%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:44:37 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 4 unt; 2 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 97 ( 35 ~; 44 |; 1 &)
% ( 13 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 44 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) )
=> ! [X0,X1] :
( equalish(X0,X1)
<=> equalish(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ( ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) )
=> ! [X0,X1] :
( equalish(X0,X1)
<=> equalish(X1,X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) )
=> ! [X3,X4] :
( equalish(X3,X4)
<=> equalish(X4,X3) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X3,X4] :
( equalish(X3,X4)
<~> equalish(X4,X3) )
& ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
! [X2,X0,X1] :
( ~ a_member_of(X2,X1)
| a_member_of(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X2,X0,X1] :
( a_member_of(X2,X1)
| ~ a_member_of(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f7,plain,
! [X0,X1] :
( a_member_of(sK2(X0,X1),X1)
| a_member_of(sK2(X0,X1),X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f8,plain,
! [X0,X1] :
( ~ a_member_of(sK2(X0,X1),X1)
| ~ a_member_of(sK2(X0,X1),X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f9,plain,
( equalish(sK1,sK0)
| equalish(sK0,sK1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f10,plain,
( ~ equalish(sK1,sK0)
| ~ equalish(sK0,sK1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f12,definition,
( spl3_1
<=> equalish(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f13,plain,
( ~ equalish(sK0,sK1)
| spl3_1 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f14,plain,
( equalish(sK0,sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f16,definition,
( spl3_2
<=> equalish(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f17,plain,
( ~ equalish(sK1,sK0)
| spl3_2 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f18,plain,
( equalish(sK1,sK0)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f19,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f9,f16,f12]) ).
fof(f20,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f10,f16,f12]) ).
fof(f34,plain,
! [X2,X0,X1] :
( a_member_of(sK2(X0,X1),X0)
| a_member_of(sK2(X0,X1),X2)
| equalish(X0,X1)
| ~ equalish(X1,X2) ),
inference(resolution,[],[f7,f6]) ).
fof(f38,plain,
! [X2,X0,X1] :
( a_member_of(sK2(X0,X1),X1)
| a_member_of(sK2(X0,X1),X2)
| equalish(X0,X1)
| ~ equalish(X2,X0) ),
inference(resolution,[],[f7,f5]) ).
fof(f149,plain,
! [X0,X1] :
( a_member_of(sK2(X0,X1),X0)
| equalish(X0,X1)
| ~ equalish(X1,X0) ),
inference(factoring,[],[f34]) ).
fof(f160,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ equalish(X1,X0)
| ~ a_member_of(sK2(X0,X1),X1)
| equalish(X0,X1) ),
inference(resolution,[],[f149,f8]) ).
fof(f161,plain,
! [X0,X1] :
( ~ a_member_of(sK2(X0,X1),X1)
| ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(duplicate_literal_removal,[],[f160]) ).
fof(f257,plain,
! [X0,X1] :
( a_member_of(sK2(X0,X1),X1)
| equalish(X0,X1)
| ~ equalish(X1,X0) ),
inference(factoring,[],[f38]) ).
fof(f262,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ equalish(X1,X0) ),
inference(forward_subsumption_resolution,[],[f257,f161]) ).
fof(f264,plain,
( equalish(sK0,sK1)
| ~ spl3_2 ),
inference(resolution,[],[f262,f18]) ).
fof(f266,plain,
( $false
| spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f264,f13]) ).
fof(f267,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f266]) ).
fof(f268,plain,
( ~ equalish(sK0,sK1)
| spl3_2 ),
inference(resolution,[],[f17,f262]) ).
fof(f269,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f268,f14]) ).
fof(f270,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f269]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f19]) ).
cnf(s2,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f20]) ).
cnf(s3,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f267]) ).
cnf(s4,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f270]) ).
cnf(s5,plain,
spl3_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl3_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f271,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 % Computer : n026.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 02:52:12 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.43 Running first-order model finding
% 0.10/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.47 % (3425669)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (3425678)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1681870861:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (3425675)% WARNING: option uhcvi not known.
% 0.16/0.47 % (3425678) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3425669-3425678"...
% 0.16/0.47 % (3425678)...printing done.
% 0.16/0.47 % (3425674)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2957485419_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (3425675)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1138654621:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (3425676)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1204792419:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (3425678)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3425678)------------------------------
% 0.16/0.47 % (3425678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3425678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3425678)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3425678)Termination reason: Refutation
% 0.16/0.47 % (3425678)Time elapsed: 0.005 s
% 0.16/0.47 % (3425678)Peak memory usage: 12 MB
% 0.16/0.47 % (3425678)Instructions burned: 15 (million)
% 0.16/0.47 % (3425669)Success in time 0.036 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------