%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU317+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:48:19 PM UTC 2026
% Result : Theorem 2.65s 1.27s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 12 unt; 3 def)
% Number of atoms : 199 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 244 ( 102 ~; 99 |; 24 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 83 ( 0 sgn 77 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f36,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f37,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( in(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( closed_subset(X3,X0)
& subset(X1,X3) )
=> in(X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_pre_topc) ).
fof(f38,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(X1,topstr_closure(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_pre_topc) ).
fof(f39,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(X1,topstr_closure(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f74,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( in(X2,X3)
| ~ closed_subset(X3,X0)
| ~ subset(X1,X3)
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ in(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( in(X2,X3)
| ~ closed_subset(X3,X0)
| ~ subset(X1,X3)
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ in(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
? [X0] :
( ? [X1] :
( ~ subset(X1,topstr_closure(X0,X1))
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f90,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f74]) ).
fof(f91,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f91]) ).
fof(f98,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,topstr_closure(X0,X1))
| ? [X3] :
( ~ in(X2,X3)
& closed_subset(X3,X0)
& subset(X1,X3)
& element(X3,powerset(the_carrier(X0))) ) )
& ( ! [X3] :
( in(X2,X3)
| ~ closed_subset(X3,X0)
| ~ subset(X1,X3)
| ~ element(X3,powerset(the_carrier(X0))) )
| ~ in(X2,topstr_closure(X0,X1)) ) )
| ~ in(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f82]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,topstr_closure(X0,X1))
| ? [X3] :
( ~ in(X2,X3)
& closed_subset(X3,X0)
& subset(X1,X3)
& element(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( in(X2,X4)
| ~ closed_subset(X4,X0)
| ~ subset(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X2,topstr_closure(X0,X1)) ) )
| ~ in(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,topstr_closure(X0,X1))
| ( ~ in(X2,sK6(X0,X1,X2))
& closed_subset(sK6(X0,X1,X2),X0)
& subset(X1,sK6(X0,X1,X2))
& element(sK6(X0,X1,X2),powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( in(X2,X4)
| ~ closed_subset(X4,X0)
| ~ subset(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X2,topstr_closure(X0,X1)) ) )
| ~ in(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X3,sK6(X0,X1,X2))],[f100]) ).
fof(f102,plain,
( ~ subset(sK8,topstr_closure(sK7,sK8))
& element(sK8,powerset(the_carrier(sK7)))
& top_str(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f83]) ).
fof(f128,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f129,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f130,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f154,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f98]) ).
fof(f158,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| subset(X1,sK6(X0,X1,X2))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ in(X2,sK6(X0,X1,X2))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f161,plain,
top_str(sK7),
inference(cnf_transformation,[],[f102]) ).
fof(f162,plain,
element(sK8,powerset(the_carrier(sK7))),
inference(cnf_transformation,[],[f102]) ).
fof(f163,plain,
~ subset(sK8,topstr_closure(sK7,sK8)),
inference(cnf_transformation,[],[f102]) ).
fof(f234,plain,
in(sK0(sK8,topstr_closure(sK7,sK8)),sK8),
inference(resolution,[],[f129,f163]) ).
fof(f239,plain,
~ in(sK0(sK8,topstr_closure(sK7,sK8)),topstr_closure(sK7,sK8)),
inference(resolution,[],[f130,f163]) ).
fof(f248,plain,
! [X2,X0,X1] :
( in(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(resolution,[],[f128,f154]) ).
fof(f256,plain,
! [X0,X1] :
( subset(X0,sK6(sK7,X0,X1))
| ~ in(X1,the_carrier(sK7))
| ~ element(X0,powerset(the_carrier(sK7)))
| in(X1,topstr_closure(sK7,X0)) ),
inference(resolution,[],[f158,f161]) ).
fof(f258,plain,
! [X2,X0,X1] :
( in(X2,sK6(sK7,X1,X0))
| ~ element(X1,powerset(the_carrier(sK7)))
| in(X0,topstr_closure(sK7,X1))
| ~ in(X2,X1)
| ~ in(X0,the_carrier(sK7)) ),
inference(resolution,[],[f256,f128]) ).
