%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU328+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 : 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 12:48:22 PM UTC 2026
% Result : Theorem 2.67s 1.35s
% Output : Refutation 2.67s
% 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(f27,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(meet_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_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
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tops_2) ).
fof(f49,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,meet_of_subsets(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f54,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(f89,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f92,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f27]) ).
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] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,meet_of_subsets(X0,X1))
& X1 != empty_set
& element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f109,plain,
? [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) != subset_complement(X0,meet_of_subsets(X0,X1))
& X1 != empty_set
& element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f108]) ).
fof(f114,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f54]) ).
fof(f115,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f114]) ).
fof(f126,plain,
( union_of_subsets(sK4,complements_of_subsets(sK4,sK5)) != subset_complement(sK4,meet_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(f157,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f92]) ).
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,
union_of_subsets(sK4,complements_of_subsets(sK4,sK5)) != subset_complement(sK4,meet_of_subsets(sK4,sK5)),
inference(cnf_transformation,[],[f126]) ).
fof(f206,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_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(f288,definition,
( spl6_3
<=> element(meet_of_subsets(sK4,sK5),powerset(sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f289,plain,
( element(meet_of_subsets(sK4,sK5),powerset(sK4))
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f290,plain,
( ~ element(meet_of_subsets(sK4,sK5),powerset(sK4))
| spl6_3 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f297,plain,
( ~ element(sK5,powerset(powerset(sK4)))
| spl6_3 ),
inference(resolution,[],[f290,f157]) ).
fof(f303,plain,
( $false
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f297,f199]) ).
fof(f304,plain,
spl6_3,
inference(avatar_contradiction_clause,[],[f303]) ).
fof(f309,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(forward_demodulation,[],[f206,f152]) ).
fof(f312,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = set_difference(X0,meet_of_subsets(X0,X1))
| ~ element(X0,powerset(X0))
| ~ element(meet_of_subsets(X0,X1),powerset(X0))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(superposition,[],[f197,f309]) ).
fof(f316,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = set_difference(X0,meet_of_subsets(X0,X1))
| ~ element(meet_of_subsets(X0,X1),powerset(X0))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[],[f312,f213]) ).
fof(f319,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = set_difference(X0,meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[],[f316,f157]) ).
fof(f493,plain,
( subset_complement(sK4,meet_of_subsets(sK4,sK5)) != set_difference(sK4,meet_of_subsets(sK4,sK5))
| empty_set = sK5
| ~ element(sK5,powerset(powerset(sK4))) ),
inference(superposition,[],[f201,f319]) ).
fof(f500,plain,
( subset_complement(sK4,meet_of_subsets(sK4,sK5)) != set_difference(sK4,meet_of_subsets(sK4,sK5))
| ~ element(sK5,powerset(powerset(sK4))) ),
inference(forward_subsumption_resolution,[],[f493,f200]) ).
fof(f503,plain,
subset_complement(sK4,meet_of_subsets(sK4,sK5)) != set_difference(sK4,meet_of_subsets(sK4,sK5)),
inference(forward_subsumption_resolution,[],[f500,f199]) ).
fof(f519,plain,
( set_difference(sK4,meet_of_subsets(sK4,sK5)) != set_difference(sK4,meet_of_subsets(sK4,sK5))
| ~ element(meet_of_subsets(sK4,sK5),powerset(sK4)) ),
inference(superposition,[],[f503,f153]) ).
fof(f520,plain,
~ element(meet_of_subsets(sK4,sK5),powerset(sK4)),
inference(trivial_inequality_removal,[],[f519]) ).
fof(f521,plain,
( $false
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f520,f289]) ).
fof(f522,plain,
~ spl6_3,
inference(avatar_contradiction_clause,[],[f521]) ).
cnf(s4,plain,
spl6_3,
inference(sat_conversion,[],[f304]) ).
cnf(s21,plain,
~ spl6_3,
inference(sat_conversion,[],[f522]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s4,s21]) ).
fof(f524,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU328+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:47:01 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.67/1.35 % (2262796)Detected formulas, will run a generic FOF schedule.
% 2.67/1.35 % (2262806)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3798909724:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.35 % (2262806)First to succeed.
% 2.67/1.35 % (2262806)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2262796"
% 2.67/1.35 % (2262807)dis-21_1_sil=8000:lcm=predicate:random_seed=1850646367: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)
% 2.67/1.35 % (2262803)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=2733077532:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.35 % (2262801)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=2134028037:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.35 % (2262804)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=403099240:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.35 % (2262802)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=3585412947:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.35 % (2262804)Refutation not found, incomplete strategy
% 2.67/1.35 % (2262804)------------------------------
% 2.67/1.35 % (2262804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.35 % (2262804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.35 % (2262804)CaDiCaL version: 2.1.3
% 2.67/1.35 % (2262804)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.35 % (2262804)Time elapsed: 0.002 s
% 2.67/1.35 % (2262804)Peak memory usage: 88 MB
% 2.67/1.35 % (2262804)Instructions burned: 1 (million)
% 2.67/1.35 % (2262805)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2119989811:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.35 % (2262807)Instruction limit reached!
% 2.67/1.35 % (2262807)------------------------------
% 2.67/1.35 % (2262807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.35 % (2262807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.35 % (2262807)CaDiCaL version: 2.1.3
% 2.67/1.35 % (2262807)Termination reason: Instruction limit
% 2.67/1.35 % (2262807)Termination phase: Saturation
% 2.67/1.35 % (2262807)Time elapsed: 0.077 s
% 2.67/1.35 % (2262807)Peak memory usage: 90 MB
% 2.67/1.35 % (2262807)Instructions burned: 131 (million)
% 2.67/1.35 % (2262805)Instruction limit reached!
% 2.67/1.35 % (2262805)------------------------------
% 2.67/1.35 % (2262805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.35 % (2262805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.35 % (2262805)CaDiCaL version: 2.1.3
% 2.67/1.35 % (2262805)Termination reason: Instruction limit
% 2.67/1.35 % (2262805)Termination phase: Saturation
% 2.67/1.35 % (2262805)Time elapsed: 0.068 s
% 2.67/1.35 % (2262805)Peak memory usage: 88 MB
% 2.67/1.35 % (2262805)Instructions burned: 120 (million)
% 2.67/1.35 % (2262806)Refutation found. Thanks to Tanya!
% 2.67/1.35 % SZS status Theorem for theBenchmark
% 2.67/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.35 % (2262806)------------------------------
% 2.67/1.35 % (2262806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.35 % (2262806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.35 % (2262806)CaDiCaL version: 2.1.3
% 2.67/1.35 % (2262806)Termination reason: Refutation
% 2.67/1.35 % (2262806)Time elapsed: 0.007 s
% 2.67/1.35 % (2262806)Peak memory usage: 90 MB
% 2.67/1.35 % (2262806)Instructions burned: 15 (million)
% 2.67/1.35 % (2262806)------------------------------
% 2.67/1.35 % (2262806)------------------------------
% 2.67/1.35 % (2262796)Success in time 0.295 s
% 2.67/1.35 % Vampire exiting
%------------------------------------------------------------------------------