%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO017_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 02:24:43 PM UTC 2026
% Result : Theorem 2.14s 0.76s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 8 unt; 0 typ; 5 def)
% Number of atoms : 213 ( 18 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 141 ( 60 ~; 69 |; 4 &)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 82 ( 78 fml; 4 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 2 ( 0 sgn 2 !; 0 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_2,type,
bG0: $o ).
tff(pred_def_1,type,
h: $o > $o ).
tff(f1,conjecture,
h(h($true) = h($false)) = h($false),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
h(h($true) = h($false)) != h($false),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,definition,
( ( h($true)
<=> h($false) )
<=> ( $true = bG0 ) ),
introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition]) ).
tff(f4,plain,
~ ( h(bG0)
<=> h($false) ),
inference(fool_elimination,[],[f2,f3]) ).
tff(f5,plain,
( h(bG0)
<~> h($false) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
( ( ( ( h($true)
| ~ h($false) )
& ( h($false)
| ~ h($true) ) )
| ( $true != bG0 ) )
& ( ( $true = bG0 )
| ( ( ~ h($false)
| ~ h($true) )
& ( h($false)
| h($true) ) ) ) ),
inference(nnf_transformation,[],[f3]) ).
tff(f7,plain,
( ( ~ h($false)
| ~ h(bG0) )
& ( h($false)
| h(bG0) ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f10,plain,
( h($false)
| ~ h($true)
| ( $true != bG0 ) ),
inference(cnf_transformation,[],[f6]) ).
tff(f11,plain,
( h($true)
| ~ h($false)
| ( $true != bG0 ) ),
inference(cnf_transformation,[],[f6]) ).
tff(f12,plain,
( h($false)
| h(bG0) ),
inference(cnf_transformation,[],[f7]) ).
tff(f13,plain,
( ~ h($false)
| ~ h(bG0) ),
inference(cnf_transformation,[],[f7]) ).
tff(f15,plain,
! [X0: $o] :
( ( $false = (X0) )
| ( $true = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f17,definition,
( spl1_1
<=> h(bG0) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f18,plain,
( ~ h(bG0)
| spl1_1 ),
inference(avatar_component_clause,[],[f17]) ).
tff(f19,plain,
( h(bG0)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f17]) ).
tff(f21,definition,
( spl1_2
<=> h($false) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f22,plain,
( ~ h($false)
| spl1_2 ),
inference(avatar_component_clause,[],[f21]) ).
tff(f23,plain,
( h($false)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f21]) ).
tff(f24,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f12,f21,f17]) ).
tff(f25,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f13,f21,f17]) ).
tff(f27,definition,
( spl1_3
<=> h($true) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
tff(f28,plain,
( ~ h($true)
| spl1_3 ),
inference(avatar_component_clause,[],[f27]) ).
tff(f31,definition,
( spl1_4
<=> ( $true = bG0 ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
tff(f32,plain,
( ( $true != bG0 )
| spl1_4 ),
inference(avatar_component_clause,[],[f31]) ).
tff(f33,plain,
( ( $true = bG0 )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f31]) ).
tff(f36,plain,
( ~ spl1_4
| ~ spl1_3
| spl1_2 ),
inference(avatar_split_clause,[],[f10,f21,f27,f31]) ).
tff(f37,plain,
( ~ spl1_4
| ~ spl1_2
| spl1_3 ),
inference(avatar_split_clause,[],[f11,f27,f21,f31]) ).
tff(f41,plain,
( ~ h($false)
| ( $true = bG0 )
| spl1_1 ),
inference(superposition,[],[f18,f15]) ).
tff(f43,plain,
( ( $true = bG0 )
| spl1_1
| ~ spl1_2 ),
inference(forward_subsumption_resolution,[],[f41,f23]) ).
tff(f44,plain,
( $false
| spl1_1
| ~ spl1_2
| spl1_4 ),
inference(forward_subsumption_resolution,[],[f43,f32]) ).
tff(f45,plain,
( spl1_1
| ~ spl1_2
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f44]) ).
tff(f48,plain,
( ! [X0: $o] :
( ~ h((X0))
| ( $true = (X0) ) )
| spl1_2 ),
inference(superposition,[],[f22,f15]) ).
tff(f49,plain,
( ( $true = bG0 )
| ~ spl1_1
| spl1_2 ),
inference(resolution,[],[f48,f19]) ).
tff(f50,plain,
( spl1_4
| ~ spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f49,f21,f17,f31]) ).
tff(f52,plain,
( h($true)
| ~ spl1_1
| ~ spl1_4 ),
inference(superposition,[],[f19,f33]) ).
tff(f54,plain,
( $false
| ~ spl1_1
| spl1_3
| ~ spl1_4 ),
inference(forward_subsumption_resolution,[],[f52,f28]) ).
