%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU321+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 12:52:51 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 10 unt; 2 def)
% Number of atoms : 148 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 161 ( 66 ~; 60 |; 17 &)
% ( 4 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 34 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f34,axiom,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).
fof(f40,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f42,axiom,
! [X0] :
( X0 != empty_set
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f43,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,subset_complement(X0,X2))
& in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f80,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f81,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f80]) ).
fof(f88,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,subset_complement(the_carrier(X0),X1))
<~> ~ in(X2,X1) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f89,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,subset_complement(the_carrier(X0),X1))
<~> ~ in(X2,X1) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& one_sorted_str(X0) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(ennf_transformation,[],[f42]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ in(X1,subset_complement(X0,X2))
| ~ in(X1,X2)
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ in(X1,subset_complement(X0,X2))
| ~ in(X1,X2)
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f92]) ).
fof(f137,plain,
! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f143,plain,
empty(empty_set),
inference(cnf_transformation,[],[f34]) ).
fof(f149,plain,
( ~ in(sK7,sK6)
| in(sK7,subset_complement(the_carrier(sK5),sK6)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f150,plain,
( in(sK7,sK6)
| ~ in(sK7,subset_complement(the_carrier(sK5),sK6)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f151,plain,
element(sK7,the_carrier(sK5)),
inference(cnf_transformation,[],[f89]) ).
fof(f152,plain,
element(sK6,powerset(the_carrier(sK5))),
inference(cnf_transformation,[],[f89]) ).
fof(f153,plain,
one_sorted_str(sK5),
inference(cnf_transformation,[],[f89]) ).
fof(f154,plain,
~ empty_carrier(sK5),
inference(cnf_transformation,[],[f89]) ).
fof(f155,plain,
! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| ~ element(X1,powerset(X0))
| ~ element(X2,X0)
| in(X2,X1)
| empty_set = X0 ),
inference(cnf_transformation,[],[f91]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ in(X1,subset_complement(X0,X2))
| ~ in(X1,X2)
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f158,definition,
( spl8_1
<=> in(sK7,subset_complement(the_carrier(sK5),sK6)) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f159,plain,
( ~ in(sK7,subset_complement(the_carrier(sK5),sK6))
| spl8_1 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f160,plain,
( in(sK7,subset_complement(the_carrier(sK5),sK6))
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f162,definition,
( spl8_2
<=> in(sK7,sK6) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f163,plain,
( in(sK7,sK6)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f164,plain,
( ~ in(sK7,sK6)
| spl8_2 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,plain,
( spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f149,f162,f158]) ).
fof(f166,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f150,f162,f158]) ).
fof(f175,plain,
( ~ one_sorted_str(sK5)
| ~ empty(the_carrier(sK5)) ),
inference(resolution,[],[f137,f154]) ).
fof(f178,plain,
~ empty(the_carrier(sK5)),
inference(forward_subsumption_resolution,[],[f175,f153]) ).
fof(f228,plain,
( ~ element(sK6,powerset(the_carrier(sK5)))
| ~ element(sK7,the_carrier(sK5))
| in(sK7,sK6)
| empty_set = the_carrier(sK5)
| spl8_1 ),
inference(resolution,[],[f155,f159]) ).
fof(f230,plain,
( ~ element(sK7,the_carrier(sK5))
| in(sK7,sK6)
| empty_set = the_carrier(sK5)
| spl8_1 ),
inference(forward_subsumption_resolution,[],[f228,f152]) ).
fof(f231,plain,
( in(sK7,sK6)
| empty_set = the_carrier(sK5)
| spl8_1 ),
inference(forward_subsumption_resolution,[],[f230,f151]) ).
fof(f232,plain,
( empty_set = the_carrier(sK5)
| spl8_1
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f231,f164]) ).
fof(f236,plain,
( ~ empty(empty_set)
| spl8_1
| spl8_2 ),
inference(superposition,[],[f178,f232]) ).
fof(f243,plain,
( $false
| spl8_1
| spl8_2 ),
inference(forward_subsumption_resolution,[],[f236,f143]) ).
fof(f244,plain,
( spl8_1
| spl8_2 ),
inference(avatar_contradiction_clause,[],[f243]) ).
fof(f249,plain,
( ~ in(sK7,sK6)
| ~ element(sK6,powerset(the_carrier(sK5)))
| ~ spl8_1 ),
inference(resolution,[],[f160,f156]) ).
fof(f252,plain,
( ~ element(sK6,powerset(the_carrier(sK5)))
| ~ spl8_1
| ~ spl8_2 ),
inference(forward_subsumption_resolution,[],[f249,f163]) ).
fof(f253,plain,
( $false
| ~ spl8_1
| ~ spl8_2 ),
inference(forward_subsumption_resolution,[],[f252,f152]) ).
fof(f254,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_contradiction_clause,[],[f253]) ).
cnf(s1,plain,
( spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f165]) ).
cnf(s2,plain,
( ~ spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f166]) ).
cnf(s4,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f244]) ).
cnf(s5,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f254]) ).
cnf(s6,plain,
spl8_1,
inference(rat,[],[s1,s4]) ).
cnf(s7,plain,
~ spl8_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7,s6]) ).
fof(f255,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU321+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 04:47:18 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.11/0.45 % (24173)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (24180)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4102317788:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (24179)% WARNING: option uhcvi not known.
% 0.11/0.45 % (24178)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2063413617_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % (24183)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1692662125:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (24181)dis+10_1_sil=32000:sp=arity:random_seed=3890103445:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (24182)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2849241131:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (24184)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3031201406:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.45 % (24179)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1925320293:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45 % TRYING [1]
% 0.11/0.45 % TRYING [2]
% 0.11/0.45 % TRYING [3]
% 0.11/0.45 % (24182) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-24173-24182"...
% 0.11/0.45 % TRYING [4]
% 0.11/0.45 % (24181) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-24173-24181"...
% 0.11/0.45 % (24182)...printing done.
% 0.11/0.45 % (24183) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-24173-24183"...
% 0.11/0.45 % (24179) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-24173-24179"...
% 0.11/0.45 % (24182)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (24182)------------------------------
% 0.11/0.45 % (24182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (24182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (24182)CaDiCaL version: 2.1.3
% 0.11/0.45 % (24182)Termination reason: Refutation
% 0.11/0.45 % (24182)Time elapsed: 0.005 s
% 0.11/0.45 % (24182)Peak memory usage: 12 MB
% 0.11/0.45 % (24182)Instructions burned: 6 (million)
% 0.11/0.45 % (24173)Success in time 0.042 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------