%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM383+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 : 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 12:24:05 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 12 unt; 2 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 101 ( 48 ~; 39 |; 7 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 65 ( 0 sgn 62 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f5,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f21,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f22,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f23,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f24,axiom,
! [X0,X1,X2] :
~ ( in(X0,X1)
& element(X1,powerset(X2))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f26,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f27,conjecture,
! [X0,X1] :
~ ( in(X0,X1)
& subset(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
~ ( in(X0,X1)
& subset(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f31,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f44,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f47,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f48,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f51,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f52,plain,
? [X0,X1] :
( in(X0,X1)
& subset(X1,X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f54,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f57,plain,
! [X0] : element(sK0(X0),X0),
inference(cnf_transformation,[],[f5]) ).
fof(f83,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f84,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f86,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f88,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f89,plain,
subset(sK12,sK11),
inference(cnf_transformation,[],[f52]) ).
fof(f90,plain,
in(sK11,sK12),
inference(cnf_transformation,[],[f52]) ).
fof(f96,plain,
~ empty(sK12),
inference(resolution,[],[f88,f90]) ).
fof(f99,plain,
element(sK12,powerset(sK11)),
inference(resolution,[],[f84,f89]) ).
fof(f116,plain,
! [X0] :
( in(sK0(X0),X0)
| empty(X0) ),
inference(resolution,[],[f83,f57]) ).
fof(f132,plain,
! [X0] :
( ~ empty(sK11)
| ~ in(X0,sK12) ),
inference(resolution,[],[f86,f99]) ).
fof(f134,definition,
( spl13_3
<=> ! [X0] : ~ in(X0,sK12) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f135,plain,
( ! [X0] : ~ in(X0,sK12)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,definition,
( spl13_4
<=> empty(sK11) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f139,plain,
( ~ empty(sK11)
| spl13_4 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,plain,
( spl13_3
| ~ spl13_4 ),
inference(avatar_split_clause,[],[f132,f137,f134]) ).
fof(f144,plain,
! [X0] :
( element(X0,sK11)
| ~ in(X0,sK12) ),
inference(resolution,[],[f85,f99]) ).
fof(f152,plain,
! [X0] :
( ~ in(X0,sK12)
| in(X0,sK11)
| empty(sK11) ),
inference(resolution,[],[f144,f83]) ).
fof(f153,plain,
( ! [X0] :
( ~ in(X0,sK12)
| in(X0,sK11) )
| spl13_4 ),
inference(forward_subsumption_resolution,[],[f152,f139]) ).
fof(f157,plain,
( in(sK11,sK11)
| spl13_4 ),
inference(resolution,[],[f153,f90]) ).
fof(f161,plain,
( ~ in(sK11,sK11)
| spl13_4 ),
inference(resolution,[],[f157,f54]) ).
fof(f166,plain,
( $false
| spl13_4 ),
inference(forward_subsumption_resolution,[],[f161,f157]) ).
fof(f167,plain,
spl13_4,
inference(avatar_contradiction_clause,[],[f166]) ).
fof(f181,plain,
( empty(sK12)
| ~ spl13_3 ),
inference(resolution,[],[f135,f116]) ).
fof(f183,plain,
( $false
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f181,f96]) ).
fof(f184,plain,
~ spl13_3,
inference(avatar_contradiction_clause,[],[f183]) ).
cnf(s3,plain,
( spl13_3
| ~ spl13_4 ),
inference(sat_conversion,[],[f140]) ).
cnf(s5,plain,
spl13_4,
inference(sat_conversion,[],[f167]) ).
cnf(s7,plain,
~ spl13_3,
inference(sat_conversion,[],[f184]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s3,s5,s7]) ).
fof(f185,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM383+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 % Computer : n015.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 19:48:31 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.44 Running first-order model finding
% 0.11/0.44 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
% 0.17/0.48 % (1973130)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (1973141)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=116497377:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (1973136)% WARNING: option uhcvi not known.
% 0.17/0.48 % (1973135)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3819079753_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (1973139)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1635121299:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (1973136)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=595752870:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (1973137)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1607947546:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (1973138)dis+10_1_sil=32000:sp=arity:random_seed=3821220241:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (1973140)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1683831536:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % (1973139) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1973130-1973139"...
% 0.17/0.48 % (1973138) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1973130-1973138"...
% 0.17/0.48 % (1973136) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1973130-1973136"...
% 0.17/0.48 % (1973140) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1973130-1973140"...
% 0.17/0.48 % TRYING [5]
% 0.17/0.48 % (1973139)...printing done.
% 0.17/0.48 % (1973136)...printing done.
% 0.17/0.48 % (1973138)...printing done.
% 0.17/0.48 % (1973140)...printing done.
% 0.17/0.48 % (1973139)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (1973139)------------------------------
% 0.17/0.48 % (1973139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (1973139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (1973139)CaDiCaL version: 2.1.3
% 0.17/0.48 % (1973139)Termination reason: Refutation
% 0.17/0.48 % (1973139)Time elapsed: 0.004 s
% 0.17/0.48 % (1973139)Peak memory usage: 12 MB
% 0.17/0.48 % (1973139)Instructions burned: 4 (million)
% 0.17/0.48 % (1973130)Success in time 0.038 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------