%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN349+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 02:07:25 PM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 32 ( 7 unt; 1 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 197 ( 71 ~; 83 |; 28 &)
% ( 12 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% Number of variables : 47 ( 0 sgn 37 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] :
! [X1] :
? [X2] :
! [X3] :
( ( big_f(X0,X3)
<=> big_f(X1,X3) )
=> ( ( ( big_f(X0,X3)
<=> big_f(X3,X2) )
<=> big_f(X2,X3) )
<=> big_f(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_17_5) ).
fof(f2,negated_conjecture,
~ ? [X0] :
! [X1] :
? [X2] :
! [X3] :
( ( big_f(X0,X3)
<=> big_f(X1,X3) )
=> ( ( ( big_f(X0,X3)
<=> big_f(X3,X2) )
<=> big_f(X2,X3) )
<=> big_f(X3,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X0] :
? [X1] :
! [X2] :
? [X3] :
( ( ( ( big_f(X0,X3)
<=> big_f(X3,X2) )
<=> big_f(X2,X3) )
<~> big_f(X3,X1) )
& ( big_f(X0,X3)
<=> big_f(X1,X3) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X0] :
? [X1] :
! [X2] :
? [X3] :
( ( ~ big_f(X3,X1)
| ( ( ~ big_f(X2,X3)
| ( ( ~ big_f(X3,X2)
| ~ big_f(X0,X3) )
& ( big_f(X3,X2)
| big_f(X0,X3) ) ) )
& ( big_f(X2,X3)
| ( ( big_f(X0,X3)
| ~ big_f(X3,X2) )
& ( big_f(X3,X2)
| ~ big_f(X0,X3) ) ) ) ) )
& ( big_f(X3,X1)
| ( ( ( ( big_f(X0,X3)
| ~ big_f(X3,X2) )
& ( big_f(X3,X2)
| ~ big_f(X0,X3) ) )
| ~ big_f(X2,X3) )
& ( big_f(X2,X3)
| ( ( ~ big_f(X3,X2)
| ~ big_f(X0,X3) )
& ( big_f(X3,X2)
| big_f(X0,X3) ) ) ) ) )
& ( big_f(X0,X3)
| ~ big_f(X1,X3) )
& ( big_f(X1,X3)
| ~ big_f(X0,X3) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
! [X0] :
? [X1] :
! [X2] :
? [X3] :
( ( ~ big_f(X3,X1)
| ( ( ~ big_f(X2,X3)
| ( ( ~ big_f(X3,X2)
| ~ big_f(X0,X3) )
& ( big_f(X3,X2)
| big_f(X0,X3) ) ) )
& ( big_f(X2,X3)
| ( ( big_f(X0,X3)
| ~ big_f(X3,X2) )
& ( big_f(X3,X2)
| ~ big_f(X0,X3) ) ) ) ) )
& ( big_f(X3,X1)
| ( ( ( ( big_f(X0,X3)
| ~ big_f(X3,X2) )
& ( big_f(X3,X2)
| ~ big_f(X0,X3) ) )
| ~ big_f(X2,X3) )
& ( big_f(X2,X3)
| ( ( ~ big_f(X3,X2)
| ~ big_f(X0,X3) )
& ( big_f(X3,X2)
| big_f(X0,X3) ) ) ) ) )
& ( big_f(X0,X3)
| ~ big_f(X1,X3) )
& ( big_f(X1,X3)
| ~ big_f(X0,X3) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
! [X0,X2] :
( ( ~ big_f(sK1(X0,X2),sK0(X0))
| ( ( ~ big_f(X2,sK1(X0,X2))
| ( ( ~ big_f(sK1(X0,X2),X2)
| ~ big_f(X0,sK1(X0,X2)) )
& ( big_f(sK1(X0,X2),X2)
| big_f(X0,sK1(X0,X2)) ) ) )
& ( big_f(X2,sK1(X0,X2))
| ( ( big_f(X0,sK1(X0,X2))
| ~ big_f(sK1(X0,X2),X2) )
& ( big_f(sK1(X0,X2),X2)
| ~ big_f(X0,sK1(X0,X2)) ) ) ) ) )
& ( big_f(sK1(X0,X2),sK0(X0))
| ( ( ( ( big_f(X0,sK1(X0,X2))
| ~ big_f(sK1(X0,X2),X2) )
& ( big_f(sK1(X0,X2),X2)
| ~ big_f(X0,sK1(X0,X2)) ) )
| ~ big_f(X2,sK1(X0,X2)) )
& ( big_f(X2,sK1(X0,X2))
| ( ( ~ big_f(sK1(X0,X2),X2)
| ~ big_f(X0,sK1(X0,X2)) )
& ( big_f(sK1(X0,X2),X2)
| big_f(X0,sK1(X0,X2)) ) ) ) ) )
& ( big_f(X0,sK1(X0,X2))
| ~ big_f(sK0(X0),sK1(X0,X2)) )
& ( big_f(sK0(X0),sK1(X0,X2))
| ~ big_f(X0,sK1(X0,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(X3,sK1(X0,X2))],[f5]) ).
