%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET887+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 12:44:55 PM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 15 unt; 4 def)
% Number of atoms : 122 ( 62 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 124 ( 56 ~; 49 |; 9 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 54 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f6,axiom,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( X0 != empty_set
& X0 != singleton(X1)
& X0 != singleton(X2)
& X0 != unordered_pair(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1,X2,X3] :
~ ( subset(unordered_pair(X0,X1),unordered_pair(X2,X3))
& X0 != X2
& X0 != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( subset(unordered_pair(X0,X1),unordered_pair(X2,X3))
& X0 != X2
& X0 != X3 ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f16,plain,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0 ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f18,plain,
? [X0,X1,X2,X3] :
( subset(unordered_pair(X0,X1),unordered_pair(X2,X3))
& X0 != X2
& X0 != X3 ),
inference(ennf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1,X2] :
( X0 = X1
| unordered_pair(X1,X2) != singleton(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f23,plain,
! [X0,X1] :
( ~ in(X1,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f3]) ).
fof(f27,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| X0 = X3
| ~ in(X3,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f29,plain,
! [X2,X3,X0,X1] :
( X0 != X3
| in(X3,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ subset(X0,unordered_pair(X1,X2))
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| unordered_pair(X1,X2) = X0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
sK4 != sK7,
inference(cnf_transformation,[],[f18]) ).
fof(f41,plain,
sK4 != sK6,
inference(cnf_transformation,[],[f18]) ).
fof(f42,plain,
subset(unordered_pair(sK4,sK5),unordered_pair(sK6,sK7)),
inference(cnf_transformation,[],[f18]) ).
fof(f43,plain,
! [X2,X0,X1] :
( unordered_pair(X1,X2) != singleton(X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X1] : ~ in(X1,empty_set),
inference(equality_resolution,[],[f23]) ).
fof(f45,plain,
! [X2,X3,X1] :
( in(X3,X2)
| unordered_pair(X3,X1) != X2 ),
inference(equality_resolution,[],[f29]) ).
fof(f46,plain,
! [X3,X1] : in(X3,unordered_pair(X3,X1)),
inference(equality_resolution,[],[f45]) ).
fof(f49,plain,
! [X3,X0,X1] :
( ~ in(X3,unordered_pair(X0,X1))
| X0 = X3
| X1 = X3 ),
inference(equality_resolution,[],[f27]) ).
fof(f86,plain,
( unordered_pair(sK4,sK5) = singleton(sK7)
| unordered_pair(sK4,sK5) = singleton(sK6)
| empty_set = unordered_pair(sK4,sK5)
| unordered_pair(sK4,sK5) = unordered_pair(sK6,sK7) ),
inference(resolution,[],[f31,f42]) ).
fof(f93,definition,
( spl8_1
<=> unordered_pair(sK4,sK5) = unordered_pair(sK6,sK7) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f95,plain,
( unordered_pair(sK4,sK5) = unordered_pair(sK6,sK7)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f97,definition,
( spl8_2
<=> empty_set = unordered_pair(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f99,plain,
( empty_set = unordered_pair(sK4,sK5)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f101,definition,
( spl8_3
<=> unordered_pair(sK4,sK5) = singleton(sK6) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
fof(f103,plain,
( unordered_pair(sK4,sK5) = singleton(sK6)
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f105,definition,
( spl8_4
<=> unordered_pair(sK4,sK5) = singleton(sK7) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
fof(f107,plain,
( unordered_pair(sK4,sK5) = singleton(sK7)
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,plain,
( spl8_1
| spl8_2
| spl8_3
| spl8_4 ),
inference(avatar_split_clause,[],[f86,f105,f101,f97,f93]) ).
fof(f114,plain,
( in(sK4,empty_set)
| ~ spl8_2 ),
inference(superposition,[],[f46,f99]) ).
fof(f126,plain,
( $false
| ~ spl8_2 ),
inference(forward_subsumption_resolution,[],[f114,f44]) ).
fof(f127,plain,
~ spl8_2,
inference(avatar_contradiction_clause,[],[f126]) ).
