%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU097+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:47:14 PM UTC 2026
% Result : Theorem 3.36s 1.38s
% Output : Refutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 46 ( 2 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 43 ( 20 ~; 10 |; 9 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
fof(f30,axiom,
! [X0,X1] :
( ( finite(X0)
& finite(X1) )
=> finite(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_finset_1) ).
fof(f57,axiom,
! [X0,X1] :
( finite(X0)
=> finite(set_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finset_1) ).
fof(f60,conjecture,
! [X0,X1] :
( ( finite(X0)
& finite(X1) )
=> finite(symmetric_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finset_1) ).
fof(f61,negated_conjecture,
~ ! [X0,X1] :
( ( finite(X0)
& finite(X1) )
=> finite(symmetric_difference(X0,X1)) ),
inference(negated_conjecture,[status(cth)],[f60]) ).
fof(f73,plain,
? [X0,X1] :
( ~ finite(symmetric_difference(X0,X1))
& finite(X0)
& finite(X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f74,plain,
? [X0,X1] :
( ~ finite(symmetric_difference(X0,X1))
& finite(X0)
& finite(X1) ),
inference(flattening,[],[f73]) ).
fof(f78,plain,
! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f79,plain,
! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(flattening,[],[f78]) ).
fof(f86,plain,
! [X0,X1] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f91,plain,
( ~ finite(symmetric_difference(sK0,sK1))
& finite(sK0)
& finite(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f74]) ).
fof(f97,plain,
finite(sK1),
inference(cnf_transformation,[],[f91]) ).
fof(f98,plain,
finite(sK0),
inference(cnf_transformation,[],[f91]) ).
fof(f99,plain,
~ finite(symmetric_difference(sK0,sK1)),
inference(cnf_transformation,[],[f91]) ).
fof(f101,plain,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f112,plain,
! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f121,plain,
! [X0,X1] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f131,plain,
~ finite(set_union2(set_difference(sK0,sK1),set_difference(sK1,sK0))),
inference(definition_unfolding,[],[f99,f101]) ).
fof(f155,plain,
( ~ finite(set_difference(sK1,sK0))
| ~ finite(set_difference(sK0,sK1)) ),
inference(resolution,[],[f112,f131]) ).
fof(f161,plain,
( ~ finite(set_difference(sK0,sK1))
| ~ finite(sK1) ),
inference(resolution,[],[f155,f121]) ).
fof(f163,plain,
~ finite(set_difference(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f161,f97]) ).
fof(f164,plain,
~ finite(sK0),
inference(resolution,[],[f163,f121]) ).
fof(f166,plain,
$false,
inference(forward_subsumption_resolution,[],[f164,f98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU097+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n002.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 03:35:52 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 3.36/1.38 % (4123710)Detected formulas, will run a generic FOF schedule.
% 3.36/1.38 % (4123716)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=407242459:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.36/1.38 % (4123719)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2441250633:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.36/1.38 % (4123721)dis-21_1_sil=8000:lcm=predicate:random_seed=358352625: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)
% 3.36/1.38 % (4123717)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=3969744916:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.36/1.38 % (4123718)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=542591109:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.36/1.38 % (4123715)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=2353508966:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.36/1.38 % (4123718)Refutation not found, incomplete strategy
% 3.36/1.38 % (4123718)------------------------------
% 3.36/1.38 % (4123718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.38 % (4123718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.38 % (4123718)CaDiCaL version: 2.1.3
% 3.36/1.38 % (4123718)Termination reason: Refutation not found, incomplete strategy
% 3.36/1.38 % (4123718)Time elapsed: 0.001 s
% 3.36/1.38 % (4123718)Peak memory usage: 88 MB
% 3.36/1.38 % (4123719)First to succeed.
% 3.36/1.38 % (4123719)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4123710"
% 3.36/1.38 % (4123721)Also succeeded, but the first one will report.
% 3.36/1.38 % (4123720)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4128148477:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.36/1.38 % (4123720)Also succeeded, but the first one will report.
% 3.36/1.38 % (4123718)------------------------------
% 3.36/1.38 % (4123718)------------------------------
% 3.36/1.38 % (4123719)Refutation found. Thanks to Tanya!
% 3.36/1.38 % SZS status Theorem for theBenchmark
% 3.36/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.36/1.38 % (4123719)------------------------------
% 3.36/1.38 % (4123719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.38 % (4123719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.38 % (4123719)CaDiCaL version: 2.1.3
% 3.36/1.38 % (4123719)Termination reason: Refutation
% 3.36/1.38 % (4123719)Time elapsed: 0.003 s
% 3.36/1.38 % (4123719)Peak memory usage: 88 MB
% 3.36/1.38 % (4123719)Instructions burned: 3 (million)
% 3.36/1.38 % (4123719)------------------------------
% 3.36/1.38 % (4123719)------------------------------
% 3.36/1.38 % (4123710)Success in time 0.413 s
% 3.36/1.39 % Vampire exiting
%------------------------------------------------------------------------------