fof(f270,definition,
( spl10_2
<=> in(sK0(sK8,topstr_closure(sK7,sK8)),the_carrier(sK7)) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f271,plain,
( ~ in(sK0(sK8,topstr_closure(sK7,sK8)),the_carrier(sK7))
| spl10_2 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f273,definition,
( spl10_3
<=> element(sK8,powerset(the_carrier(sK7))) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f274,plain,
( ~ element(sK8,powerset(the_carrier(sK7)))
| spl10_3 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f276,plain,
! [X0,X1] :
( ~ in(X0,sK6(sK7,X1,X0))
| ~ in(X0,the_carrier(sK7))
| ~ element(X1,powerset(the_carrier(sK7)))
| in(X0,topstr_closure(sK7,X1)) ),
inference(resolution,[],[f160,f161]) ).
fof(f323,plain,
! [X0,X1] :
( ~ element(X0,powerset(the_carrier(sK7)))
| in(X1,topstr_closure(sK7,X0))
| ~ in(X1,X0)
| ~ in(X1,the_carrier(sK7))
| ~ in(X1,the_carrier(sK7))
| ~ element(X0,powerset(the_carrier(sK7)))
| in(X1,topstr_closure(sK7,X0)) ),
inference(resolution,[],[f258,f276]) ).
fof(f333,plain,
! [X0,X1] :
( in(X1,topstr_closure(sK7,X0))
| ~ element(X0,powerset(the_carrier(sK7)))
| ~ in(X1,X0)
| ~ in(X1,the_carrier(sK7)) ),
inference(duplicate_literal_removal,[],[f323]) ).
fof(f343,plain,
( ~ element(sK8,powerset(the_carrier(sK7)))
| ~ in(sK0(sK8,topstr_closure(sK7,sK8)),sK8)
| ~ in(sK0(sK8,topstr_closure(sK7,sK8)),the_carrier(sK7)) ),
inference(resolution,[],[f333,f239]) ).
fof(f548,plain,
( ! [X0] :
( ~ in(sK0(sK8,topstr_closure(sK7,sK8)),X0)
| ~ element(X0,powerset(the_carrier(sK7))) )
| spl10_2 ),
inference(resolution,[],[f248,f271]) ).
fof(f576,plain,
( ~ element(sK8,powerset(the_carrier(sK7)))
| spl10_2 ),
inference(resolution,[],[f548,f234]) ).
fof(f590,plain,
( ~ spl10_3
| spl10_2 ),
inference(avatar_split_clause,[],[f576,f270,f273]) ).
fof(f591,plain,
( $false
| spl10_3 ),
inference(resolution,[],[f274,f162]) ).
fof(f592,plain,
spl10_3,
inference(avatar_contradiction_clause,[],[f591]) ).
fof(f645,definition,
( spl10_33
<=> in(sK0(sK8,topstr_closure(sK7,sK8)),sK8) ),
introduced(definition,[new_symbols(definition,[spl10_33])],[avatar_definition]) ).
fof(f646,plain,
( ~ in(sK0(sK8,topstr_closure(sK7,sK8)),sK8)
| spl10_33 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f667,plain,
( ~ spl10_2
| ~ spl10_33
| ~ spl10_3 ),
inference(avatar_split_clause,[],[f343,f273,f645,f270]) ).
fof(f674,plain,
( $false
| spl10_33 ),
inference(resolution,[],[f646,f234]) ).
fof(f678,plain,
spl10_33,
inference(avatar_contradiction_clause,[],[f674]) ).
cnf(s15,plain,
( spl10_2
| ~ spl10_3 ),
inference(sat_conversion,[],[f590]) ).
cnf(s16,plain,
spl10_3,
inference(sat_conversion,[],[f592]) ).
cnf(s33,plain,
( ~ spl10_2
| ~ spl10_3
| ~ spl10_33 ),
inference(sat_conversion,[],[f667]) ).
cnf(s35,plain,
spl10_33,
inference(sat_conversion,[],[f678]) ).
cnf(s38,plain,
( ~ spl10_2
| ~ spl10_3 ),
inference(rat,[],[s33,s35]) ).
cnf(s40,plain,
~ spl10_2,
inference(rat,[],[s38,s16]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s15,s16,s40]) ).
fof(f687,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU317+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 04:39:37 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.65/1.27 % (805469)Detected formulas, will run a generic FOF schedule.
