%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET776+4 : 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 : n011.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 12:41:54 PM UTC 2026
% Result : Theorem 2.66s 1.32s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 56 ( 17 unt; 2 def)
% Number of atoms : 279 ( 0 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 345 ( 122 ~; 103 |; 94 &)
% ( 8 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 113 ( 0 sgn 78 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0,X1] :
( pre_order(X0,X1)
<=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X2,X3,X4] :
( ( member(X2,X1)
& member(X3,X1)
& member(X4,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X4) )
=> apply(X0,X2,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pre_order) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( ( pre_order(X1,X0)
& ! [X3,X4] :
( ( member(X3,X0)
& member(X4,X0) )
=> ( apply(X2,X3,X4)
<=> ( apply(X1,X3,X4)
& apply(X1,X4,X3) ) ) ) )
=> ! [X5,X6,X7,X8] :
( ( member(X5,X0)
& member(X6,X0)
& member(X7,X0)
& member(X8,X0) )
=> ( ( apply(X2,X5,X7)
& apply(X2,X6,X8)
& apply(X1,X5,X6) )
=> apply(X1,X7,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII12) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( pre_order(X1,X0)
& ! [X3,X4] :
( ( member(X3,X0)
& member(X4,X0) )
=> ( apply(X2,X3,X4)
<=> ( apply(X1,X3,X4)
& apply(X1,X4,X3) ) ) ) )
=> ! [X5,X6,X7,X8] :
( ( member(X5,X0)
& member(X6,X0)
& member(X7,X0)
& member(X8,X0) )
=> ( ( apply(X2,X5,X7)
& apply(X2,X6,X8)
& apply(X1,X5,X6) )
=> apply(X1,X7,X8) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( pre_order(X0,X1)
<=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X3,X4,X5] :
( ( member(X3,X1)
& member(X4,X1)
& member(X5,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X4,X5) )
=> apply(X0,X3,X5) ) ) ) ),
inference(rectify,[],[f16]) ).
fof(f20,plain,
! [X0,X1] :
( pre_order(X0,X1)
=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X3,X4,X5] :
( ( member(X3,X1)
& member(X4,X1)
& member(X5,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X4,X5) )
=> apply(X0,X3,X5) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f21,plain,
? [X0,X1,X2] :
( ? [X5,X6,X7,X8] :
( ~ apply(X1,X7,X8)
& apply(X2,X5,X7)
& apply(X2,X6,X8)
& apply(X1,X5,X6)
& member(X5,X0)
& member(X6,X0)
& member(X7,X0)
& member(X8,X0) )
& pre_order(X1,X0)
& ! [X3,X4] :
( ( apply(X2,X3,X4)
<=> ( apply(X1,X3,X4)
& apply(X1,X4,X3) ) )
| ~ member(X3,X0)
| ~ member(X4,X0) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
? [X0,X1,X2] :
( ? [X5,X6,X7,X8] :
( ~ apply(X1,X7,X8)
& apply(X2,X5,X7)
& apply(X2,X6,X8)
& apply(X1,X5,X6)
& member(X5,X0)
& member(X6,X0)
& member(X7,X0)
& member(X8,X0) )
& pre_order(X1,X0)
& ! [X3,X4] :
( ( apply(X2,X3,X4)
<=> ( apply(X1,X3,X4)
& apply(X1,X4,X3) ) )
| ~ member(X3,X0)
| ~ member(X4,X0) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& ! [X3,X4,X5] :
( apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X1) ) )
| ~ pre_order(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f24,plain,
! [X0,X1] :
( ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& ! [X3,X4,X5] :
( apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X1) ) )
| ~ pre_order(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
? [X0,X1,X2] :
( ? [X5,X6,X7,X8] :
( ~ apply(X1,X7,X8)
& apply(X2,X5,X7)
& apply(X2,X6,X8)
& apply(X1,X5,X6)
& member(X5,X0)
& member(X6,X0)
& member(X7,X0)
& member(X8,X0) )
& pre_order(X1,X0)
& ! [X3,X4] :
( ( ( apply(X2,X3,X4)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X4,X3) )
& ( ( apply(X1,X3,X4)
& apply(X1,X4,X3) )
| ~ apply(X2,X3,X4) ) )
| ~ member(X3,X0)
| ~ member(X4,X0) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f26,plain,
? [X0,X1,X2] :
( ? [X5,X6,X7,X8] :
( ~ apply(X1,X7,X8)
& apply(X2,X5,X7)
& apply(X2,X6,X8)
& apply(X1,X5,X6)
& member(X5,X0)
& member(X6,X0)
& member(X7,X0)
& member(X8,X0) )
& pre_order(X1,X0)
& ! [X3,X4] :
( ( ( apply(X2,X3,X4)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X4,X3) )
& ( ( apply(X1,X3,X4)
& apply(X1,X4,X3) )
| ~ apply(X2,X3,X4) ) )
| ~ member(X3,X0)
| ~ member(X4,X0) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
? [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( ~ apply(X1,X5,X6)
& apply(X2,X3,X5)
& apply(X2,X4,X6)
& apply(X1,X3,X4)
& member(X3,X0)
& member(X4,X0)
& member(X5,X0)
& member(X6,X0) )
& pre_order(X1,X0)
& ! [X7,X8] :
( ( ( apply(X2,X7,X8)
| ~ apply(X1,X7,X8)
| ~ apply(X1,X8,X7) )
& ( ( apply(X1,X7,X8)
& apply(X1,X8,X7) )
| ~ apply(X2,X7,X8) ) )
| ~ member(X7,X0)
| ~ member(X8,X0) ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
( ~ apply(sK1,sK5,sK6)
& apply(sK2,sK3,sK5)
& apply(sK2,sK4,sK6)
& apply(sK1,sK3,sK4)
& member(sK3,sK0)
& member(sK4,sK0)
& member(sK5,sK0)
& member(sK6,sK0)
& pre_order(sK1,sK0)
& ! [X7,X8] :
( ( ( apply(sK2,X7,X8)
| ~ apply(sK1,X7,X8)
| ~ apply(sK1,X8,X7) )
& ( ( apply(sK1,X7,X8)
& apply(sK1,X8,X7) )
| ~ apply(sK2,X7,X8) ) )
| ~ member(X7,sK0)
| ~ member(X8,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f27]) ).
