%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET009-1 : 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 : n013.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 12:39:28 PM UTC 2026
% Result : Unsatisfiable 2.90s 1.38s
% Output : Refutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 39 ( 12 unt; 1 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 83 ( 43 ~; 39 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',membership_in_subsets) ).
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(f7,axiom,
! [X2,X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ difference(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_difference) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_member_of_difference) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( member(X0,X3)
| ~ difference(X1,X2,X3)
| ~ member(X0,X1)
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_difference_or_set2) ).
fof(f13,axiom,
subset(d,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_a_subset_of_a) ).
fof(f14,axiom,
difference(b,a,bDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_minus_a) ).
fof(f15,axiom,
difference(b,d,bDd),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_minus_d) ).
fof(f16,negated_conjecture,
~ subset(bDa,bDd),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_bDa_is_a_subset_of_bDd) ).
fof(f17,plain,
! [X0] :
( subset(X0,X0)
| subset(X0,X0) ),
inference(resolution,[],[f3,f2]) ).
fof(f18,plain,
! [X0] : subset(X0,X0),
inference(duplicate_literal_removal,[],[f17]) ).
fof(f19,plain,
! [X2,X0,X1] :
( subset(X2,X1)
| ~ member(member_of_1_not_of_2(X2,X1),X0)
| ~ subset(X0,X1) ),
inference(resolution,[],[f1,f3]) ).
fof(f23,plain,
! [X0] :
( ~ member(X0,bDa)
| ~ member(X0,a) ),
inference(resolution,[],[f8,f14]) ).
fof(f25,plain,
! [X0] :
( ~ subset(X0,bDd)
| ~ member(member_of_1_not_of_2(bDa,bDd),X0) ),
inference(resolution,[],[f19,f16]) ).
fof(f27,plain,
! [X0,X1] :
( ~ subset(X1,bDd)
| ~ member(member_of_1_not_of_2(X0,bDd),X1)
| ~ member(member_of_1_not_of_2(bDa,bDd),X0) ),
inference(resolution,[],[f25,f19]) ).
fof(f32,plain,
! [X0] :
( ~ member(member_of_1_not_of_2(X0,bDd),bDd)
| ~ member(member_of_1_not_of_2(bDa,bDd),X0) ),
inference(resolution,[],[f27,f18]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ difference(X1,X2,bDd)
| ~ member(member_of_1_not_of_2(bDa,bDd),X0)
| ~ member(member_of_1_not_of_2(X0,bDd),X1)
| member(member_of_1_not_of_2(X0,bDd),X2) ),
inference(resolution,[],[f32,f9]) ).
fof(f38,plain,
! [X0] :
( ~ member(member_of_1_not_of_2(bDa,X0),a)
| subset(bDa,X0) ),
inference(resolution,[],[f23,f2]) ).
fof(f51,definition,
( spl0_2
<=> member(member_of_1_not_of_2(bDa,bDd),b) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f52,plain,
( member(member_of_1_not_of_2(bDa,bDd),b)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f53,plain,
( ~ member(member_of_1_not_of_2(bDa,bDd),b)
| spl0_2 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f63,plain,
( ! [X0,X1] :
( ~ difference(b,X1,X0)
| ~ member(member_of_1_not_of_2(bDa,bDd),X0) )
| spl0_2 ),
inference(resolution,[],[f53,f7]) ).
fof(f71,plain,
( ~ member(member_of_1_not_of_2(bDa,bDd),bDa)
| spl0_2 ),
inference(resolution,[],[f63,f14]) ).
fof(f75,plain,
! [X0,X1] :
( ~ subset(X1,a)
| subset(bDa,X0)
| ~ member(member_of_1_not_of_2(bDa,X0),X1) ),
inference(resolution,[],[f38,f1]) ).
fof(f76,plain,
( subset(bDa,bDd)
| spl0_2 ),
inference(resolution,[],[f71,f2]) ).
fof(f80,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f76,f16]) ).
fof(f81,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f116,plain,
! [X0] :
( member(member_of_1_not_of_2(X0,bDd),d)
| ~ member(member_of_1_not_of_2(X0,bDd),b)
| ~ member(member_of_1_not_of_2(bDa,bDd),X0) ),
inference(resolution,[],[f35,f15]) ).
fof(f269,plain,
! [X0] :
( ~ member(member_of_1_not_of_2(bDa,X0),d)
| subset(bDa,X0) ),
inference(resolution,[],[f75,f13]) ).
fof(f676,plain,
( subset(bDa,bDd)
| ~ member(member_of_1_not_of_2(bDa,bDd),b)
| ~ member(member_of_1_not_of_2(bDa,bDd),bDa) ),
inference(resolution,[],[f269,f116]) ).
fof(f697,plain,
( subset(bDa,bDd)
| ~ member(member_of_1_not_of_2(bDa,bDd),b) ),
inference(forward_subsumption_resolution,[],[f676,f2]) ).
fof(f709,plain,
~ member(member_of_1_not_of_2(bDa,bDd),b),
inference(forward_subsumption_resolution,[],[f697,f16]) ).
fof(f712,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f709,f52]) ).
fof(f713,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f712]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f81]) ).
cnf(s47,plain,
~ spl0_2,
inference(sat_conversion,[],[f713]) ).
cnf(s48,plain,
$false,
inference(rat,[],[s2,s47]) ).
fof(f714,plain,
$false,
inference(avatar_sat_refutation,[],[s48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.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 00:02:36 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 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
% 2.90/1.38 % (680972)Input is clausal, will run a generic CNF schedule.
% 2.90/1.38 % (680982)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=174088130:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.90/1.38 % (680982)First to succeed.
% 2.90/1.38 % (680982)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-680972"
% 2.90/1.38 % (680979)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=854364778:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.90/1.38 % (680983)dis-21_1_sil=8000:lcm=predicate:random_seed=2423650685: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)
% 2.90/1.38 % (680977)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=1248863223:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.90/1.38 % (680980)lrs+10_1_sil=8000:sp=occurrence:random_seed=3749971040:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.90/1.38 % (680978)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2826756390:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.90/1.38 % (680981)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4047032168:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.90/1.38 % (680981)Refutation not found, incomplete strategy
% 2.90/1.38 % (680981)------------------------------
% 2.90/1.38 % (680981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.38 % (680981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.38 % (680981)CaDiCaL version: 2.1.3
% 2.90/1.38 % (680981)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.38 % (680981)Time elapsed: 0.001 s
% 2.90/1.38 % (680981)Peak memory usage: 87 MB
% 2.90/1.38 % (680983)Also succeeded, but the first one will report.
% 2.90/1.38 % (680980)Also succeeded, but the first one will report.
% 2.90/1.38 % (680982)Refutation found. Thanks to Tanya!
% 2.90/1.38 % SZS status Unsatisfiable for theBenchmark
% 2.90/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.90/1.38 % (680982)------------------------------
% 2.90/1.38 % (680982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.38 % (680982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.38 % (680982)CaDiCaL version: 2.1.3
% 2.90/1.38 % (680982)Termination reason: Refutation
% 2.90/1.38 % (680982)Time elapsed: 0.030 s
% 2.90/1.38 % (680982)Peak memory usage: 89 MB
% 2.90/1.38 % (680982)Instructions burned: 111 (million)
% 2.90/1.38 % (680982)------------------------------
% 2.90/1.38 % (680982)------------------------------
% 2.90/1.38 % (680972)Success in time 0.332 s
% 2.90/1.38 % Vampire exiting
%------------------------------------------------------------------------------