%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:39:26 PM UTC 2026
% Result : Unsatisfiable 2.53s 1.32s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 10 unt; 1 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 44 ( 19 ~; 24 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(member_of_1_not_of_2(X0,X1),X1)
| subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom2) ).
fof(f6,axiom,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_sets(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ union(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X0)
| member(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_union_is_member_of_one_set) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( ~ union(X0,X1,X2)
| ~ member(X3,X0)
| member(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_set1_is_member_of_union) ).
fof(f13,axiom,
union(a,a,aUa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_union_a_is_aUa) ).
fof(f14,negated_conjecture,
~ equal_sets(aUa,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_equals_aUa) ).
fof(f20,plain,
! [X0] :
( ~ member(X0,a)
| member(X0,aUa) ),
inference(resolution,[],[f8,f13]) ).
fof(f24,plain,
! [X0] :
( member(member_of_1_not_of_2(a,X0),aUa)
| subset(a,X0) ),
inference(resolution,[],[f20,f2]) ).
fof(f25,plain,
! [X0] :
( ~ member(X0,aUa)
| member(X0,a)
| member(X0,a) ),
inference(resolution,[],[f7,f13]) ).
fof(f26,plain,
! [X0] :
( ~ member(X0,aUa)
| member(X0,a) ),
inference(duplicate_literal_removal,[],[f25]) ).
fof(f27,plain,
! [X0] :
( member(member_of_1_not_of_2(aUa,X0),a)
| subset(aUa,X0) ),
inference(resolution,[],[f26,f2]) ).
fof(f28,plain,
( subset(a,aUa)
| subset(a,aUa) ),
inference(resolution,[],[f24,f3]) ).
fof(f30,plain,
subset(a,aUa),
inference(duplicate_literal_removal,[],[f28]) ).
fof(f38,definition,
( spl0_2
<=> subset(aUa,a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f39,plain,
( subset(aUa,a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f40,plain,
( ~ subset(aUa,a)
| spl0_2 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f65,plain,
( subset(aUa,a)
| subset(aUa,a) ),
inference(resolution,[],[f27,f3]) ).
fof(f67,plain,
subset(aUa,a),
inference(duplicate_literal_removal,[],[f65]) ).
fof(f68,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f67,f40]) ).
fof(f69,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f68]) ).
fof(f91,plain,
( ~ subset(a,aUa)
| equal_sets(aUa,a)
| ~ spl0_2 ),
inference(resolution,[],[f39,f6]) ).
fof(f93,plain,
( equal_sets(aUa,a)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f91,f30]) ).
fof(f94,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f93,f14]) ).
fof(f95,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f94]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f69]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f95]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f96,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n016.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 00:07:33 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 2.53/1.32 % (3133866)Input is clausal, will run a generic CNF schedule.
% 2.53/1.32 % (3133893)lrs+10_1_sil=8000:sp=occurrence:random_seed=2074065987:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.53/1.32 % (3133893)First to succeed.
% 2.53/1.32 % (3133893)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3133866"
% 2.53/1.32 % (3133891)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3127699162:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.53/1.32 % (3133895)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=873451811:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.53/1.32 % (3133894)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3107008154:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.53/1.32 % (3133894)Refutation not found, incomplete strategy
% 2.53/1.32 % (3133894)------------------------------
% 2.53/1.32 % (3133894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.32 % (3133894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.32 % (3133894)CaDiCaL version: 2.1.3
% 2.53/1.32 % (3133894)Termination reason: Refutation not found, incomplete strategy
% 2.53/1.32 % (3133894)Time elapsed: 0.001 s
% 2.53/1.32 % (3133894)Peak memory usage: 88 MB
% 2.53/1.32 % (3133895)Also succeeded, but the first one will report.
% 2.53/1.32 % (3133889)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=1397132410:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.53/1.32 % (3133892)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1902748142:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.53/1.32 % (3133896)dis-21_1_sil=8000:lcm=predicate:random_seed=2918659048: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)
% 2.53/1.32 % (3133896)Also succeeded, but the first one will report.
% 2.53/1.32 % (3133893)Refutation found. Thanks to Tanya!
% 2.53/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.53/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/1.32 % (3133893)------------------------------
% 2.53/1.32 % (3133893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.32 % (3133893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.32 % (3133893)CaDiCaL version: 2.1.3
% 2.53/1.32 % (3133893)Termination reason: Refutation
% 2.53/1.32 % (3133893)Time elapsed: 0.002 s
% 2.53/1.32 % (3133893)Peak memory usage: 89 MB
% 2.53/1.32 % (3133893)Instructions burned: 3 (million)
% 2.53/1.32 % (3133893)------------------------------
% 2.53/1.32 % (3133893)------------------------------
% 2.53/1.32 % (3133866)Success in time 0.261 s
% 2.53/1.32 % Vampire exiting
%------------------------------------------------------------------------------