%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET014+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 : 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 12:39:32 PM UTC 2026
% Result : Theorem 3.45s 1.44s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 55 ( 6 unt; 0 def)
% Number of atoms : 166 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 184 ( 73 ~; 85 |; 19 &)
% ( 5 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 124 ( 113 !; 11 ?)
% 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(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,X1,X2] :
( ( subset(X1,X0)
& subset(X2,X0) )
<=> subset(union(X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI45) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X1,X0)
& subset(X2,X0) )
<=> subset(union(X1,X2),X0) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1,X2] :
( ( subset(X1,X0)
& subset(X2,X0) )
<~> subset(union(X1,X2),X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ( ~ subset(union(X1,X2),X0)
| ~ subset(X1,X0)
| ~ subset(X2,X0) )
& ( subset(union(X1,X2),X0)
| ( subset(X1,X0)
& subset(X2,X0) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ( ~ subset(union(X1,X2),X0)
| ~ subset(X1,X0)
| ~ subset(X2,X0) )
& ( subset(union(X1,X2),X0)
| ( subset(X1,X0)
& subset(X2,X0) ) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( ( ~ subset(union(sK1,sK2),sK0)
| ~ subset(sK1,sK0)
| ~ subset(sK2,sK0) )
& ( subset(union(sK1,sK2),sK0)
| ( subset(sK1,sK0)
& subset(sK2,sK0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f20]) ).
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(nnf_transformation,[],[f5]) ).
fof(f23,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,[],[f22]) ).
fof(f24,plain,
( subset(union(sK1,sK2),sK0)
| subset(sK2,sK0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f25,plain,
( subset(union(sK1,sK2),sK0)
| subset(sK1,sK0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
( ~ subset(union(sK1,sK2),sK0)
| ~ subset(sK1,sK0)
| ~ subset(sK2,sK0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f28,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f29,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f31,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f32,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(sK3(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ),
inference(resolution,[],[f31,f29]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(sK3(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[],[f32,f29]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ member(sK3(X0,X1),X2)
| ~ subset(X2,X1)
| subset(X0,X1) ),
inference(resolution,[],[f27,f29]) ).
fof(f40,plain,
! [X2,X0,X1] :
( member(sK3(union(X0,X1),X2),X1)
| member(sK3(union(X0,X1),X2),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[],[f30,f28]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( ~ member(sK3(X3,X2),X0)
| subset(X3,X2)
| ~ subset(union(X0,X1),X2) ),
inference(resolution,[],[f39,f32]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( ~ member(sK3(X3,X2),X1)
| subset(X3,X2)
| ~ subset(union(X0,X1),X2) ),
inference(resolution,[],[f39,f31]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ member(sK3(X2,X1),X3)
| subset(X2,X1)
| ~ subset(X0,X1)
| ~ subset(X3,X0) ),
inference(resolution,[],[f39,f27]) ).
fof(f59,plain,
! [X2,X0,X1] :
( subset(X0,X1)
| ~ subset(union(X0,X2),X1)
| subset(X0,X1) ),
inference(resolution,[],[f45,f28]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ subset(union(X0,X2),X1)
| subset(X0,X1) ),
inference(duplicate_literal_removal,[],[f59]) ).
fof(f67,plain,
( subset(sK1,sK0)
| subset(sK1,sK0) ),
inference(resolution,[],[f63,f25]) ).
fof(f72,plain,
subset(sK1,sK0),
inference(duplicate_literal_removal,[],[f67]) ).
fof(f75,plain,
! [X2,X0,X1] :
( member(sK3(union(X0,X1),X2),X0)
| subset(union(X0,X1),X2)
| ~ subset(X1,X2)
| subset(union(X0,X1),X2) ),
inference(resolution,[],[f40,f39]) ).
fof(f77,plain,
! [X2,X0,X1] :
( member(sK3(union(X0,X1),union(X1,X2)),X0)
| subset(union(X0,X1),union(X1,X2))
| subset(union(X0,X1),union(X1,X2)) ),
inference(resolution,[],[f40,f38]) ).
fof(f79,plain,
! [X2,X0,X1] :
( member(sK3(union(X0,X1),union(X1,X2)),X0)
| subset(union(X0,X1),union(X1,X2)) ),
inference(duplicate_literal_removal,[],[f77]) ).
fof(f81,plain,
! [X2,X0,X1] :
( member(sK3(union(X0,X1),X2),X0)
| subset(union(X0,X1),X2)
| ~ subset(X1,X2) ),
inference(duplicate_literal_removal,[],[f75]) ).
fof(f97,plain,
! [X2,X0,X1] :
( subset(X0,X1)
| ~ subset(union(X2,X0),X1)
| subset(X0,X1) ),
inference(resolution,[],[f46,f28]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ subset(union(X2,X0),X1)
| subset(X0,X1) ),
inference(duplicate_literal_removal,[],[f97]) ).
