fof(f144,plain,
( i = inv(o)
| spl0_2 ),
inference(trivial_inequality_removal,[],[f116]) ).
fof(f154,definition,
( spl0_3
<=> i = inv(o) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f156,plain,
( i = inv(o)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f158,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f144,f19,f154]) ).
fof(f476,plain,
! [X0] : i = unpack1(o,X0,pack1(i,X0)),
inference(equality_resolution,[],[f33]) ).
fof(f486,plain,
! [X0] :
( i = unpack1(o,X0,i)
| o = pack1(i,X0) ),
inference(superposition,[],[f476,f2]) ).
fof(f519,plain,
! [X0,X1] :
( o != i
| unpack1(X0,X1,o) = X0
| pack1(X0,X1) = inv(o) ),
inference(superposition,[],[f44,f105]) ).
fof(f548,plain,
! [X0] : i = unpack2(X0,o,pack1(X0,i)),
inference(equality_resolution,[],[f53]) ).
fof(f569,plain,
! [X0,X1] :
( o != i
| unpack2(X0,X1,o) = X1
| pack1(X0,X1) = inv(o) ),
inference(superposition,[],[f59,f105]) ).
fof(f1630,plain,
! [X0] :
( o = i
| o = pack1(o,X0)
| o = pack1(i,X0) ),
inference(superposition,[],[f24,f486]) ).
fof(f1633,plain,
( ! [X0] :
( o = pack1(i,X0)
| o = pack1(o,X0) )
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f1630,f21]) ).
fof(f1705,plain,
( i = unpack2(i,o,o)
| o = pack1(o,i)
| spl0_2 ),
inference(superposition,[],[f548,f1633]) ).
fof(f1711,definition,
( spl0_9
<=> o = pack1(o,i) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f1713,plain,
( o = pack1(o,i)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f1711]) ).
fof(f1720,definition,
( spl0_11
<=> i = unpack2(i,o,o) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f1722,plain,
( i = unpack2(i,o,o)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f1720]) ).
fof(f1723,plain,
( spl0_9
| spl0_11
| spl0_2 ),
inference(avatar_split_clause,[],[f1705,f19,f1720,f1711]) ).
fof(f1749,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f32,f19]) ).
fof(f1774,plain,
( ! [X0,X1] :
( i = pack1(X0,X1)
| o != i
| unpack1(X0,X1,o) = X0 )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f519,f156]) ).
fof(f1777,plain,
( ! [X0,X1] :
( i = pack1(X0,X1)
| o != i
| unpack2(X0,X1,o) = X1 )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f569,f156]) ).
fof(f1906,plain,
( ! [X0,X1] :
( i = pack1(X0,X1)
| unpack1(X0,X1,o) = X0 )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f1774,f74]) ).
fof(f1907,plain,
( ! [X0,X1] :
( i = pack1(X0,X1)
| unpack2(X0,X1,o) = X1 )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f1777,f78]) ).
fof(f1917,plain,
( ! [X0,X1] : unpack1(X0,X1,o) = X0
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f1906,f44]) ).
fof(f1918,plain,
( ! [X0,X1] : unpack2(X0,X1,o) = X1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f1907,f59]) ).
fof(f2985,definition,
( spl0_78
<=> ! [X0,X1] : unpack2(X0,X1,o) = X1 ),
introduced(definition,[new_symbols(definition,[spl0_78])],[avatar_definition]) ).
fof(f2986,plain,
( ! [X0,X1] : unpack2(X0,X1,o) = X1
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f2985]) ).
fof(f2989,plain,
( spl0_78
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f1918,f154,f2985]) ).
fof(f3115,plain,
( o = i
| ~ spl0_11
| ~ spl0_78 ),
inference(forward_demodulation,[],[f1722,f2986]) ).
fof(f3116,plain,
( $false
| spl0_2
| ~ spl0_11
| ~ spl0_78 ),
inference(forward_subsumption_resolution,[],[f3115,f21]) ).
fof(f3117,plain,
( spl0_2
| ~ spl0_11
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f3116]) ).
fof(f3193,plain,
( o = unpack1(i,i,o)
| o = inv(o)
| ~ spl0_9 ),
inference(superposition,[],[f34,f1713]) ).
fof(f3205,plain,
( o = unpack1(i,i,o)
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f3193,f3]) ).
fof(f3217,plain,
( o = i
| ~ spl0_3
| ~ spl0_9 ),
inference(forward_demodulation,[],[f3205,f1917]) ).
