%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 02:28:28 PM UTC 2026
% Result : Unsatisfiable 2.25s 0.87s
% Output : Refutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 69 ( 16 unt; 10 def)
% Number of atoms : 173 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 182 ( 78 ~; 94 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 12 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ 'E'(f(X0),s(s('0')))
| ~ 'E'(f(X1),s(s(s(s('0')))))
| ~ 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X4),'0')
| ~ 'E'(f(X5),s(s(s(s(s('0')))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5_03) ).
fof(f4,axiom,
! [X0] : 'E'(f(X0),s(s(s(s('0'))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6_04) ).
fof(f5,axiom,
! [X0] : 'E'(f(X0),s(s(s(s(s('0')))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8_05) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ 'E'(f(X0),s(s('0')))
| ~ 'E'(f(X1),s(s(s(s('0')))))
| ~ 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X4),s(s(s(s(s('0'))))))
| 'E'(f('AP'(s(s(s(s(s(s('0')))))),X5)),'0') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2_07) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4] :
( ~ 'E'(f(X0),s(s(s(s('0')))))
| ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| ~ 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X3),s(s('0')))
| 'E'(f('AP'(s(s(s(s(s(s('0')))))),X4)),s('0')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12_09) ).
fof(f10,axiom,
! [X0,X1] :
( ~ 'E'(f(X0),s(s(s(s('0')))))
| ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| 'E'(f(X1),s(s(s('0')))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1_10) ).
fof(f12,axiom,
! [X2,X3,X0,X1] :
( ~ 'E'(f(X0),s(s(s(s('0')))))
| ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| ~ 'E'(f(X2),s(s(s('0'))))
| 'E'(f('AP'(s(s(s(s(s(s('0')))))),X3)),s(s('0'))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4_12) ).
fof(f15,definition,
( spl0_1
<=> ! [X3] : 'E'(f('AP'(s(s(s(s(s(s('0')))))),X3)),s(s('0'))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f16,plain,
( ! [X3] : 'E'(f('AP'(s(s(s(s(s(s('0')))))),X3)),s(s('0')))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f18,definition,
( spl0_2
<=> ! [X2] : ~ 'E'(f(X2),s(s(s('0')))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f19,plain,
( ! [X2] : ~ 'E'(f(X2),s(s(s('0'))))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f21,definition,
( spl0_3
<=> ! [X1] : ~ 'E'(f(X1),s(s(s(s(s('0')))))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f22,plain,
( ! [X1] : ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f24,definition,
( spl0_4
<=> ! [X0] : ~ 'E'(f(X0),s(s(s(s('0'))))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f25,plain,
( ! [X0] : ~ 'E'(f(X0),s(s(s(s('0')))))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f26,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f12,f24,f21,f18,f15]) ).
fof(f28,definition,
( spl0_5
<=> ! [X1] :
( ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| 'E'(f(X1),s(s(s('0')))) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f29,plain,
( ! [X1] :
( ~ 'E'(f(X1),s(s(s(s(s('0'))))))
| 'E'(f(X1),s(s(s('0')))) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f30,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f10,f24,f28]) ).
fof(f32,definition,
( spl0_6
<=> ! [X4] : 'E'(f('AP'(s(s(s(s(s(s('0')))))),X4)),s('0')) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f33,plain,
( ! [X4] : 'E'(f('AP'(s(s(s(s(s(s('0')))))),X4)),s('0'))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,definition,
( spl0_7
<=> ! [X3] : ~ 'E'(f(X3),s(s('0'))) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f36,plain,
( ! [X3] : ~ 'E'(f(X3),s(s('0')))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f37,plain,
( spl0_6
| spl0_7
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f9,f24,f21,f18,f35,f32]) ).
fof(f39,definition,
( spl0_8
<=> ! [X5] : 'E'(f('AP'(s(s(s(s(s(s('0')))))),X5)),'0') ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f40,plain,
( ! [X5] : 'E'(f('AP'(s(s(s(s(s(s('0')))))),X5)),'0')
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,definition,
( spl0_9
<=> ! [X3] : ~ 'E'(f(X3),s('0')) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f43,plain,
( ! [X3] : ~ 'E'(f(X3),s('0'))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f44,plain,
( spl0_8
| spl0_3
| spl0_9
| spl0_2
| spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f7,f35,f24,f18,f42,f21,f39]) ).
fof(f46,definition,
( spl0_10
<=> ! [X4] : ~ 'E'(f(X4),'0') ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f47,plain,
( ! [X4] : ~ 'E'(f(X4),'0')
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f48,plain,
( spl0_3
| spl0_10
| spl0_9
| spl0_2
| spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f3,f35,f24,f18,f42,f46,f21]) ).
fof(f49,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f25,f4]) ).
fof(f50,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f49]) ).
fof(f51,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f22,f5]) ).
fof(f52,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f51]) ).
fof(f53,plain,
( $false
| ~ spl0_1
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f16,f36]) ).
fof(f54,plain,
( ~ spl0_1
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f53]) ).
fof(f55,plain,
( ! [X1] : 'E'(f(X1),s(s(s('0'))))
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f29,f5]) ).
fof(f56,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f55,f19]) ).
fof(f57,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f56]) ).
fof(f58,plain,
( $false
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f33,f43]) ).
