%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET004-1 : 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 : n018.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 12:39:27 PM UTC 2026
% Result : Unsatisfiable 3.65s 1.47s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 10 ( 6 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
| member(member_of_1_not_of_2(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom1) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom2) ).
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,b,aUb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_union_b_is_aUb) ).
fof(f14,negated_conjecture,
~ subset(a,aUb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_is_a_subset_of_aUb) ).
fof(f15,plain,
member(member_of_1_not_of_2(a,aUb),a),
inference(resolution,[],[f2,f14]) ).
fof(f16,plain,
~ member(member_of_1_not_of_2(a,aUb),aUb),
inference(resolution,[],[f3,f14]) ).
fof(f21,plain,
! [X0] :
( member(X0,aUb)
| ~ member(X0,a) ),
inference(resolution,[],[f8,f13]) ).
fof(f23,plain,
~ member(member_of_1_not_of_2(a,aUb),a),
inference(resolution,[],[f21,f16]) ).
fof(f25,plain,
$false,
inference(resolution,[],[f23,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 00:05:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.65/1.47 % (2868670)Input is clausal, will run a generic CNF schedule.
% 3.65/1.47 % (2868676)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3578886468:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.65/1.47 % (2868679)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3151061439:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.65/1.47 % (2868677)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3095309616:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.65/1.47 % (2868675)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=3019195713:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.65/1.47 % (2868678)lrs+10_1_sil=8000:sp=occurrence:random_seed=2071020106:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.65/1.47 % (2868681)dis-21_1_sil=8000:lcm=predicate:random_seed=1288401187: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)
% 3.65/1.47 % (2868680)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=674018022:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.65/1.47 % (2868679)Refutation not found, incomplete strategy
% 3.65/1.47 % (2868679)------------------------------
% 3.65/1.47 % (2868679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.47 % (2868679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.47 % (2868679)CaDiCaL version: 2.1.3
% 3.65/1.47 % (2868679)Termination reason: Refutation not found, incomplete strategy
% 3.65/1.47 % (2868679)Time elapsed: 0.001 s
% 3.65/1.47 % (2868679)Peak memory usage: 87 MB
% 3.65/1.47 % (2868681)First to succeed.
% 3.65/1.47 % (2868678)Also succeeded, but the first one will report.
% 3.65/1.47 % (2868681)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2868670"
% 3.65/1.47 % (2868680)Also succeeded, but the first one will report.
% 3.65/1.47 % (2868679)------------------------------
% 3.65/1.47 % (2868679)------------------------------
% 3.65/1.47 % (2868681)Refutation found. Thanks to Tanya!
% 3.65/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.65/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.47 % (2868681)------------------------------
% 3.65/1.47 % (2868681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.47 % (2868681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.47 % (2868681)CaDiCaL version: 2.1.3
% 3.65/1.47 % (2868681)Termination reason: Refutation
% 3.65/1.47 % (2868681)Time elapsed: 0.002 s
% 3.65/1.47 % (2868681)Peak memory usage: 88 MB
% 3.65/1.47 % (2868681)Instructions burned: 1 (million)
% 3.65/1.47 % (2868681)------------------------------
% 3.65/1.47 % (2868681)------------------------------
% 3.65/1.47 % (2868670)Success in time 0.434 s
% 3.65/1.47 % Vampire exiting
%------------------------------------------------------------------------------