%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n001.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 02:32:15 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 70 ( 16 unt; 10 def)
% Number of atoms : 174 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 191 ( 87 ~; 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 : 55 ( 0 sgn 55 !; 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(f45,plain,
! [X2,X3,X0,X4,X5] :
( ~ 'E'(f(X0),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')))))) ),
inference(forward_subsumption_resolution,[],[f3,f4]) ).
fof(f46,plain,
! [X2,X3,X0,X4] :
( ~ 'E'(f(X0),s(s('0')))
| ~ 'E'(f(X2),s(s(s('0'))))
| ~ 'E'(f(X3),s('0'))
| ~ 'E'(f(X4),'0') ),
inference(forward_subsumption_resolution,[],[f45,f5]) ).
fof(f48,definition,
( spl0_10
<=> ! [X4] : ~ 'E'(f(X4),'0') ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f49,plain,
( ! [X4] : ~ 'E'(f(X4),'0')
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f50,plain,
( spl0_10
| spl0_9
| spl0_2
| spl0_7 ),
inference(avatar_split_clause,[],[f46,f35,f18,f42,f48]) ).
fof(f51,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f25,f4]) ).
fof(f52,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f51]) ).
fof(f53,plain,
( ! [X1] : 'E'(f(X1),s(s(s('0'))))
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f29,f5]) ).
fof(f54,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f53,f19]) ).
fof(f55,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f54]) ).
fof(f56,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f22,f5]) ).
fof(f57,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f56]) ).
fof(f58,plain,
( $false
| ~ spl0_1
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f16,f36]) ).
fof(f59,plain,
( ~ spl0_1
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f58]) ).
fof(f60,plain,
( $false
| ~ spl0_6
| ~ spl0_9 ),
inference(resolution,[],[f33,f43]) ).
fof(f61,plain,
( ~ spl0_6
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f60]) ).
fof(f62,plain,
( $false
| ~ spl0_8
| ~ spl0_10 ),
inference(resolution,[],[f40,f49]) ).
fof(f63,plain,
( ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f62]) ).
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_7
| spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f50]) ).
cnf(s6,plain,
~ spl0_4,
inference(sat_conversion,[],[f52]) ).
cnf(s7,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f55]) ).
cnf(s8,plain,
~ spl0_3,
inference(sat_conversion,[],[f57]) ).
cnf(s9,plain,
( ~ spl0_1
| ~ spl0_7 ),
inference(sat_conversion,[],[f59]) ).
cnf(s10,plain,
( ~ spl0_6
| ~ spl0_9 ),
inference(sat_conversion,[],[f61]) ).
cnf(s11,plain,
( ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f63]) ).
cnf(s12,plain,
( spl0_2
| spl0_7
| spl0_8
| spl0_9 ),
inference(rat,[],[s4,s6,s8]) ).
cnf(s13,plain,
( spl0_2
| spl0_6
| spl0_7 ),
inference(rat,[],[s3,s6,s8]) ).
cnf(s14,plain,
spl0_5,
inference(rat,[],[s2,s6]) ).
cnf(s15,plain,
~ spl0_2,
inference(rat,[],[s7,s14]) ).
cnf(s16,plain,
spl0_1,
inference(rat,[],[s1,s6,s8,s15]) ).
cnf(s17,plain,
~ spl0_7,
inference(rat,[],[s9,s16]) ).
cnf(s18,plain,
spl0_6,
inference(rat,[],[s13,s15,s17]) ).
cnf(s19,plain,
~ spl0_9,
inference(rat,[],[s10,s18]) ).
cnf(s20,plain,
spl0_10,
inference(rat,[],[s5,s17,s15,s19]) ).
cnf(s21,plain,
spl0_8,
inference(rat,[],[s12,s17,s15,s19]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s11,s20,s21]) ).
fof(f64,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.08/0.19 % Computer : n001.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 18:05:19 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.28 % (579314)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (579319)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2651787786_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % TRYING [1]
% 0.19/0.28 % TRYING [2]
% 0.19/0.28 % TRYING [3]
% 0.19/0.28 % (579320)% WARNING: option uhcvi not known.
% 0.19/0.28 % TRYING [4]
% 0.19/0.28 % (579320)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1168373783:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (579321)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4042197458:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (579324)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1014739988:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (579322)dis+10_1_sil=32000:sp=arity:random_seed=2654722815:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (579323)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2298935561:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (579325)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=722706669:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % (579320) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-579314-579320"...
% 0.19/0.28 % (579324) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-579314-579324"...
% 0.19/0.28 % (579322) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-579314-579322"...
% 0.19/0.28 % (579321) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-579314-579321"...
% 0.19/0.28 % (579323) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-579314-579323"...
% 0.19/0.28 % (579325) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-579314-579325"...
% 0.19/0.28 % (579324)...printing done.
% 0.19/0.28 % (579320)...printing done.
% 0.19/0.28 % (579322)...printing done.
% 0.19/0.28 % (579321)...printing done.
% 0.19/0.28 % (579323)...printing done.
% 0.19/0.28 % (579325)...printing done.
% 0.19/0.28 % (579324)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (579324)------------------------------
% 0.19/0.28 % (579324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (579324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (579324)CaDiCaL version: 2.1.3
% 0.19/0.28 % (579324)Termination reason: Refutation
% 0.19/0.28 % (579324)Time elapsed: 0.002 s
% 0.19/0.28 % (579324)Peak memory usage: 12 MB
% 0.19/0.28 % (579324)Instructions burned: 1 (million)
% 0.19/0.28 % (579314)Success in time 0.043 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------