%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU309+2 : 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 : 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 12:48:16 PM UTC 2026
% Result : Theorem 0.15s 1.50s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 10 unt; 2 def)
% Number of atoms : 72 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 63 ( 28 ~; 21 |; 4 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f139,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f235,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f361,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(f380,conjecture,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_pre_topc) ).
fof(f381,negated_conjecture,
~ ! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f380]) ).
fof(f668,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f139]) ).
fof(f750,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f235]) ).
fof(f883,plain,
! [X0] :
( ! [X1] :
( subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f361]) ).
fof(f908,plain,
? [X0] :
( ? [X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) != X1
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f381]) ).
fof(f1515,plain,
( sK334 != subset_difference(the_carrier(sK333),cast_as_carrier_subset(sK333),subset_difference(the_carrier(sK333),cast_as_carrier_subset(sK333),sK334))
& element(sK334,powerset(the_carrier(sK333)))
& one_sorted_str(sK333) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK333,sK334]),skolemize(X0,sK333),skolemize(X1,sK334)],[f908]) ).
fof(f1958,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f668]) ).
fof(f2120,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f750]) ).
fof(f2629,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ),
inference(cnf_transformation,[],[f883]) ).
fof(f2654,plain,
one_sorted_str(sK333),
inference(cnf_transformation,[],[f1515]) ).
fof(f2655,plain,
element(sK334,powerset(the_carrier(sK333))),
inference(cnf_transformation,[],[f1515]) ).
fof(f2656,plain,
sK334 != subset_difference(the_carrier(sK333),cast_as_carrier_subset(sK333),subset_difference(the_carrier(sK333),cast_as_carrier_subset(sK333),sK334)),
inference(cnf_transformation,[],[f1515]) ).
fof(f3511,plain,
! [X0] :
( subset_complement(the_carrier(sK333),X0) = subset_difference(the_carrier(sK333),cast_as_carrier_subset(sK333),X0)
| ~ element(X0,powerset(the_carrier(sK333))) ),
inference(resolution,[],[f2629,f2654]) ).
fof(f3560,plain,
( sK334 != subset_difference(the_carrier(sK333),cast_as_carrier_subset(sK333),subset_complement(the_carrier(sK333),sK334))
| ~ element(sK334,powerset(the_carrier(sK333))) ),
inference(superposition,[],[f2656,f3511]) ).
fof(f3567,plain,
sK334 != subset_difference(the_carrier(sK333),cast_as_carrier_subset(sK333),subset_complement(the_carrier(sK333),sK334)),
inference(forward_subsumption_resolution,[],[f3560,f2655]) ).
fof(f3600,plain,
( sK334 != subset_complement(the_carrier(sK333),subset_complement(the_carrier(sK333),sK334))
| ~ element(subset_complement(the_carrier(sK333),sK334),powerset(the_carrier(sK333))) ),
inference(superposition,[],[f3567,f3511]) ).
fof(f3603,definition,
( spl358_68
<=> element(subset_complement(the_carrier(sK333),sK334),powerset(the_carrier(sK333))) ),
introduced(definition,[new_symbols(definition,[spl358_68])],[avatar_definition]) ).
fof(f3605,plain,
( ~ element(subset_complement(the_carrier(sK333),sK334),powerset(the_carrier(sK333)))
| spl358_68 ),
inference(avatar_component_clause,[],[f3603]) ).
fof(f3607,definition,
( spl358_69
<=> sK334 = subset_complement(the_carrier(sK333),subset_complement(the_carrier(sK333),sK334)) ),
introduced(definition,[new_symbols(definition,[spl358_69])],[avatar_definition]) ).
fof(f3609,plain,
( sK334 != subset_complement(the_carrier(sK333),subset_complement(the_carrier(sK333),sK334))
| spl358_69 ),
inference(avatar_component_clause,[],[f3607]) ).
fof(f3610,plain,
( ~ spl358_68
| ~ spl358_69 ),
inference(avatar_split_clause,[],[f3600,f3607,f3603]) ).
fof(f3613,plain,
( ~ element(sK334,powerset(the_carrier(sK333)))
| spl358_68 ),
inference(resolution,[],[f3605,f1958]) ).
fof(f3621,plain,
( $false
| spl358_68 ),
inference(forward_subsumption_resolution,[],[f3613,f2655]) ).
fof(f3622,plain,
spl358_68,
inference(avatar_contradiction_clause,[],[f3621]) ).
fof(f3627,plain,
( sK334 != sK334
| ~ element(sK334,powerset(the_carrier(sK333)))
| spl358_69 ),
inference(superposition,[],[f3609,f2120]) ).
fof(f3629,plain,
( ~ element(sK334,powerset(the_carrier(sK333)))
| spl358_69 ),
inference(trivial_inequality_removal,[],[f3627]) ).
