%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET044+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:39:46 PM UTC 2026
% Result : Theorem 3.48s 1.37s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 4 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 61 ( 26 ~; 17 |; 10 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 35 ( 25 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
! [X1] :
( element(X1,X0)
<=> element(X1,X1) )
=> ~ ! [X2] :
? [X3] :
! [X4] :
( element(X4,X3)
<=> ~ element(X4,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel40) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
! [X1] :
( element(X1,X0)
<=> element(X1,X1) )
=> ~ ! [X2] :
? [X3] :
! [X4] :
( element(X4,X3)
<=> ~ element(X4,X2) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X2] :
? [X3] :
! [X4] :
( element(X4,X3)
<=> ~ element(X4,X2) )
& ? [X0] :
! [X1] :
( element(X1,X0)
<=> element(X1,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ! [X2] :
? [X3] :
! [X4] :
( ( element(X4,X3)
| element(X4,X2) )
& ( ~ element(X4,X2)
| ~ element(X4,X3) ) )
& ? [X0] :
! [X1] :
( ( element(X1,X0)
| ~ element(X1,X1) )
& ( element(X1,X1)
| ~ element(X1,X0) ) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
( ! [X0] :
? [X1] :
! [X2] :
( ( element(X2,X1)
| element(X2,X0) )
& ( ~ element(X2,X0)
| ~ element(X2,X1) ) )
& ? [X3] :
! [X4] :
( ( element(X4,X3)
| ~ element(X4,X4) )
& ( element(X4,X4)
| ~ element(X4,X3) ) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ! [X0,X2] :
( ( element(X2,sK0(X0))
| element(X2,X0) )
& ( ~ element(X2,X0)
| ~ element(X2,sK0(X0)) ) )
& ! [X4] :
( ( element(X4,sK1)
| ~ element(X4,X4) )
& ( element(X4,X4)
| ~ element(X4,sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(X3,sK1)],[f5]) ).
fof(f7,plain,
! [X4] :
( element(X4,X4)
| ~ element(X4,sK1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
! [X4] :
( element(X4,sK1)
| ~ element(X4,X4) ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
! [X2,X0] :
( ~ element(X2,sK0(X0))
| ~ element(X2,X0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X2,X0] :
( element(X2,sK0(X0))
| element(X2,X0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f11,plain,
! [X0] :
( ~ element(sK0(X0),sK1)
| ~ element(sK0(X0),X0) ),
inference(resolution,[],[f9,f7]) ).
fof(f14,plain,
~ element(sK0(sK1),sK1),
inference(factoring,[],[f11]) ).
fof(f15,plain,
~ element(sK0(sK1),sK0(sK1)),
inference(resolution,[],[f14,f8]) ).
fof(f16,plain,
element(sK0(sK1),sK1),
inference(resolution,[],[f15,f10]) ).
fof(f18,plain,
$false,
inference(forward_subsumption_resolution,[],[f16,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET044+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 00:21:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.48/1.37 % (4027557)Detected formulas, will run a generic FOF schedule.
% 3.48/1.37 % (4027562)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=3425349442:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.37 % (4027564)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=997041497:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.37 % (4027566)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2899687497:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.37 % (4027565)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2414342130:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.37 % (4027563)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=884310098:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.37 % (4027567)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3281064930:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.37 % (4027566)First to succeed.
% 3.48/1.37 % (4027565)Also succeeded, but the first one will report.
% 3.48/1.37 % (4027567)Refutation not found, incomplete strategy
% 3.48/1.37 % (4027567)------------------------------
% 3.48/1.37 % (4027567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.37 % (4027567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.37 % (4027567)CaDiCaL version: 2.1.3
% 3.48/1.37 % (4027567)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.37 % (4027567)Time elapsed: 0.001 s
% 3.48/1.37 % (4027567)Peak memory usage: 88 MB
% 3.48/1.37 % (4027566)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4027557"
% 3.48/1.37 % (4027568)dis-21_1_sil=8000:lcm=predicate:random_seed=2808177962: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)
% 3.48/1.37 % (4027568)Also succeeded, but the first one will report.
% 3.48/1.37 % (4027567)------------------------------
% 3.48/1.37 % (4027567)------------------------------
% 3.48/1.37 % (4027566)Refutation found. Thanks to Tanya!
% 3.48/1.37 % SZS status Theorem for theBenchmark
% 3.48/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.37 % (4027566)------------------------------
% 3.48/1.37 % (4027566)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.37 % (4027566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.37 % (4027566)CaDiCaL version: 2.1.3
% 3.48/1.37 % (4027566)Termination reason: Refutation
% 3.48/1.37 % (4027566)Time elapsed: 0.002 s
% 3.48/1.37 % (4027566)Peak memory usage: 88 MB
% 3.48/1.37 % (4027566)------------------------------
% 3.48/1.37 % (4027566)------------------------------
% 3.48/1.37 % (4027557)Success in time 0.425 s
% 3.48/1.37 % Vampire exiting
%------------------------------------------------------------------------------