%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET633+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 : n020.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 12:41:28 PM UTC 2026
% Result : Theorem 3.68s 1.47s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 37 ( 2 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 34 ( 15 ~; 7 |; 9 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 22 !; 6 ?)
% 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,X2] :
( ( subset(X0,X1)
& subset(X2,X1) )
=> subset(union(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_subset) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( ( subset(difference(X0,X1),X2)
& subset(difference(X1,X0),X2) )
=> subset(symmetric_difference(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th115) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(difference(X0,X1),X2)
& subset(difference(X1,X0),X2) )
=> subset(symmetric_difference(X0,X1),X2) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
? [X0,X1,X2] :
( ~ subset(symmetric_difference(X0,X1),X2)
& subset(difference(X0,X1),X2)
& subset(difference(X1,X0),X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f12,plain,
? [X0,X1,X2] :
( ~ subset(symmetric_difference(X0,X1),X2)
& subset(difference(X0,X1),X2)
& subset(difference(X1,X0),X2) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( subset(union(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f14,plain,
! [X0,X1,X2] :
( subset(union(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(flattening,[],[f13]) ).
fof(f16,plain,
( ~ subset(symmetric_difference(sK0,sK1),sK2)
& subset(difference(sK0,sK1),sK2)
& subset(difference(sK1,sK0),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f12]) ).
fof(f25,plain,
subset(difference(sK1,sK0),sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
subset(difference(sK0,sK1),sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
~ subset(symmetric_difference(sK0,sK1),sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X2,X0,X1] :
( subset(union(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f43,plain,
~ subset(union(difference(sK0,sK1),difference(sK1,sK0)),sK2),
inference(definition_unfolding,[],[f27,f29]) ).
fof(f57,plain,
( ~ subset(difference(sK0,sK1),sK2)
| ~ subset(difference(sK1,sK0),sK2) ),
inference(resolution,[],[f35,f43]) ).
fof(f60,plain,
~ subset(difference(sK1,sK0),sK2),
inference(forward_subsumption_resolution,[],[f57,f26]) ).
fof(f61,plain,
$false,
inference(forward_subsumption_resolution,[],[f60,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET633+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 : n020.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 02:24:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 3.68/1.47 % (3975312)Detected formulas, will run a generic FOF schedule.
% 3.68/1.47 % (3975319)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=1576311537:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.68/1.47 % (3975323)dis-21_1_sil=8000:lcm=predicate:random_seed=208467577: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)
% 3.68/1.47 % (3975317)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=2947669446:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.68/1.47 % (3975320)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3681863561:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.68/1.47 % (3975321)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4131857915:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.68/1.47 % (3975318)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=2575149545:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.68/1.47 % (3975322)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=528683247:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.68/1.47 % (3975320)Refutation not found, incomplete strategy
% 3.68/1.47 % (3975320)------------------------------
% 3.68/1.47 % (3975320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.47 % (3975320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.47 % (3975320)CaDiCaL version: 2.1.3
% 3.68/1.47 % (3975320)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.47 % (3975320)Time elapsed: 0.001 s
% 3.68/1.47 % (3975320)Peak memory usage: 88 MB
% 3.68/1.47 % (3975321)First to succeed.
% 3.68/1.47 % (3975323)Also succeeded, but the first one will report.
% 3.68/1.47 % (3975321)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3975312"
% 3.68/1.47 % (3975322)Also succeeded, but the first one will report.
% 3.68/1.47 % (3975320)------------------------------
% 3.68/1.47 % (3975320)------------------------------
% 3.68/1.47 % (3975321)Refutation found. Thanks to Tanya!
% 3.68/1.47 % SZS status Theorem for theBenchmark
% 3.68/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.47 % (3975321)------------------------------
% 3.68/1.47 % (3975321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.47 % (3975321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.47 % (3975321)CaDiCaL version: 2.1.3
% 3.68/1.47 % (3975321)Termination reason: Refutation
% 3.68/1.47 % (3975321)Time elapsed: 0.002 s
% 3.68/1.47 % (3975321)Peak memory usage: 88 MB
% 3.68/1.47 % (3975321)Instructions burned: 2 (million)
% 3.68/1.47 % (3975321)------------------------------
% 3.68/1.47 % (3975321)------------------------------
% 3.68/1.47 % (3975312)Success in time 0.441 s
% 3.68/1.47 % Vampire exiting
%------------------------------------------------------------------------------