%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU327+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 : 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 12:48:22 PM UTC 2026
% Result : Theorem 0.79s 1.02s
% Output : Refutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 16 unt; 1 def)
% Number of atoms : 101 ( 42 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 99 ( 46 ~; 36 |; 7 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 53 ( 0 sgn 49 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f18,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f22,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f26,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(union_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f48,conjecture,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,union_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_tops_2) ).
fof(f49,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,union_of_subsets(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f54,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_setfam_1) ).
fof(f89,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f91,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f26]) ).
fof(f106,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f46]) ).
fof(f107,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
? [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,union_of_subsets(X0,X1))
& X1 != empty_set
& element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f109,plain,
? [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,union_of_subsets(X0,X1))
& X1 != empty_set
& element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f108]) ).
fof(f114,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f54]) ).
fof(f115,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f114]) ).
fof(f126,plain,
( meet_of_subsets(sK4,complements_of_subsets(sK4,sK5)) != subset_complement(sK4,union_of_subsets(sK4,sK5))
& empty_set != sK5
& element(sK5,powerset(powerset(sK4))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f109]) ).
fof(f152,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f17]) ).
fof(f153,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f154,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f156,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f91]) ).
fof(f197,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f199,plain,
element(sK5,powerset(powerset(sK4))),
inference(cnf_transformation,[],[f126]) ).
fof(f200,plain,
empty_set != sK5,
inference(cnf_transformation,[],[f126]) ).
fof(f201,plain,
meet_of_subsets(sK4,complements_of_subsets(sK4,sK5)) != subset_complement(sK4,union_of_subsets(sK4,sK5)),
inference(cnf_transformation,[],[f126]) ).
fof(f206,plain,
! [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f115]) ).
fof(f213,plain,
! [X0] : element(X0,powerset(X0)),
inference(forward_demodulation,[],[f154,f152]) ).
fof(f290,definition,
( spl6_3
<=> element(union_of_subsets(sK4,sK5),powerset(sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f291,plain,
( element(union_of_subsets(sK4,sK5),powerset(sK4))
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f292,plain,
( ~ element(union_of_subsets(sK4,sK5),powerset(sK4))
| spl6_3 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f299,plain,
( ~ element(sK5,powerset(powerset(sK4)))
| spl6_3 ),
inference(resolution,[],[f292,f156]) ).
fof(f305,plain,
( $false
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f299,f199]) ).
fof(f306,plain,
spl6_3,
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f311,plain,
! [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(forward_demodulation,[],[f206,f152]) ).
fof(f314,plain,
! [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = set_difference(X0,union_of_subsets(X0,X1))
| ~ element(X0,powerset(X0))
| ~ element(union_of_subsets(X0,X1),powerset(X0))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(superposition,[],[f197,f311]) ).
fof(f318,plain,
! [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = set_difference(X0,union_of_subsets(X0,X1))
| ~ element(union_of_subsets(X0,X1),powerset(X0))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[],[f314,f213]) ).
fof(f321,plain,
! [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = set_difference(X0,union_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[],[f318,f156]) ).
fof(f484,plain,
( subset_complement(sK4,union_of_subsets(sK4,sK5)) != set_difference(sK4,union_of_subsets(sK4,sK5))
| empty_set = sK5
| ~ element(sK5,powerset(powerset(sK4))) ),
inference(superposition,[],[f201,f321]) ).
fof(f491,plain,
( subset_complement(sK4,union_of_subsets(sK4,sK5)) != set_difference(sK4,union_of_subsets(sK4,sK5))
| ~ element(sK5,powerset(powerset(sK4))) ),
inference(forward_subsumption_resolution,[],[f484,f200]) ).
fof(f494,plain,
subset_complement(sK4,union_of_subsets(sK4,sK5)) != set_difference(sK4,union_of_subsets(sK4,sK5)),
inference(forward_subsumption_resolution,[],[f491,f199]) ).
fof(f510,plain,
( set_difference(sK4,union_of_subsets(sK4,sK5)) != set_difference(sK4,union_of_subsets(sK4,sK5))
| ~ element(union_of_subsets(sK4,sK5),powerset(sK4)) ),
inference(superposition,[],[f494,f153]) ).