fof(f59,plain,
( ~ spl0_6
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f58]) ).
fof(f60,plain,
( $false
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f40,f47]) ).
fof(f61,plain,
( ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f60]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f26]) ).
cnf(s2,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f30]) ).
cnf(s3,plain,
( spl0_2
| spl0_3
| spl0_4
| spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f37]) ).
cnf(s4,plain,
( spl0_2
| spl0_3
| spl0_4
| spl0_7
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f44]) ).
cnf(s5,plain,
( spl0_2
| spl0_3
| spl0_4
| spl0_7
| spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f48]) ).
cnf(s6,plain,
~ spl0_4,
inference(sat_conversion,[],[f50]) ).
cnf(s7,plain,
~ spl0_3,
inference(sat_conversion,[],[f52]) ).
cnf(s8,plain,
( ~ spl0_1
| ~ spl0_7 ),
inference(sat_conversion,[],[f54]) ).
cnf(s9,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f57]) ).
cnf(s10,plain,
( ~ spl0_6
| ~ spl0_9 ),
inference(sat_conversion,[],[f59]) ).
cnf(s11,plain,
( ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f61]) ).
cnf(s12,plain,
( spl0_2
| spl0_7
| spl0_9
| spl0_10 ),
inference(rat,[],[s5,s6,s7]) ).
cnf(s13,plain,
( spl0_2
| spl0_7
| spl0_8
| spl0_9 ),
inference(rat,[],[s4,s6,s7]) ).
cnf(s14,plain,
( spl0_2
| spl0_6
| spl0_7 ),
inference(rat,[],[s3,s6,s7]) ).
cnf(s15,plain,
spl0_5,
inference(rat,[],[s2,s6]) ).
cnf(s16,plain,
~ spl0_2,
inference(rat,[],[s9,s15]) ).
cnf(s17,plain,
spl0_1,
inference(rat,[],[s1,s6,s7,s16]) ).
cnf(s18,plain,
~ spl0_7,
inference(rat,[],[s8,s17]) ).
cnf(s19,plain,
spl0_6,
inference(rat,[],[s14,s16,s18]) ).
cnf(s20,plain,
~ spl0_9,
inference(rat,[],[s10,s19]) ).
cnf(s21,plain,
spl0_10,
inference(rat,[],[s12,s18,s16,s20]) ).
cnf(s22,plain,
spl0_8,
inference(rat,[],[s13,s18,s16,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s11,s21,s22]) ).
fof(f62,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 18:02:47 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.25/0.87 % (2852037)Input is clausal, will run a generic CNF schedule.
% 2.25/0.87 % (2852047)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1543070169:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.25/0.87 % (2852047)First to succeed.
% 2.25/0.87 % (2852047)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2852037"
% 2.25/0.87 % (2852046)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1327978009:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.25/0.87 % (2852044)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2458018415:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.25/0.87 % (2852046)Refutation not found, incomplete strategy
% 2.25/0.87 % (2852046)------------------------------
% 2.25/0.87 % (2852046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.25/0.87 % (2852046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.25/0.87 % (2852046)CaDiCaL version: 2.1.3
% 2.25/0.87 % (2852046)Termination reason: Refutation not found, incomplete strategy
% 2.25/0.87 % (2852046)Time elapsed: 0.0000 s
% 2.25/0.87 % (2852046)Peak memory usage: 86 MB
% 2.25/0.87 % (2852042)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=1270552489:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.25/0.87 % (2852045)lrs+10_1_sil=8000:sp=occurrence:random_seed=572742784:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.25/0.87 % (2852043)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1697231740:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.25/0.87 % (2852045)Refutation not found, incomplete strategy
% 2.25/0.87 % (2852045)------------------------------
% 2.25/0.87 % (2852045)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.25/0.87 % (2852045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.25/0.87 % (2852045)CaDiCaL version: 2.1.3
% 2.25/0.87 % (2852045)Termination reason: Refutation not found, incomplete strategy
% 2.25/0.87 % (2852045)Time elapsed: 0.001 s
% 2.25/0.87 % (2852045)Peak memory usage: 86 MB
% 2.25/0.87 % (2852048)dis-21_1_sil=8000:lcm=predicate:random_seed=1748157531: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)
% 2.25/0.87 % (2852048)Also succeeded, but the first one will report.
% 2.25/0.87 % (2852047)Refutation found. Thanks to Tanya!
% 2.25/0.87 % SZS status Unsatisfiable for theBenchmark
% 2.25/0.87 % SZS output start Proof for theBenchmark
% See solution above
% 2.25/0.87 % (2852047)------------------------------
% 2.25/0.87 % (2852047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.25/0.87 % (2852047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.25/0.87 % (2852047)CaDiCaL version: 2.1.3
% 2.25/0.87 % (2852047)Termination reason: Refutation
% 2.25/0.87 % (2852047)Time elapsed: 0.002 s
% 2.25/0.87 % (2852047)Peak memory usage: 89 MB
% 2.25/0.87 % (2852047)Instructions burned: 2 (million)
% 2.25/0.87 % (2852047)------------------------------
% 2.25/0.87 % (2852047)------------------------------
% 2.25/0.87 % (2852037)Success in time 0.26 s
% 2.25/0.87 % Vampire exiting
%------------------------------------------------------------------------------