fof(f141,plain,
( ! [X0] :
( singleton(X0) != singleton(sK6)
| sK4 = X0 )
| ~ spl8_3 ),
inference(superposition,[],[f43,f103]) ).
fof(f248,plain,
( sK4 = sK6
| ~ spl8_3 ),
inference(equality_resolution,[],[f141]) ).
fof(f249,plain,
( $false
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f248,f41]) ).
fof(f250,plain,
~ spl8_3,
inference(avatar_contradiction_clause,[],[f249]) ).
fof(f356,plain,
( ! [X0] :
( singleton(X0) != singleton(sK7)
| sK4 = X0 )
| ~ spl8_4 ),
inference(superposition,[],[f43,f107]) ).
fof(f376,plain,
( sK4 = sK7
| ~ spl8_4 ),
inference(equality_resolution,[],[f356]) ).
fof(f377,plain,
( $false
| ~ spl8_4 ),
inference(forward_subsumption_resolution,[],[f376,f40]) ).
fof(f378,plain,
~ spl8_4,
inference(avatar_contradiction_clause,[],[f377]) ).
fof(f389,plain,
( ! [X0] :
( ~ in(X0,unordered_pair(sK4,sK5))
| sK6 = X0
| sK7 = X0 )
| ~ spl8_1 ),
inference(superposition,[],[f49,f95]) ).
fof(f468,plain,
( sK4 = sK6
| sK4 = sK7
| ~ spl8_1 ),
inference(resolution,[],[f389,f46]) ).
fof(f477,plain,
( sK4 = sK7
| ~ spl8_1 ),
inference(forward_subsumption_resolution,[],[f468,f41]) ).
fof(f478,plain,
( $false
| ~ spl8_1 ),
inference(forward_subsumption_resolution,[],[f477,f40]) ).
fof(f479,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[],[f478]) ).
cnf(s1,plain,
( spl8_1
| spl8_2
| spl8_3
| spl8_4 ),
inference(sat_conversion,[],[f108]) ).
cnf(s3,plain,
~ spl8_2,
inference(sat_conversion,[],[f127]) ).
cnf(s6,plain,
~ spl8_3,
inference(sat_conversion,[],[f250]) ).
cnf(s17,plain,
~ spl8_4,
inference(sat_conversion,[],[f378]) ).
cnf(s20,plain,
~ spl8_1,
inference(sat_conversion,[],[f479]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s17,s6,s3,s20]) ).
fof(f480,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET887+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 % Computer : n006.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Mon Sep 28 03:06:25 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.43 Running first-order model finding
% 0.14/0.43 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
% 0.18/0.49 % (3544313)Will run a generic schedule for satisfiability detection.
% 0.18/0.49 % (3544322)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2256001700:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.49 % (3544319)% WARNING: option uhcvi not known.
% 0.18/0.49 % (3544318)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3367258021_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.49 % (3544319)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3044762217:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.49 % (3544320)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1123860211:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.49 % (3544321)dis+10_1_sil=32000:sp=arity:random_seed=1648933173:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.49 % (3544322) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3544313-3544322"...
% 0.18/0.49 % (3544323)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3652033994:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.49 % (3544324)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3199104787:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.49 % (3544322)...printing done.
% 0.18/0.49 % TRYING [1]
% 0.18/0.49 % (3544322)Refutation found. Thanks to Tanya!
% 0.18/0.49 % SZS status Theorem for theBenchmark
% 0.18/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49 % (3544322)------------------------------
% 0.18/0.49 % (3544322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.49 % (3544322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.49 % (3544322)CaDiCaL version: 2.1.3
% 0.18/0.49 % (3544322)Termination reason: Refutation
% 0.18/0.49 % (3544322)Time elapsed: 0.008 s
% 0.18/0.49 % (3544322)Peak memory usage: 12 MB
% 0.18/0.49 % (3544322)Instructions burned: 23 (million)
% 0.18/0.49 % (3544313)Success in time 0.046 s
% 0.18/0.49 % Vampire exiting
%------------------------------------------------------------------------------