fof(f511,plain,
~ element(union_of_subsets(sK4,sK5),powerset(sK4)),
inference(trivial_inequality_removal,[],[f510]) ).
fof(f512,plain,
( $false
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f511,f291]) ).
fof(f513,plain,
~ spl6_3,
inference(avatar_contradiction_clause,[],[f512]) ).
cnf(s4,plain,
spl6_3,
inference(sat_conversion,[],[f306]) ).
cnf(s20,plain,
~ spl6_3,
inference(sat_conversion,[],[f513]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s4,s20]) ).
fof(f515,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU327+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 28 04:49:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.79/1.02 % (25894)Detected formulas, will run a generic FOF schedule.
% 0.79/1.02 % (25903)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4167452641:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.79/1.02 % (25904)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2950291578:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.79/1.02 % (25900)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=3241997985:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.79/1.02 % (25902)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3511818224:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.79/1.02 % (25905)dis-21_1_sil=8000:lcm=predicate:random_seed=1374210130: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)
% 0.79/1.02 % (25901)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=1211322591:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.79/1.02 % (25899)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=2506168606:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.79/1.02 % (25902)Refutation not found, incomplete strategy
% 0.79/1.02 % (25902)------------------------------
% 0.79/1.02 % (25902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.79/1.02 % (25902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/1.02 % (25902)CaDiCaL version: 2.1.3
% 0.79/1.02 % (25902)Termination reason: Refutation not found, incomplete strategy
% 0.79/1.02 % (25902)Time elapsed: 0.002 s
% 0.79/1.02 % (25902)Peak memory usage: 88 MB
% 0.79/1.02 % (25902)Instructions burned: 1 (million)
% 0.79/1.02 % (25904)First to succeed.
% 0.79/1.02 % (25904)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-25894"
% 0.79/1.02 % (25903)Instruction limit reached!
% 0.79/1.02 % (25903)------------------------------
% 0.79/1.02 % (25903)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.79/1.02 % (25903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/1.02 % (25903)CaDiCaL version: 2.1.3
% 0.79/1.02 % (25903)Termination reason: Instruction limit
% 0.79/1.02 % (25903)Termination phase: Saturation
% 0.79/1.02 % (25903)Time elapsed: 0.067 s
% 0.79/1.02 % (25903)Peak memory usage: 88 MB
% 0.79/1.02 % (25903)Instructions burned: 120 (million)
% 0.79/1.02 % (25905)Instruction limit reached!
% 0.79/1.02 % (25905)------------------------------
% 0.79/1.02 % (25905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.79/1.02 % (25905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/1.02 % (25905)CaDiCaL version: 2.1.3
% 0.79/1.02 % (25905)Termination reason: Instruction limit
% 0.79/1.02 % (25905)Termination phase: Saturation
% 0.79/1.02 % (25905)Time elapsed: 0.073 s
% 0.79/1.02 % (25905)Peak memory usage: 90 MB
% 0.79/1.02 % (25905)Instructions burned: 130 (million)
% 0.79/1.02 % (25913)lrs+10_1_sil=8000:sp=occurrence:random_seed=3476732527:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.79/1.02 % (25914)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2071520747:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.79/1.02 % (25902)------------------------------
% 0.79/1.02 % (25902)------------------------------
% 0.79/1.02 % (25904)Refutation found. Thanks to Tanya!
% 0.79/1.02 % SZS status Theorem for theBenchmark
% 0.79/1.02 % SZS output start Proof for theBenchmark
% See solution above
% 3.22/1.13 % (25904)------------------------------
% 3.22/1.13 % (25904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.22/1.13 % (25904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/1.13 % (25904)CaDiCaL version: 2.1.3
% 3.22/1.13 % (25904)Termination reason: Refutation
% 3.22/1.13 % (25904)Time elapsed: 0.012 s
% 3.22/1.13 % (25904)Peak memory usage: 89 MB
% 3.22/1.13 % (25904)Instructions burned: 15 (million)
% 3.22/1.13 % (25904)------------------------------
% 3.22/1.13 % (25904)------------------------------
% 3.22/1.13 % (25894)Success in time 0.423 s
% 3.22/1.13 % Vampire exiting
%------------------------------------------------------------------------------