fof(f7,plain,
! [X2,X0] :
( big_f(sK0(X0),sK1(X0,X2))
| ~ big_f(X0,sK1(X0,X2)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
! [X2,X0] :
( ~ big_f(sK0(X0),sK1(X0,X2))
| big_f(X0,sK1(X0,X2)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
! [X2,X0] :
( big_f(sK1(X0,X2),sK0(X0))
| big_f(sK1(X0,X2),X2)
| big_f(X2,sK1(X0,X2))
| big_f(X0,sK1(X0,X2)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f11,plain,
! [X2,X0] :
( ~ big_f(X2,sK1(X0,X2))
| big_f(sK1(X0,X2),X2)
| ~ big_f(X0,sK1(X0,X2))
| big_f(sK1(X0,X2),sK0(X0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f14,plain,
! [X2,X0] :
( ~ big_f(sK1(X0,X2),sK0(X0))
| big_f(X2,sK1(X0,X2))
| big_f(X0,sK1(X0,X2))
| ~ big_f(sK1(X0,X2),X2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f16,plain,
! [X2,X0] :
( ~ big_f(sK1(X0,X2),sK0(X0))
| ~ big_f(X2,sK1(X0,X2))
| ~ big_f(sK1(X0,X2),X2)
| ~ big_f(X0,sK1(X0,X2)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f281,plain,
! [X0] :
( big_f(sK1(X0,sK0(X0)),sK0(X0))
| big_f(sK0(X0),sK1(X0,sK0(X0)))
| big_f(X0,sK1(X0,sK0(X0))) ),
inference(factoring,[],[f9]) ).
fof(f282,plain,
! [X0] :
( big_f(sK1(X0,sK0(X0)),sK0(X0))
| big_f(X0,sK1(X0,sK0(X0))) ),
inference(forward_subsumption_resolution,[],[f281,f8]) ).
fof(f284,definition,
( spl2_11
<=> ! [X0] : big_f(sK1(X0,sK0(X0)),sK0(X0)) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f285,plain,
( ! [X0] : big_f(sK1(X0,sK0(X0)),sK0(X0))
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f290,plain,
( ! [X0] :
( ~ big_f(sK0(X0),sK1(X0,sK0(X0)))
| ~ big_f(sK1(X0,sK0(X0)),sK0(X0))
| ~ big_f(X0,sK1(X0,sK0(X0))) )
| ~ spl2_11 ),
inference(resolution,[],[f285,f16]) ).
fof(f291,plain,
( ! [X0] :
( ~ big_f(sK1(X0,sK0(X0)),sK0(X0))
| ~ big_f(X0,sK1(X0,sK0(X0))) )
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f290,f7]) ).
fof(f292,plain,
( ! [X0] : ~ big_f(X0,sK1(X0,sK0(X0)))
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f291,f285]) ).
fof(f299,plain,
! [X0] :
( big_f(sK1(X0,sK0(X0)),sK0(X0))
| ~ big_f(X0,sK1(X0,sK0(X0)))
| big_f(sK1(X0,sK0(X0)),sK0(X0))
| ~ big_f(X0,sK1(X0,sK0(X0))) ),
inference(resolution,[],[f11,f7]) ).
fof(f300,plain,
! [X0] :
( big_f(sK1(X0,sK0(X0)),sK0(X0))
| ~ big_f(X0,sK1(X0,sK0(X0))) ),
inference(duplicate_literal_removal,[],[f299]) ).
fof(f311,plain,
( ! [X0] :
( big_f(sK0(X0),sK1(X0,sK0(X0)))
| big_f(X0,sK1(X0,sK0(X0)))
| ~ big_f(sK1(X0,sK0(X0)),sK0(X0)) )
| ~ spl2_11 ),
inference(resolution,[],[f14,f285]) ).
fof(f316,plain,
( ! [X0] :
( big_f(X0,sK1(X0,sK0(X0)))
| ~ big_f(sK1(X0,sK0(X0)),sK0(X0)) )
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f311,f8]) ).
fof(f318,plain,
( ! [X0] : big_f(X0,sK1(X0,sK0(X0)))
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f316,f282]) ).
fof(f321,plain,
( $false
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f318,f292]) ).
fof(f322,plain,
~ spl2_11,
inference(avatar_contradiction_clause,[],[f321]) ).
fof(f323,plain,
! [X0] : big_f(sK1(X0,sK0(X0)),sK0(X0)),
inference(forward_subsumption_resolution,[],[f300,f282]) ).
fof(f325,plain,
spl2_11,
inference(avatar_split_clause,[],[f323,f284]) ).
cnf(s310,plain,
~ spl2_11,
inference(sat_conversion,[],[f322]) ).
cnf(s318,plain,
spl2_11,
inference(sat_conversion,[],[f325]) ).
cnf(s319,plain,
$false,
inference(rat,[],[s310,s318]) ).
fof(f326,plain,
$false,
inference(avatar_sat_refutation,[],[s319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN349+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.17 % Computer : n009.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 15:47:30 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 Running first-order model finding
% 0.10/0.20 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
% 0.10/0.25 % (3177133)Will run a generic schedule for satisfiability detection.
% 0.10/0.25 % (3177140)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=337845701:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.25 % (3177140) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3177133-3177140"...
% 0.10/0.25 % (3177139)% WARNING: option uhcvi not known.
% 0.10/0.25 % (3177140)...printing done.
% 0.10/0.25 % (3177138)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=211833652_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.25 % (3177141)dis+10_1_sil=32000:sp=arity:random_seed=2987147950:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.25 % (3177142)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2481922727:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.25 % (3177140)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.25 % (3177140)------------------------------
% 0.10/0.25 % (3177140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (3177140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (3177140)CaDiCaL version: 2.1.3
% 0.10/0.25 % (3177140)Termination reason: Refutation
% 0.10/0.25 % (3177140)Time elapsed: 0.006 s
% 0.10/0.25 % (3177140)Peak memory usage: 12 MB
% 0.10/0.25 % (3177140)Instructions burned: 12 (million)
% 0.10/0.25 % (3177133)Success in time 0.035 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------