fof(f110,plain,
! [X2,X0,X1] :
( subset(X0,X1)
| ~ subset(X2,X1)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(resolution,[],[f47,f28]) ).
fof(f118,plain,
! [X2,X0,X1] :
( subset(X0,X1)
| ~ subset(X2,X1)
| ~ subset(X0,X2) ),
inference(duplicate_literal_removal,[],[f110]) ).
fof(f131,plain,
( subset(sK2,sK0)
| subset(sK2,sK0) ),
inference(resolution,[],[f105,f24]) ).
fof(f139,plain,
subset(sK2,sK0),
inference(duplicate_literal_removal,[],[f131]) ).
fof(f156,plain,
! [X2,X0,X1] :
( subset(union(X0,X1),X2)
| ~ subset(X1,X2)
| ~ subset(X0,X2)
| subset(union(X0,X1),X2) ),
inference(resolution,[],[f81,f39]) ).
fof(f166,plain,
! [X2,X0,X1] :
( subset(union(X0,X1),X2)
| ~ subset(X1,X2)
| ~ subset(X0,X2) ),
inference(duplicate_literal_removal,[],[f156]) ).
fof(f233,plain,
! [X0] :
( ~ subset(X0,sK0)
| ~ subset(union(sK1,sK2),X0)
| ~ subset(sK1,sK0)
| ~ subset(sK2,sK0) ),
inference(resolution,[],[f118,f26]) ).
fof(f237,plain,
! [X0] :
( ~ subset(X0,sK0)
| ~ subset(union(sK1,sK2),X0)
| ~ subset(sK2,sK0) ),
inference(forward_subsumption_resolution,[],[f233,f72]) ).
fof(f238,plain,
! [X0] :
( ~ subset(union(sK1,sK2),X0)
| ~ subset(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f237,f139]) ).
fof(f255,plain,
! [X0,X1] :
( subset(union(X0,X1),union(X1,X0))
| subset(union(X0,X1),union(X1,X0)) ),
inference(resolution,[],[f79,f37]) ).
fof(f281,plain,
! [X0,X1] : subset(union(X0,X1),union(X1,X0)),
inference(duplicate_literal_removal,[],[f255]) ).
fof(f358,plain,
~ subset(union(sK2,sK1),sK0),
inference(resolution,[],[f281,f238]) ).
fof(f508,plain,
( ~ subset(sK1,sK0)
| ~ subset(sK2,sK0) ),
inference(resolution,[],[f166,f358]) ).
fof(f527,plain,
~ subset(sK2,sK0),
inference(forward_subsumption_resolution,[],[f508,f72]) ).
fof(f532,plain,
$false,
inference(forward_subsumption_resolution,[],[f527,f139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 00:08:47 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.45/1.44 % (3136634)Detected formulas, will run a generic FOF schedule.
% 3.45/1.44 % (3136640)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=932850472:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.45/1.44 % (3136643)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1211234929:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.45/1.44 % (3136642)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3416974818:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.45/1.44 % (3136639)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=3423090037:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.45/1.44 % (3136641)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=2986344678:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.45/1.44 % (3136642)Refutation not found, incomplete strategy
% 3.45/1.44 % (3136642)------------------------------
% 3.45/1.44 % (3136642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.44 % (3136642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.44 % (3136642)CaDiCaL version: 2.1.3
% 3.45/1.44 % (3136642)Termination reason: Refutation not found, incomplete strategy
% 3.45/1.44 % (3136642)Time elapsed: 0.001 s
% 3.45/1.44 % (3136642)Peak memory usage: 88 MB
% 3.45/1.44 % (3136644)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1625822387:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.45/1.44 % (3136643)First to succeed.
% 3.45/1.44 % (3136643)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3136634"
% 3.45/1.44 % (3136644)Also succeeded, but the first one will report.
% 3.45/1.44 % (3136645)dis-21_1_sil=8000:lcm=predicate:random_seed=2502038660:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.45/1.44 % (3136645)Also succeeded, but the first one will report.
% 3.45/1.44 % (3136642)------------------------------
% 3.45/1.44 % (3136642)------------------------------
% 3.45/1.44 % (3136643)Refutation found. Thanks to Tanya!
% 3.45/1.44 % SZS status Theorem for theBenchmark
% 3.45/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.45/1.44 % (3136643)------------------------------
% 3.45/1.44 % (3136643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.44 % (3136643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.44 % (3136643)CaDiCaL version: 2.1.3
% 3.45/1.44 % (3136643)Termination reason: Refutation
% 3.45/1.44 % (3136643)Time elapsed: 0.009 s
% 3.45/1.44 % (3136643)Peak memory usage: 88 MB
% 3.45/1.44 % (3136643)Instructions burned: 11 (million)
% 3.45/1.44 % (3136643)------------------------------
% 3.45/1.44 % (3136643)------------------------------
% 3.45/1.44 % (3136634)Success in time 0.402 s
% 3.45/1.44 % Vampire exiting
%------------------------------------------------------------------------------