%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN082+1 : TPTP v9.3.1. Released v2.0.0.
% 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 01:49:37 PM UTC 2026
% Result : Theorem 2.47s 1.12s
% Output : Refutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 5 unt; 5 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 137 ( 58 ~; 57 |; 12 &)
% ( 7 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 30 ( 0 sgn 20 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( big_f(X0,f(X0))
<=> ? [X1] :
( ! [X2] :
( big_f(X2,X1)
=> big_f(X2,f(X0)) )
& big_f(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel60) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( big_f(X0,f(X0))
<=> ? [X1] :
( ! [X2] :
( big_f(X2,X1)
=> big_f(X2,f(X0)) )
& big_f(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0] :
( big_f(X0,f(X0))
<~> ? [X1] :
( ! [X2] :
( big_f(X2,f(X0))
| ~ big_f(X2,X1) )
& big_f(X0,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0] :
( ( ! [X1] :
( ? [X2] :
( ~ big_f(X2,f(X0))
& big_f(X2,X1) )
| ~ big_f(X0,X1) )
| ~ big_f(X0,f(X0)) )
& ( ? [X1] :
( ! [X2] :
( big_f(X2,f(X0))
| ~ big_f(X2,X1) )
& big_f(X0,X1) )
| big_f(X0,f(X0)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
? [X0] :
( ( ! [X1] :
( ? [X2] :
( ~ big_f(X2,f(X0))
& big_f(X2,X1) )
| ~ big_f(X0,X1) )
| ~ big_f(X0,f(X0)) )
& ( ? [X3] :
( ! [X4] :
( big_f(X4,f(X0))
| ~ big_f(X4,X3) )
& big_f(X0,X3) )
| big_f(X0,f(X0)) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ( ! [X1] :
( ( ~ big_f(sK1(X1),f(sK0))
& big_f(sK1(X1),X1) )
| ~ big_f(sK0,X1) )
| ~ big_f(sK0,f(sK0)) )
& ( ( ! [X4] :
( big_f(X4,f(sK0))
| ~ big_f(X4,sK2) )
& big_f(sK0,sK2) )
| big_f(sK0,f(sK0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X2,sK1(X1)),skolemize(X3,sK2)],[f5]) ).
fof(f7,plain,
( big_f(sK0,sK2)
| big_f(sK0,f(sK0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
! [X4] :
( big_f(X4,f(sK0))
| ~ big_f(X4,sK2)
| big_f(sK0,f(sK0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
! [X1] :
( big_f(sK1(X1),X1)
| ~ big_f(sK0,X1)
| ~ big_f(sK0,f(sK0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X1] :
( ~ big_f(sK1(X1),f(sK0))
| ~ big_f(sK0,X1)
| ~ big_f(sK0,f(sK0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f12,definition,
( spl3_1
<=> big_f(sK0,f(sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f15,definition,
( spl3_2
<=> big_f(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f16,plain,
( big_f(sK0,sK2)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f17,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f7,f15,f12]) ).
fof(f19,definition,
( spl3_3
<=> ! [X4] :
( big_f(X4,f(sK0))
| ~ big_f(X4,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f20,plain,
( ! [X4] :
( big_f(X4,f(sK0))
| ~ big_f(X4,sK2) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f21,plain,
( spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f8,f19,f12]) ).
fof(f22,plain,
( ~ big_f(sK0,f(sK0))
| spl3_1 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f24,definition,
( spl3_4
<=> ! [X1] :
( big_f(sK1(X1),X1)
| ~ big_f(sK0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f25,plain,
( ! [X1] :
( big_f(sK1(X1),X1)
| ~ big_f(sK0,X1) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f26,plain,
( ~ spl3_1
| spl3_4 ),
inference(avatar_split_clause,[],[f9,f24,f12]) ).
fof(f28,definition,
( spl3_5
<=> ! [X1] :
( ~ big_f(sK1(X1),f(sK0))
| ~ big_f(sK0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f29,plain,
( ! [X1] :
( ~ big_f(sK1(X1),f(sK0))
| ~ big_f(sK0,X1) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f30,plain,
( ~ spl3_1
| spl3_5 ),
inference(avatar_split_clause,[],[f10,f28,f12]) ).
fof(f31,plain,
( ~ big_f(sK0,sK2)
| spl3_1
| ~ spl3_3 ),
inference(resolution,[],[f20,f22]) ).
fof(f32,plain,
( $false
| spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(resolution,[],[f31,f16]) ).
fof(f33,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f32]) ).
fof(f34,plain,
( ~ big_f(sK0,f(sK0))
| ~ big_f(sK0,f(sK0))
| ~ spl3_4
| ~ spl3_5 ),
inference(resolution,[],[f29,f25]) ).
fof(f36,plain,
( ~ big_f(sK0,f(sK0))
| ~ spl3_4
| ~ spl3_5 ),
inference(duplicate_literal_removal,[],[f34]) ).
fof(f37,plain,
( ~ spl3_1
| ~ spl3_4
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f36,f28,f24,f12]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f17]) ).
cnf(s2,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f21]) ).
cnf(s3,plain,
( ~ spl3_1
| spl3_4 ),
inference(sat_conversion,[],[f26]) ).
cnf(s4,plain,
( ~ spl3_1
| spl3_5 ),
inference(sat_conversion,[],[f30]) ).
cnf(s5,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f33]) ).
cnf(s6,plain,
( ~ spl3_1
| ~ spl3_4
| ~ spl3_5 ),
inference(sat_conversion,[],[f37]) ).
cnf(s7,plain,
spl3_1,
inference(rat,[],[s5,s1,s2]) ).
cnf(s8,plain,
spl3_5,
inference(rat,[],[s4,s7]) ).
cnf(s9,plain,
spl3_4,
inference(rat,[],[s3,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s8,s7,s9]) ).
fof(f38,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN082+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n015.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:35:47 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.47/1.12 % (2718100)Detected formulas, will run a generic FOF schedule.
% 2.47/1.12 % (2718191)dis-21_1_sil=8000:lcm=predicate:random_seed=2395550636: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)
% 2.47/1.12 % (2718191)First to succeed.
% 2.47/1.12 % (2718191)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2718100"
% 2.47/1.12 % (2718183)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=3335091932:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 2.47/1.12 % (2718186)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=3765587853:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 2.47/1.12 % (2718184)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=953881644:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 2.47/1.12 % (2718190)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=216321387:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 2.47/1.12 % (2718189)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4129803104:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 2.47/1.12 % (2718187)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1921847191:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 2.47/1.12 % (2718189)Also succeeded, but the first one will report.
% 2.47/1.12 % (2718187)Also succeeded, but the first one will report.
% 2.47/1.12 % (2718190)Also succeeded, but the first one will report.
% 2.47/1.12 % (2718191)Refutation found. Thanks to Tanya!
% 2.47/1.12 % SZS status Theorem for theBenchmark
% 2.47/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.47/1.12 % (2718191)------------------------------
% 2.47/1.12 % (2718191)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.12 % (2718191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.12 % (2718191)CaDiCaL version: 2.1.3
% 2.47/1.12 % (2718191)Termination reason: Refutation
% 2.47/1.12 % (2718191)Time elapsed: 0.001 s
% 2.47/1.12 % (2718191)Peak memory usage: 89 MB
% 2.47/1.12 % (2718191)Instructions burned: 1 (million)
% 2.47/1.12 % (2718191)------------------------------
% 2.47/1.12 % (2718191)------------------------------
% 2.47/1.12 % (2718100)Success in time 0.27 s
% 2.47/1.12 % Vampire exiting
%------------------------------------------------------------------------------