fof(f3630,plain,
( $false
| spl358_69 ),
inference(forward_subsumption_resolution,[],[f3629,f2655]) ).
fof(f3631,plain,
spl358_69,
inference(avatar_contradiction_clause,[],[f3630]) ).
cnf(s69,plain,
( ~ spl358_68
| ~ spl358_69 ),
inference(sat_conversion,[],[f3610]) ).
cnf(s70,plain,
spl358_68,
inference(sat_conversion,[],[f3622]) ).
cnf(s72,plain,
spl358_69,
inference(sat_conversion,[],[f3631]) ).
cnf(s73,plain,
$false,
inference(rat,[],[s69,s72,s70]) ).
fof(f3632,plain,
$false,
inference(avatar_sat_refutation,[],[s73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU309+2 : 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 : n015.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 04:41:31 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.15/1.50 % (2260818)Detected formulas, will run a generic FOF schedule.
% 0.15/1.50 % (2260824)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=3856989414:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.15/1.50 % (2260829)dis-21_1_sil=8000:lcm=predicate:random_seed=569441336: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)
% 0.15/1.50 % (2260827)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3960914171:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.15/1.50 % (2260823)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=1062100:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.15/1.50 % (2260825)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=3483494269:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.15/1.50 % (2260826)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=662110313:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.15/1.50 % (2260828)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=197437536:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.15/1.50 % (2260828)First to succeed.
% 0.15/1.50 % (2260826)Instruction limit reached!
% 0.15/1.50 % (2260826)------------------------------
% 0.15/1.50 % (2260826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (2260828)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2260818"
% 0.15/1.50 % (2260826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (2260826)CaDiCaL version: 2.1.3
% 0.15/1.50 % (2260826)Termination reason: Instruction limit
% 0.15/1.50 % (2260826)Termination phase: Saturation
% 0.15/1.50 % (2260826)Time elapsed: 0.061 s
% 0.15/1.50 % (2260826)Peak memory usage: 91 MB
% 0.15/1.50 % (2260826)Instructions burned: 109 (million)
% 0.15/1.50 % (2260829)Instruction limit reached!
% 0.15/1.50 % (2260829)------------------------------
% 0.15/1.50 % (2260829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (2260829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (2260829)CaDiCaL version: 2.1.3
% 0.15/1.50 % (2260829)Termination reason: Instruction limit
% 0.15/1.50 % (2260829)Termination phase: Saturation
% 0.15/1.50 % (2260829)Time elapsed: 0.066 s
% 0.15/1.50 % (2260829)Peak memory usage: 90 MB
% 0.15/1.50 % (2260829)Instructions burned: 131 (million)
% 0.15/1.50 % (2260827)Instruction limit reached!
% 0.15/1.50 % (2260827)------------------------------
% 0.15/1.50 % (2260827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (2260827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (2260827)CaDiCaL version: 2.1.3
% 0.15/1.50 % (2260827)Termination reason: Instruction limit
% 0.15/1.50 % (2260827)Termination phase: Saturation
% 0.15/1.50 % (2260827)Time elapsed: 0.078 s
% 0.15/1.50 % (2260827)Peak memory usage: 90 MB
% 0.15/1.50 % (2260827)Instructions burned: 119 (million)
% 0.15/1.50 % (2260837)lrs+10_1_sil=8000:sp=occurrence:random_seed=1289029629:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.15/1.50 % (2260838)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1616191224:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.15/1.50 % (2260839)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2036352752:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 0.15/1.50 % (2260838)Instruction limit reached!
% 0.15/1.50 % (2260838)------------------------------
% 0.15/1.50 % (2260838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (2260838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (2260838)CaDiCaL version: 2.1.3
% 0.15/1.50 % (2260838)Termination reason: Instruction limit
% 0.15/1.50 % (2260838)Termination phase: Saturation
% 0.15/1.50 % (2260838)Time elapsed: 0.082 s
% 0.15/1.50 % (2260838)Peak memory usage: 91 MB
% 0.15/1.50 % (2260838)Instructions burned: 159 (million)
% 0.15/1.50 % (2260828)Refutation found. Thanks to Tanya!
% 0.15/1.50 % SZS status Theorem for theBenchmark
% 0.15/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.50 % (2260828)------------------------------
% 0.15/1.50 % (2260828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (2260828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (2260828)CaDiCaL version: 2.1.3
% 0.15/1.50 % (2260828)Termination reason: Refutation
% 0.15/1.50 % (2260828)Time elapsed: 0.048 s
% 0.15/1.50 % (2260828)Peak memory usage: 92 MB
% 0.15/1.50 % (2260828)Instructions burned: 75 (million)
% 0.15/1.50 % (2260828)------------------------------
% 0.15/1.50 % (2260828)------------------------------
% 0.15/1.50 % (2260818)Success in time 0.474 s
% 0.15/1.50 % Vampire exiting
%------------------------------------------------------------------------------