%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : TOP005-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 02:33:49 PM UTC 2026
% Result : Unsatisfiable 5.28s 1.65s
% Output : Refutation 5.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 7 unt; 2 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 123 ( 65 ~; 56 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( element_of_set(X0,f1(X1,X0))
| ~ element_of_set(X0,union_of_members(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_1) ).
fof(f2,axiom,
! [X0,X1] :
( element_of_collection(f1(X1,X0),X1)
| ~ element_of_set(X0,union_of_members(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_2) ).
fof(f3,axiom,
! [X2,X0,X1] :
( element_of_set(X2,f10(X1,X0,X2))
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_37) ).
fof(f4,axiom,
! [X2,X0,X1] :
( element_of_collection(f10(X1,X0,X2),X1)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_38) ).
fof(f5,axiom,
! [X2,X0,X1] :
( subset_sets(f10(X1,X0,X2),X0)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_39) ).
fof(f6,axiom,
! [X0,X1] :
( element_of_set(f11(X1,X0),X0)
| element_of_collection(X0,top_of_basis(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_40) ).
fof(f7,axiom,
! [X2,X0,X1] :
( element_of_collection(X0,top_of_basis(X1))
| ~ element_of_set(f11(X1,X0),X2)
| ~ element_of_collection(X2,X1)
| ~ subset_sets(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_41) ).
fof(f9,axiom,
! [X2,X0,X1] :
( subset_sets(X0,union_of_members(X2))
| ~ element_of_collection(X1,X2)
| ~ subset_sets(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_20) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ subset_collections(X0,X1)
| ~ element_of_collection(X2,X0)
| element_of_collection(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_21) ).
fof(f11,negated_conjecture,
subset_collections(g,top_of_basis(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_2) ).
fof(f12,negated_conjecture,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_3) ).
fof(f13,plain,
! [X0] :
( element_of_collection(X0,top_of_basis(f))
| ~ element_of_collection(X0,g) ),
inference(resolution,[],[f10,f11]) ).
fof(f15,plain,
! [X0] :
( ~ element_of_collection(X0,f)
| ~ element_of_set(f11(f,union_of_members(g)),X0)
| ~ subset_sets(X0,union_of_members(g)) ),
inference(resolution,[],[f7,f12]) ).
fof(f17,plain,
! [X0,X1] :
( ~ element_of_set(f11(f,union_of_members(g)),f10(f,X0,X1))
| ~ subset_sets(f10(f,X0,X1),union_of_members(g))
| ~ element_of_set(X1,X0)
| ~ element_of_collection(X0,top_of_basis(f)) ),
inference(resolution,[],[f15,f4]) ).
fof(f29,plain,
! [X0] :
( ~ subset_sets(f10(f,X0,f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),X0)
| ~ element_of_collection(X0,top_of_basis(f))
| ~ element_of_set(f11(f,union_of_members(g)),X0)
| ~ element_of_collection(X0,top_of_basis(f)) ),
inference(resolution,[],[f17,f3]) ).
fof(f30,plain,
! [X0] :
( ~ subset_sets(f10(f,X0,f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),X0)
| ~ element_of_collection(X0,top_of_basis(f)) ),
inference(duplicate_literal_removal,[],[f29]) ).
fof(f32,plain,
! [X0,X1] :
( ~ element_of_collection(X1,g)
| ~ element_of_collection(X0,top_of_basis(f))
| ~ element_of_set(f11(f,union_of_members(g)),X0)
| ~ subset_sets(f10(f,X0,f11(f,union_of_members(g))),X1) ),
inference(resolution,[],[f30,f9]) ).
fof(f35,plain,
! [X0,X1] :
( ~ subset_sets(f10(f,X0,f11(f,union_of_members(g))),f1(g,X1))
| ~ element_of_set(f11(f,union_of_members(g)),X0)
| ~ element_of_collection(X0,top_of_basis(f))
| ~ element_of_set(X1,union_of_members(g)) ),
inference(resolution,[],[f32,f2]) ).
fof(f37,plain,
! [X0] :
( ~ element_of_set(f11(f,union_of_members(g)),f1(g,X0))
| ~ element_of_collection(f1(g,X0),top_of_basis(f))
| ~ element_of_set(X0,union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,X0))
| ~ element_of_collection(f1(g,X0),top_of_basis(f)) ),
inference(resolution,[],[f35,f5]) ).
fof(f39,plain,
! [X0] :
( ~ element_of_set(f11(f,union_of_members(g)),f1(g,X0))
| ~ element_of_collection(f1(g,X0),top_of_basis(f))
| ~ element_of_set(X0,union_of_members(g)) ),
inference(duplicate_literal_removal,[],[f37]) ).
fof(f40,plain,
( ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| ~ element_of_set(f11(f,union_of_members(g)),union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),union_of_members(g)) ),
inference(resolution,[],[f39,f1]) ).
fof(f41,plain,
( ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| ~ element_of_set(f11(f,union_of_members(g)),union_of_members(g)) ),
inference(duplicate_literal_removal,[],[f40]) ).
fof(f43,definition,
( spl0_3
<=> element_of_set(f11(f,union_of_members(g)),union_of_members(g)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f44,plain,
( element_of_set(f11(f,union_of_members(g)),union_of_members(g))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( ~ element_of_set(f11(f,union_of_members(g)),union_of_members(g))
| spl0_3 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl0_4
<=> element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f49,plain,
( ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| spl0_4 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f41,f47,f43]) ).
fof(f54,plain,
( element_of_collection(union_of_members(g),top_of_basis(f))
| spl0_3 ),
inference(resolution,[],[f45,f6]) ).