fof(f3232,plain,
( $false
| spl0_2
| ~ spl0_3
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f3217,f21]) ).
fof(f3233,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f3232]) ).
cnf(s3,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f158]) ).
cnf(s25,plain,
( spl0_2
| spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f1723]) ).
cnf(s29,plain,
~ spl0_2,
inference(sat_conversion,[],[f1749]) ).
cnf(s125,plain,
( ~ spl0_3
| spl0_78 ),
inference(sat_conversion,[],[f2989]) ).
cnf(s128,plain,
( spl0_2
| ~ spl0_11
| ~ spl0_78 ),
inference(sat_conversion,[],[f3117]) ).
cnf(s136,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_9 ),
inference(sat_conversion,[],[f3233]) ).
cnf(s145,plain,
( spl0_9
| spl0_11 ),
inference(rat,[],[s25,s29]) ).
cnf(s149,plain,
spl0_3,
inference(rat,[],[s3,s29]) ).
cnf(s150,plain,
~ spl0_9,
inference(rat,[],[s136,s29,s149]) ).
cnf(s151,plain,
spl0_78,
inference(rat,[],[s125,s149]) ).
cnf(s176,plain,
spl0_11,
inference(rat,[],[s145,s150]) ).
cnf(s178,plain,
$false,
inference(rat,[],[s128,s29,s151,s176]) ).
fof(f3234,plain,
$false,
inference(avatar_sat_refutation,[],[s178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV052-1.002.001 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 11:16:26 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/1.03 % (2818514)Input is clausal, will run a generic CNF schedule.
% 0.18/1.03 % (2818524)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4115526958:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.18/1.03 % (2818522)lrs+10_1_sil=8000:sp=occurrence:random_seed=1547387934:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.18/1.03 % (2818519)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3390948414:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.18/1.03 % (2818520)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3112237682:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.18/1.03 % (2818525)dis-21_1_sil=8000:lcm=predicate:random_seed=1295195316:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.18/1.03 % (2818523)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=74268369:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.18/1.03 % (2818521)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=315322990:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.18/1.03 % (2818523)Refutation not found, incomplete strategy
% 0.18/1.03 % (2818523)------------------------------
% 0.18/1.03 % (2818523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.03 % (2818522)Refutation not found, incomplete strategy
% 0.18/1.03 % (2818522)------------------------------
% 0.18/1.03 % (2818522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.03 % (2818523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.03 % (2818522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.03 % (2818522)CaDiCaL version: 2.1.3
% 0.18/1.03 % (2818523)CaDiCaL version: 2.1.3
% 0.18/1.03 % (2818523)Termination reason: Refutation not found, incomplete strategy
% 0.18/1.03 % (2818523)Time elapsed: 0.0000 s
% 0.18/1.03 % (2818522)Termination reason: Refutation not found, incomplete strategy
% 0.18/1.03 % (2818522)Time elapsed: 0.0000 s
% 0.18/1.03 % (2818523)Peak memory usage: 86 MB
% 0.18/1.03 % (2818522)Peak memory usage: 86 MB
% 0.18/1.03 % (2818525)Refutation not found, incomplete strategy
% 0.18/1.03 % (2818525)------------------------------
% 0.18/1.03 % (2818525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.03 % (2818525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.03 % (2818525)CaDiCaL version: 2.1.3
% 0.18/1.03 % (2818525)Termination reason: Refutation not found, incomplete strategy
% 0.18/1.03 % (2818525)Time elapsed: 0.001 s
% 0.18/1.03 % (2818525)Peak memory usage: 88 MB
% 0.18/1.03 % (2818524)First to succeed.
% 0.18/1.03 % (2818524)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2818514"
% 0.18/1.03 % (2818524)Refutation found. Thanks to Tanya!
% 0.18/1.03 % SZS status Unsatisfiable for theBenchmark
% 0.18/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.03 % (2818524)------------------------------
% 0.18/1.03 % (2818524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.03 % (2818524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.03 % (2818524)CaDiCaL version: 2.1.3
% 0.18/1.03 % (2818524)Termination reason: Refutation
% 0.18/1.03 % (2818524)Time elapsed: 0.047 s
% 0.18/1.03 % (2818524)Peak memory usage: 90 MB
% 0.18/1.03 % (2818524)Instructions burned: 160 (million)
% 0.18/1.03 % (2818524)------------------------------
% 0.18/1.03 % (2818524)------------------------------
% 0.18/1.03 % (2818514)Success in time 0.335 s
% 0.18/1.03 % Vampire exiting
%------------------------------------------------------------------------------