%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU134+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:47:21 PM UTC 2026
% Result : Theorem 2.80s 1.35s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 3 unt; 0 def)
% Number of atoms : 41 ( 18 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 42 ( 19 ~; 16 |; 3 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(f37,conjecture,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f38,negated_conjecture,
~ ! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f62,plain,
? [X0,X1] :
( set_difference(X0,X1) = empty_set
<~> subset(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f72,plain,
! [X0,X1] :
( ( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f73,plain,
? [X0,X1] :
( ( ~ subset(X0,X1)
| empty_set != set_difference(X0,X1) )
& ( subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f74,plain,
( ( ~ subset(sK0,sK1)
| empty_set != set_difference(sK0,sK1) )
& ( subset(sK0,sK1)
| empty_set = set_difference(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f73]) ).
fof(f100,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f101,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f111,plain,
( empty_set = set_difference(sK0,sK1)
| subset(sK0,sK1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f112,plain,
( empty_set != set_difference(sK0,sK1)
| ~ subset(sK0,sK1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f216,plain,
( empty_set != empty_set
| subset(sK0,sK1)
| subset(sK0,sK1) ),
inference(superposition,[],[f100,f111]) ).
fof(f220,plain,
( empty_set != empty_set
| subset(sK0,sK1) ),
inference(duplicate_literal_removal,[],[f216]) ).
fof(f221,plain,
subset(sK0,sK1),
inference(trivial_inequality_removal,[],[f220]) ).
fof(f229,plain,
( empty_set != empty_set
| ~ subset(sK0,sK1)
| ~ subset(sK0,sK1) ),
inference(superposition,[],[f112,f101]) ).
fof(f233,plain,
( empty_set != empty_set
| ~ subset(sK0,sK1) ),
inference(duplicate_literal_removal,[],[f229]) ).
fof(f234,plain,
~ subset(sK0,sK1),
inference(trivial_inequality_removal,[],[f233]) ).
fof(f235,plain,
$false,
inference(forward_subsumption_resolution,[],[f234,f221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU134+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n001.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 03:46:32 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 2.80/1.35 % (4189906)Detected formulas, will run a generic FOF schedule.
% 2.80/1.35 % (4189915)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3915843993:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.80/1.35 % (4189915)First to succeed.
% 2.80/1.35 % (4189915)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4189906"
% 2.80/1.35 % (4189914)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1924069739:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.80/1.35 % (4189913)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=1974957383:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.80/1.35 % (4189916)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=159144082:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.80/1.35 % (4189912)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=357926084:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.80/1.35 % (4189911)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=3498376945:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.80/1.35 % (4189917)dis-21_1_sil=8000:lcm=predicate:random_seed=4244434901: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)
% 2.80/1.35 % (4189917)Also succeeded, but the first one will report.
% 2.80/1.35 % (4189916)Also succeeded, but the first one will report.
% 2.80/1.35 % (4189914)Also succeeded, but the first one will report.
% 2.80/1.35 % (4189915)Refutation found. Thanks to Tanya!
% 2.80/1.35 % SZS status Theorem for theBenchmark
% 2.80/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.80/1.35 % (4189915)------------------------------
% 2.80/1.35 % (4189915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.35 % (4189915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.35 % (4189915)CaDiCaL version: 2.1.3
% 2.80/1.35 % (4189915)Termination reason: Refutation
% 2.80/1.35 % (4189915)Time elapsed: 0.003 s
% 2.80/1.35 % (4189915)Peak memory usage: 88 MB
% 2.80/1.35 % (4189915)Instructions burned: 4 (million)
% 2.80/1.35 % (4189915)------------------------------
% 2.80/1.35 % (4189915)------------------------------
% 2.80/1.35 % (4189906)Success in time 0.319 s
% 2.80/1.35 % Vampire exiting
%------------------------------------------------------------------------------