% 2.65/1.27 % (805477)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=653118918:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.27 % (805477)Refutation not found, incomplete strategy
% 2.65/1.27 % (805477)------------------------------
% 2.65/1.27 % (805477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.27 % (805477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.27 % (805477)CaDiCaL version: 2.1.3
% 2.65/1.27 % (805477)Termination reason: Refutation not found, incomplete strategy
% 2.65/1.27 % (805477)Time elapsed: 0.001 s
% 2.65/1.27 % (805477)Peak memory usage: 88 MB
% 2.65/1.27 % (805476)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=176655034:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.27 % (805479)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=439854224:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.27 % (805475)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=905984193:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.27 % (805480)dis-21_1_sil=8000:lcm=predicate:random_seed=1136122625:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.65/1.27 % (805478)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=487969376:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.27 % (805474)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=220200841:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.27 % (805480)First to succeed.
% 2.65/1.27 % (805480)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-805469"
% 2.65/1.27 % (805478)Instruction limit reached!
% 2.65/1.27 % (805478)------------------------------
% 2.65/1.27 % (805478)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.27 % (805478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.27 % (805478)CaDiCaL version: 2.1.3
% 2.65/1.27 % (805478)Termination reason: Instruction limit
% 2.65/1.27 % (805478)Termination phase: Saturation
% 2.65/1.27 % (805478)Time elapsed: 0.070 s
% 2.65/1.27 % (805478)Peak memory usage: 88 MB
% 2.65/1.27 % (805478)Instructions burned: 119 (million)
% 2.65/1.27 % (805477)------------------------------
% 2.65/1.27 % (805477)------------------------------
% 2.65/1.27 % (805479)Instruction limit reached!
% 2.65/1.27 % (805479)------------------------------
% 2.65/1.27 % (805479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.27 % (805479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.27 % (805479)CaDiCaL version: 2.1.3
% 2.65/1.27 % (805479)Termination reason: Instruction limit
% 2.65/1.27 % (805479)Termination phase: Saturation
% 2.65/1.27 % (805479)Time elapsed: 0.102 s
% 2.65/1.27 % (805479)Peak memory usage: 90 MB
% 2.65/1.27 % (805479)Instructions burned: 140 (million)
% 2.65/1.27 % (805489)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1935072000:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.65/1.27 % (805489)Also succeeded, but the first one will report.
% 2.65/1.27 % (805488)lrs+10_1_sil=8000:sp=occurrence:random_seed=51756066:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.65/1.27 % (805488)Also succeeded, but the first one will report.
% 2.65/1.27 % (805490)lrs+1011_1_sil=32000:sp=occurrence:random_seed=348749212:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.65/1.27 % (805480)Refutation found. Thanks to Tanya!
% 2.65/1.27 % SZS status Theorem for theBenchmark
% 2.65/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.36 % (805480)------------------------------
% 3.53/1.36 % (805480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.36 % (805480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.36 % (805480)CaDiCaL version: 2.1.3
% 3.53/1.36 % (805480)Termination reason: Refutation
% 3.53/1.36 % (805480)Time elapsed: 0.012 s
% 3.53/1.36 % (805480)Peak memory usage: 89 MB
% 3.53/1.36 % (805480)Instructions burned: 16 (million)
% 3.53/1.36 % (805480)------------------------------
% 3.53/1.36 % (805480)------------------------------
% 3.53/1.36 % (805469)Success in time 0.432 s
% 3.53/1.36 % Vampire exiting
%------------------------------------------------------------------------------