fof(f57,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f54,f12]) ).
fof(f58,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f57]) ).
fof(f71,plain,
( ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| spl0_4 ),
inference(resolution,[],[f49,f13]) ).
fof(f80,plain,
( ~ element_of_set(f11(f,union_of_members(g)),union_of_members(g))
| spl0_4 ),
inference(resolution,[],[f71,f2]) ).
fof(f81,plain,
( $false
| ~ spl0_3
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f80,f44]) ).
fof(f82,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f81]) ).
cnf(s2,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f50]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f58]) ).
cnf(s6,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f82]) ).
cnf(s7,plain,
spl0_4,
inference(rat,[],[s6,s3]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7,s3]) ).
fof(f83,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 % Computer : n017.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Mon Sep 28 18:43:52 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.30 Running first-order theorem proving
% 0.25/0.30 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.31/1.31 % (3873436)Input is clausal, will run a generic CNF schedule.
% 2.31/1.31 % (3873451)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=792758161:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.31/1.31 % (3873453)lrs+10_1_sil=8000:sp=occurrence:random_seed=3417977473:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.31/1.31 % (3873450)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=3046054441:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.31/1.31 % (3873452)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=361517139:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.31/1.31 % (3873454)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4227697346:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.31/1.31 % (3873455)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2390721590:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.31/1.31 % (3873456)dis-21_1_sil=8000:lcm=predicate:random_seed=2085934495:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.31/1.31 % (3873454)Refutation not found, incomplete strategy
% 2.31/1.31 % (3873454)------------------------------
% 2.31/1.31 % (3873454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/1.31 % (3873454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/1.31 % (3873454)CaDiCaL version: 2.1.3
% 2.31/1.31 % (3873454)Termination reason: Refutation not found, incomplete strategy
% 2.31/1.31 % (3873454)Time elapsed: 0.001 s
% 2.31/1.31 % (3873454)Peak memory usage: 87 MB
% 2.31/1.31 % (3873455)First to succeed.
% 2.31/1.31 % (3873455)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3873436"
% 2.31/1.31 % (3873453)Instruction limit reached!
% 2.31/1.31 % (3873453)------------------------------
% 2.31/1.31 % (3873453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/1.31 % (3873453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/1.31 % (3873453)CaDiCaL version: 2.1.3
% 2.31/1.31 % (3873453)Termination reason: Instruction limit
% 2.31/1.31 % (3873453)Termination phase: Saturation
% 2.31/1.31 % (3873453)Time elapsed: 0.051 s
% 2.31/1.31 % (3873453)Peak memory usage: 88 MB
% 2.31/1.31 % (3873453)Instructions burned: 108 (million)
% 2.31/1.31 % (3873456)Instruction limit reached!
% 2.31/1.31 % (3873456)------------------------------
% 2.31/1.31 % (3873456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/1.31 % (3873456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/1.31 % (3873456)CaDiCaL version: 2.1.3
% 2.31/1.31 % (3873456)Termination reason: Instruction limit
% 2.31/1.31 % (3873456)Termination phase: Saturation
% 2.31/1.31 % (3873456)Time elapsed: 0.119 s
% 2.31/1.31 % (3873456)Peak memory usage: 89 MB
% 2.31/1.31 % (3873456)Instructions burned: 117 (million)
% 2.31/1.31 % (3873454)------------------------------
% 2.31/1.31 % (3873454)------------------------------
% 2.31/1.31 % (3873470)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1430073796:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.31/1.31 % (3873470)Refutation not found, incomplete strategy
% 2.31/1.31 % (3873470)------------------------------
% 2.31/1.31 % (3873470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/1.31 % (3873470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/1.31 % (3873470)CaDiCaL version: 2.1.3
% 2.31/1.31 % (3873470)Termination reason: Refutation not found, incomplete strategy
% 2.31/1.31 % (3873470)Time elapsed: 0.001 s
% 2.31/1.31 % (3873470)Peak memory usage: 87 MB
% 2.31/1.31 % (3873472)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1754549120:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 2.31/1.31 % (3873472)Also succeeded, but the first one will report.
% 2.31/1.31 % (3873477)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1026458766:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 5.28/1.65 % (3873477)Refutation not found, incomplete strategy
% 5.28/1.65 % (3873477)------------------------------
% 5.28/1.65 % (3873477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.28/1.65 % (3873477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.28/1.65 % (3873477)CaDiCaL version: 2.1.3
% 5.28/1.65 % (3873477)Termination reason: Refutation not found, incomplete strategy
% 5.28/1.65 % (3873477)Time elapsed: 0.0000 s
% 5.28/1.65 % (3873477)Peak memory usage: 87 MB
% 5.28/1.65 % (3873455)Refutation found. Thanks to Tanya!
% 5.28/1.65 % SZS status Unsatisfiable for theBenchmark
% 5.28/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 5.28/1.65 % (3873455)------------------------------
% 5.28/1.65 % (3873455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.28/1.65 % (3873455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.28/1.65 % (3873455)CaDiCaL version: 2.1.3
% 5.28/1.65 % (3873455)Termination reason: Refutation
% 5.28/1.65 % (3873455)Time elapsed: 0.006 s
% 5.28/1.65 % (3873455)Peak memory usage: 89 MB
% 5.28/1.65 % (3873455)Instructions burned: 4 (million)
% 5.28/1.65 % (3873455)------------------------------
% 5.28/1.65 % (3873455)------------------------------
% 5.28/1.65 % (3873436)Success in time 0.636 s
% 5.28/1.65 % Vampire exiting
%------------------------------------------------------------------------------