%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET620+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 : n018.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 12:41:24 PM UTC 2026
% Result : Theorem 2.58s 1.23s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f2,axiom,
! [X0,X1] : difference(X0,intersection(X0,X1)) = difference(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_into_intersection) ).
fof(f3,axiom,
! [X0,X1,X2] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_distributes_over_union) ).
fof(f9,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f14,conjecture,
! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th96) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] : symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1] : symmetric_difference(X0,X1) != difference(union(X0,X1),intersection(X0,X1)),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
symmetric_difference(sK0,sK1) != difference(union(sK0,sK1),intersection(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
fof(f27,plain,
symmetric_difference(sK0,sK1) != difference(union(sK0,sK1),intersection(sK0,sK1)),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f33,plain,
! [X2,X0,X1] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
inference(cnf_transformation,[],[f3]) ).
fof(f38,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f42,plain,
! [X0,X1] : difference(X0,X1) = difference(X0,intersection(X0,X1)),
inference(cnf_transformation,[],[f2]) ).
fof(f47,plain,
difference(union(sK0,sK1),intersection(sK0,sK1)) != union(difference(sK0,sK1),difference(sK1,sK0)),
inference(definition_unfolding,[],[f27,f29]) ).
fof(f59,plain,
! [X0,X1] : difference(X1,X0) = difference(X1,intersection(X0,X1)),
inference(superposition,[],[f42,f38]) ).
fof(f85,plain,
! [X2,X0,X1] : difference(union(X0,X2),intersection(X0,X1)) = union(difference(X0,X1),difference(X2,intersection(X0,X1))),
inference(superposition,[],[f33,f42]) ).
fof(f225,plain,
! [X0,X1] : union(difference(X1,X0),difference(X0,X1)) = difference(union(X1,X0),intersection(X1,X0)),
inference(superposition,[],[f85,f59]) ).
fof(f843,plain,
union(difference(sK0,sK1),difference(sK1,sK0)) != union(difference(sK0,sK1),difference(sK1,sK0)),
inference(superposition,[],[f47,f225]) ).
fof(f871,plain,
$false,
inference(trivial_inequality_removal,[],[f843]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET620+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 02:24:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 2.58/1.23 % (2932358)Detected formulas, will run a generic FOF schedule.
% 2.58/1.23 % (2932367)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2806422996:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/1.23 % (2932367)First to succeed.
% 2.58/1.23 % (2932367)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2932358"
% 2.58/1.23 % (2932368)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2024462752:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/1.23 % (2932369)dis-21_1_sil=8000:lcm=predicate:random_seed=232967628: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)
% 2.58/1.23 % (2932366)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3480197454:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/1.23 % (2932363)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=2034714048:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/1.23 % (2932364)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=2213566888:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/1.23 % (2932365)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=822881551:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/1.23 % (2932366)Refutation not found, incomplete strategy
% 2.58/1.23 % (2932366)------------------------------
% 2.58/1.23 % (2932366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.23 % (2932366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.23 % (2932366)CaDiCaL version: 2.1.3
% 2.58/1.23 % (2932366)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.23 % (2932366)Time elapsed: 0.002 s
% 2.58/1.23 % (2932366)Peak memory usage: 88 MB
% 2.58/1.23 % (2932366)Instructions burned: 1 (million)
% 2.58/1.23 % (2932369)Also succeeded, but the first one will report.
% 2.58/1.23 % (2932368)Also succeeded, but the first one will report.
% 2.58/1.23 % (2932367)Refutation found. Thanks to Tanya!
% 2.58/1.23 % SZS status Theorem for theBenchmark
% 2.58/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.23 % (2932367)------------------------------
% 2.58/1.23 % (2932367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.23 % (2932367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.23 % (2932367)CaDiCaL version: 2.1.3
% 2.58/1.23 % (2932367)Termination reason: Refutation
% 2.58/1.23 % (2932367)Time elapsed: 0.012 s
% 2.58/1.23 % (2932367)Peak memory usage: 89 MB
% 2.58/1.23 % (2932367)Instructions burned: 34 (million)
% 2.58/1.23 % (2932367)------------------------------
% 2.58/1.23 % (2932367)------------------------------
% 2.58/1.23 % (2932358)Success in time 0.3 s
% 2.58/1.23 % Vampire exiting
%------------------------------------------------------------------------------