tff(f55,plain,
( ~ spl1_1
| spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f54]) ).
tff(f56,plain,
( ~ h($true)
| spl1_1
| ~ spl1_4 ),
inference(forward_demodulation,[],[f18,f33]) ).
tff(f57,plain,
( ~ spl1_3
| spl1_1
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f56,f31,f17,f27]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f24]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s5,plain,
( spl1_2
| ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f36]) ).
cnf(s6,plain,
( ~ spl1_2
| spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f37]) ).
cnf(s7,plain,
( spl1_1
| ~ spl1_2
| spl1_4 ),
inference(sat_conversion,[],[f45]) ).
cnf(s9,plain,
( ~ spl1_1
| spl1_2
| spl1_4 ),
inference(sat_conversion,[],[f50]) ).
cnf(s10,plain,
( ~ spl1_1
| spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f55]) ).
cnf(s11,plain,
( spl1_1
| ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f57]) ).
cnf(s12,plain,
( ~ spl1_2
| spl1_1 ),
inference(rat,[],[s11,s6,s7]) ).
cnf(s13,plain,
spl1_1,
inference(rat,[],[s12,s1]) ).
cnf(s14,plain,
~ spl1_2,
inference(rat,[],[s2,s13]) ).
cnf(s15,plain,
spl1_4,
inference(rat,[],[s9,s13,s14]) ).
cnf(s16,plain,
~ spl1_3,
inference(rat,[],[s5,s15,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s10,s13,s16,s15]) ).
tff(f58,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO017_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n011.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 17:21:16 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 2.14/0.76 % (3545398)Detected formulas, will run a generic FOF schedule.
% 2.14/0.76 % (3545436)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2149124837:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 2.14/0.76 % (3545436)First to succeed.
% 2.14/0.76 % (3545436)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3545398"
% 2.14/0.76 % (3545432)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1171043502:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 2.14/0.76 % (3545435)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2893075519:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 2.14/0.76 % (3545434)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3231664759:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 2.14/0.76 % (3545437)dis-21_1_sil=8000:lcm=predicate:random_seed=2866822535:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 2.14/0.76 % (3545431)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=309616322:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 2.14/0.76 % (3545433)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=322986220:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 2.14/0.76 % (3545435)Refutation not found, incomplete strategy
% 2.14/0.76 % (3545435)------------------------------
% 2.14/0.76 % (3545435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.14/0.76 % (3545435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.76 % (3545434)Refutation not found, incomplete strategy
% 2.14/0.76 % (3545434)------------------------------
% 2.14/0.76 % (3545434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.14/0.76 % (3545435)CaDiCaL version: 2.1.3
% 2.14/0.76 % (3545434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.76 % (3545435)Termination reason: Refutation not found, incomplete strategy
% 2.14/0.76 % (3545435)Time elapsed: 0.001 s
% 2.14/0.76 % (3545435)Peak memory usage: 88 MB
% 2.14/0.76 % (3545434)CaDiCaL version: 2.1.3
% 2.14/0.76 % (3545434)Termination reason: Refutation not found, incomplete strategy
% 2.14/0.76 % (3545434)Time elapsed: 0.001 s
% 2.14/0.76 % (3545434)Peak memory usage: 88 MB
% 2.14/0.76 % (3545437)Refutation not found, incomplete strategy
% 2.14/0.76 % (3545437)------------------------------
% 2.14/0.76 % (3545437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.14/0.76 % (3545437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.76 % (3545437)CaDiCaL version: 2.1.3
% 2.14/0.76 % (3545437)Termination reason: Refutation not found, incomplete strategy
% 2.14/0.76 % (3545437)Time elapsed: 0.001 s
% 2.14/0.76 % (3545437)Peak memory usage: 88 MB
% 2.14/0.76 % (3545436)Refutation found. Thanks to Tanya!
% 2.14/0.76 % SZS status Theorem for theBenchmark
% 2.14/0.76 % SZS output start Proof for theBenchmark
% See solution above
% 2.14/0.76 % (3545436)------------------------------
% 2.14/0.76 % (3545436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.14/0.76 % (3545436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.76 % (3545436)CaDiCaL version: 2.1.3
% 2.14/0.76 % (3545436)Termination reason: Refutation
% 2.14/0.76 % (3545436)Time elapsed: 0.002 s
% 2.14/0.76 % (3545436)Peak memory usage: 90 MB
% 2.14/0.76 % (3545436)Instructions burned: 2 (million)
% 2.14/0.76 % (3545436)------------------------------
% 2.14/0.76 % (3545436)------------------------------
% 2.14/0.76 % (3545398)Success in time 0.264 s
% 2.14/0.76 % Vampire exiting
%------------------------------------------------------------------------------