%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET002+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 : Theorem 4.05s 1.41s
% Output : Refutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 69 ( 25 ~; 29 |; 8 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 59 ( 57 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X1)
| member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f12,conjecture,
! [X0] : equal_set(union(X0,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI14) ).
fof(f13,negated_conjecture,
~ ! [X0] : equal_set(union(X0,X0),X0),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f16,plain,
? [X0] : ~ equal_set(union(X0,X0),X0),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f20,plain,
~ equal_set(union(sK0,sK0),sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f16]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f19]) ).
fof(f24,plain,
~ equal_set(union(sK0,sK0),sK0),
inference(cnf_transformation,[],[f20]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f27,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f28,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f30,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(sK1(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[],[f30,f27]) ).
fof(f35,plain,
( ~ subset(sK0,union(sK0,sK0))
| ~ subset(union(sK0,sK0),sK0) ),
inference(resolution,[],[f28,f24]) ).
fof(f38,plain,
! [X2,X0,X1] :
( member(sK1(union(X0,X1),X2),X1)
| member(sK1(union(X0,X1),X2),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[],[f25,f29]) ).
fof(f39,plain,
! [X0,X1] :
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) ),
inference(resolution,[],[f32,f29]) ).
fof(f42,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(duplicate_literal_removal,[],[f39]) ).
fof(f43,plain,
~ subset(union(sK0,sK0),sK0),
inference(resolution,[],[f42,f35]) ).
fof(f48,plain,
! [X0,X1] :
( member(sK1(union(X0,X1),X1),X0)
| subset(union(X0,X1),X1)
| subset(union(X0,X1),X1) ),
inference(resolution,[],[f38,f30]) ).
fof(f54,plain,
! [X0,X1] :
( member(sK1(union(X0,X1),X1),X0)
| subset(union(X0,X1),X1) ),
inference(duplicate_literal_removal,[],[f48]) ).
fof(f56,plain,
! [X0] :
( subset(union(X0,X0),X0)
| subset(union(X0,X0),X0) ),
inference(resolution,[],[f54,f30]) ).
fof(f62,plain,
! [X0] : subset(union(X0,X0),X0),
inference(duplicate_literal_removal,[],[f56]) ).
fof(f71,plain,
$false,
inference(resolution,[],[f62,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n001.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 00:08:17 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.46 Running first-order theorem proving
% 0.13/0.46 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
% 4.05/1.41 % (4101338)Detected formulas, will run a generic FOF schedule.
% 4.05/1.41 % (4101350)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3002333481:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 4.05/1.41 % (4101350)First to succeed.
% 4.05/1.41 % (4101350)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4101338"
% 4.05/1.41 % (4101348)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=2910264865:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 4.05/1.41 % (4101349)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1086823671:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 4.05/1.41 % (4101351)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3938222687:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 4.05/1.41 % (4101346)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=1734683551:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 4.05/1.41 % (4101352)dis-21_1_sil=8000:lcm=predicate:random_seed=2448887428:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 4.05/1.41 % (4101347)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=1532206462:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 4.05/1.41 % (4101349)Refutation not found, incomplete strategy
% 4.05/1.41 % (4101349)------------------------------
% 4.05/1.41 % (4101349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.41 % (4101349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.41 % (4101349)CaDiCaL version: 2.1.3
% 4.05/1.41 % (4101349)Termination reason: Refutation not found, incomplete strategy
% 4.05/1.41 % (4101349)Time elapsed: 0.001 s
% 4.05/1.41 % (4101349)Peak memory usage: 87 MB
% 4.05/1.41 % (4101352)Also succeeded, but the first one will report.
% 4.05/1.41 % (4101351)Also succeeded, but the first one will report.
% 4.05/1.41 % (4101350)Refutation found. Thanks to Tanya!
% 4.05/1.41 % SZS status Theorem for theBenchmark
% 4.05/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 4.05/1.41 % (4101350)------------------------------
% 4.05/1.41 % (4101350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.41 % (4101350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.41 % (4101350)CaDiCaL version: 2.1.3
% 4.05/1.41 % (4101350)Termination reason: Refutation
% 4.05/1.41 % (4101350)Time elapsed: 0.003 s
% 4.05/1.41 % (4101350)Peak memory usage: 88 MB
% 4.05/1.41 % (4101350)Instructions burned: 2 (million)
% 4.05/1.41 % (4101350)------------------------------
% 4.05/1.41 % (4101350)------------------------------
% 4.05/1.41 % (4101338)Success in time 0.502 s
% 4.05/1.42 % Vampire exiting
%------------------------------------------------------------------------------