%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET605+3 : TPTP v9.3.1. Released v2.2.0.
% 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 12:41:19 PM UTC 2026
% Result : Theorem 3.64s 6.49s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 11 unt; 1 def)
% Number of atoms : 25 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 5 |; 1 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : subset(X0,union(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_union) ).
fof(f2,axiom,
! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).
fof(f12,conjecture,
! [X0,X1] : difference(X0,union(X0,X1)) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th76) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : difference(X0,union(X0,X1)) = empty_set,
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f15,plain,
? [X0,X1] : empty_set != difference(X0,union(X0,X1)),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
! [X0,X1] :
( ( difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| difference(X0,X1) != empty_set ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f29,plain,
empty_set != difference(sK2,union(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f15]) ).
fof(f30,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X0,X1] :
( difference(X0,X1) = empty_set
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f52,plain,
empty_set != difference(sK2,union(sK2,sK3)),
inference(cnf_transformation,[],[f29]) ).
fof(f57,definition,
! [X0,X1] :
( sQ4_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ4_eqProxy])],[equality_proxy_definition]) ).
fof(f58,plain,
! [X0,X1] :
( sQ4_eqProxy(difference(X0,X1),empty_set)
| ~ subset(X0,X1) ),
inference(equality_proxy_replacement,[],[f32,f57]) ).
fof(f64,plain,
~ sQ4_eqProxy(empty_set,difference(sK2,union(sK2,sK3))),
inference(equality_proxy_replacement,[],[f52,f57]) ).
fof(f66,plain,
! [X0,X1] :
( sQ4_eqProxy(X1,X0)
| ~ sQ4_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f57]) ).
fof(f67,plain,
~ sQ4_eqProxy(difference(sK2,union(sK2,sK3)),empty_set),
inference(resolution,[],[f66,f64]) ).
fof(f69,plain,
~ subset(sK2,union(sK2,sK3)),
inference(resolution,[],[f58,f67]) ).
fof(f72,plain,
$false,
inference(resolution,[],[f69,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET605+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/5.37 % Computer : n001.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 28 02:23:38 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.40 Running first-order theorem proving
% 0.14/5.40 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
% 3.64/6.49 % (4155028)Detected formulas, will run a generic FOF schedule.
% 3.64/6.49 % (4155035)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=3841422250:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.64/6.49 % (4155039)dis-21_1_sil=8000:lcm=predicate:random_seed=1168096925: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)
% 3.64/6.49 % (4155036)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=727066328:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.64/6.49 % (4155033)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=222202492:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.64/6.49 % (4155034)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=212353576:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.64/6.49 % (4155037)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1796559474:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.64/6.49 % (4155038)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=703244521:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.64/6.49 % (4155036)Also succeeded, but the first one will report.
% 3.64/6.49 % (4155039)First to succeed.
% 3.64/6.49 % (4155037)Also succeeded, but the first one will report.
% 3.64/6.49 % (4155038)Also succeeded, but the first one will report.
% 3.64/6.49 % (4155039)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4155028"
% 3.64/6.49 % (4155039)Refutation found. Thanks to Tanya!
% 3.64/6.49 % SZS status Theorem for theBenchmark
% 3.64/6.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/6.49 % (4155039)------------------------------
% 3.64/6.49 % (4155039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/6.49 % (4155039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/6.49 % (4155039)CaDiCaL version: 2.1.3
% 3.64/6.49 % (4155039)Termination reason: Refutation
% 3.64/6.49 % (4155039)Time elapsed: 0.002 s
% 3.64/6.49 % (4155039)Peak memory usage: 88 MB
% 3.64/6.49 % (4155039)Instructions burned: 1 (million)
% 3.64/6.49 % (4155039)------------------------------
% 3.64/6.49 % (4155039)------------------------------
% 3.64/6.49 % (4155028)Success in time 0.429 s
% 3.64/6.49 % Vampire exiting
%------------------------------------------------------------------------------