%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET596+3 : 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 : 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 12:41:16 PM UTC 2026
% Result : Theorem 3.38s 16.26s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 7 unt; 1 def)
% Number of atoms : 40 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 14 ~; 7 |; 8 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_empty_set_is_empty_set) ).
fof(f2,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(intersection(X0,X2),intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_of_subset) ).
fof(f11,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X1)
& intersection(X1,X2) = empty_set )
=> intersection(X0,X2) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th55) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X1)
& intersection(X1,X2) = empty_set )
=> intersection(X0,X2) = empty_set ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
? [X0,X1,X2] :
( empty_set != intersection(X0,X2)
& subset(X0,X1)
& intersection(X1,X2) = empty_set ),
inference(ennf_transformation,[],[f12]) ).
fof(f14,plain,
? [X0,X1,X2] :
( empty_set != intersection(X0,X2)
& subset(X0,X1)
& intersection(X1,X2) = empty_set ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X2),intersection(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f17,plain,
( empty_set != intersection(sK0,sK2)
& subset(sK0,sK1)
& empty_set = intersection(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f14]) ).
fof(f25,plain,
empty_set = intersection(sK1,sK2),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
empty_set != intersection(sK0,sK2),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f42,plain,
! [X2,X0,X1] :
( subset(intersection(X0,X2),intersection(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f43,definition,
~ sP4(empty_set),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f44,plain,
sP4(intersection(sK0,sK2)),
inference(inequality_splitting,[],[f27,f43]) ).
fof(f63,plain,
! [X0] :
( subset(intersection(X0,sK2),empty_set)
| ~ subset(X0,sK1) ),
inference(superposition,[],[f42,f25]) ).
fof(f70,plain,
! [X0] :
( empty_set = intersection(X0,sK2)
| ~ subset(X0,sK1) ),
inference(resolution,[],[f63,f36]) ).
fof(f89,plain,
( sP4(empty_set)
| ~ subset(sK0,sK1) ),
inference(superposition,[],[f44,f70]) ).
fof(f92,plain,
~ subset(sK0,sK1),
inference(forward_subsumption_resolution,[],[f89,f43]) ).
fof(f94,plain,
$false,
inference(forward_subsumption_resolution,[],[f92,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET596+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/15.40 % Computer : n013.cluster.edu
% 0.12/15.40 % Model : x86_64 x86_64
% 0.12/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.40 % Memory : 8046.5625MB
% 0.12/15.40 % OS : Linux 6.8.0-71-generic
% 0.12/15.40 % CPULimit : 300
% 0.12/15.40 % WCLimit : 300
% 0.12/15.40 % DateTime : Mon Sep 28 02:16:53 UTC 2026
% 0.12/15.40 % CPUTime :
% 0.12/15.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/15.44 Running first-order theorem proving
% 0.12/15.44 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
% 3.38/16.26 % (744818)Detected formulas, will run a generic FOF schedule.
% 3.38/16.26 % (744823)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=2747608024:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.38/16.26 % (744824)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=2649993291:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.38/16.26 % (744826)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=388510454:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.38/16.26 % (744825)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=834821878:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.38/16.26 % (744827)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3248003912:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.38/16.26 % (744828)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=367829075:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.38/16.26 % (744829)dis-21_1_sil=8000:lcm=predicate:random_seed=1156641361: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)
% 3.38/16.26 % (744826)First to succeed.
% 3.38/16.26 % (744827)Also succeeded, but the first one will report.
% 3.38/16.26 % (744826)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-744818"
% 3.38/16.26 % (744828)Also succeeded, but the first one will report.
% 3.38/16.26 % (744829)Instruction limit reached!
% 3.38/16.26 % (744829)------------------------------
% 3.38/16.26 % (744829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/16.26 % (744829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/16.26 % (744829)CaDiCaL version: 2.1.3
% 3.38/16.26 % (744829)Termination reason: Instruction limit
% 3.38/16.26 % (744829)Termination phase: Saturation
% 3.38/16.26 % (744829)Time elapsed: 0.078 s
% 3.38/16.26 % (744829)Peak memory usage: 89 MB
% 3.38/16.26 % (744829)Instructions burned: 129 (million)
% 3.38/16.26 % (744837)lrs+10_1_sil=8000:sp=occurrence:random_seed=1483677108:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.38/16.26 % (744837)Also succeeded, but the first one will report.
% 3.38/16.26 % (744826)Refutation found. Thanks to Tanya!
% 3.38/16.26 % SZS status Theorem for theBenchmark
% 3.38/16.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/16.26 % (744826)------------------------------
% 3.38/16.26 % (744826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/16.26 % (744826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/16.26 % (744826)CaDiCaL version: 2.1.3
% 3.38/16.26 % (744826)Termination reason: Refutation
% 3.38/16.26 % (744826)Time elapsed: 0.003 s
% 3.38/16.26 % (744826)Peak memory usage: 89 MB
% 3.38/16.26 % (744826)Instructions burned: 2 (million)
% 3.38/16.26 % (744826)------------------------------
% 3.38/16.26 % (744826)------------------------------
% 3.38/16.26 % (744818)Success in time 0.421 s
% 3.38/16.26 % Vampire exiting
%------------------------------------------------------------------------------