fof(f29,plain,
! [X8,X7] :
( ~ apply(sK2,X7,X8)
| apply(sK1,X8,X7)
| ~ member(X7,sK0)
| ~ member(X8,sK0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f30,plain,
! [X8,X7] :
( ~ apply(sK2,X7,X8)
| apply(sK1,X7,X8)
| ~ member(X7,sK0)
| ~ member(X8,sK0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f32,plain,
pre_order(sK1,sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f33,plain,
member(sK6,sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f34,plain,
member(sK5,sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f35,plain,
member(sK4,sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f36,plain,
member(sK3,sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f37,plain,
apply(sK1,sK3,sK4),
inference(cnf_transformation,[],[f28]) ).
fof(f38,plain,
apply(sK2,sK4,sK6),
inference(cnf_transformation,[],[f28]) ).
fof(f39,plain,
apply(sK2,sK3,sK5),
inference(cnf_transformation,[],[f28]) ).
fof(f40,plain,
~ apply(sK1,sK5,sK6),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
! [X3,X0,X1,X4,X5] :
( ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X4)
| apply(X0,X3,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X1)
| ~ pre_order(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
! [X0,X1] :
( ~ apply(sK1,X0,sK3)
| apply(sK1,X0,sK4)
| ~ member(X0,X1)
| ~ member(sK3,X1)
| ~ member(sK4,X1)
| ~ pre_order(sK1,X1) ),
inference(resolution,[],[f37,f41]) ).
fof(f47,plain,
( apply(sK1,sK5,sK3)
| ~ member(sK3,sK0)
| ~ member(sK5,sK0) ),
inference(resolution,[],[f29,f39]) ).
fof(f50,plain,
( apply(sK1,sK5,sK3)
| ~ member(sK5,sK0) ),
inference(forward_subsumption_resolution,[],[f47,f36]) ).
fof(f52,plain,
apply(sK1,sK5,sK3),
inference(forward_subsumption_resolution,[],[f50,f34]) ).
fof(f55,plain,
( apply(sK1,sK4,sK6)
| ~ member(sK4,sK0)
| ~ member(sK6,sK0) ),
inference(resolution,[],[f30,f38]) ).
fof(f60,plain,
( apply(sK1,sK4,sK6)
| ~ member(sK6,sK0) ),
inference(forward_subsumption_resolution,[],[f55,f35]) ).
fof(f62,plain,
apply(sK1,sK4,sK6),
inference(forward_subsumption_resolution,[],[f60,f33]) ).
fof(f87,plain,
! [X0,X1] :
( ~ apply(sK1,X0,sK4)
| apply(sK1,X0,sK6)
| ~ member(X0,X1)
| ~ member(sK4,X1)
| ~ member(sK6,X1)
| ~ pre_order(sK1,X1) ),
inference(resolution,[],[f62,f41]) ).
fof(f108,plain,
! [X0] :
( apply(sK1,sK5,sK4)
| ~ member(sK5,X0)
| ~ member(sK3,X0)
| ~ member(sK4,X0)
| ~ pre_order(sK1,X0) ),
inference(resolution,[],[f43,f52]) ).
fof(f113,definition,
( spl7_3
<=> ! [X0] :
( ~ member(sK5,X0)
| ~ pre_order(sK1,X0)
| ~ member(sK4,X0)
| ~ member(sK3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
fof(f114,plain,
( ! [X0] :
( ~ pre_order(sK1,X0)
| ~ member(sK5,X0)
| ~ member(sK4,X0)
| ~ member(sK3,X0) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,definition,
( spl7_4
<=> apply(sK1,sK5,sK4) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
fof(f118,plain,
( apply(sK1,sK5,sK4)
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl7_3
| spl7_4 ),
inference(avatar_split_clause,[],[f108,f116,f113]) ).
fof(f120,plain,
( ~ member(sK5,sK0)
| ~ member(sK4,sK0)
| ~ member(sK3,sK0)
| ~ spl7_3 ),
inference(resolution,[],[f114,f32]) ).
fof(f121,plain,
( ~ member(sK4,sK0)
| ~ member(sK3,sK0)
| ~ spl7_3 ),
inference(forward_subsumption_resolution,[],[f120,f34]) ).
fof(f122,plain,
( ~ member(sK3,sK0)
| ~ spl7_3 ),
inference(forward_subsumption_resolution,[],[f121,f35]) ).
fof(f123,plain,
( $false
| ~ spl7_3 ),
inference(forward_subsumption_resolution,[],[f122,f36]) ).
fof(f124,plain,
~ spl7_3,
inference(avatar_contradiction_clause,[],[f123]) ).
fof(f170,plain,
( ! [X0] :
( apply(sK1,sK5,sK6)
| ~ member(sK5,X0)
| ~ member(sK4,X0)
| ~ member(sK6,X0)
| ~ pre_order(sK1,X0) )
| ~ spl7_4 ),
inference(resolution,[],[f87,f118]) ).
fof(f176,plain,
( ! [X0] :
( ~ pre_order(sK1,X0)
| ~ member(sK4,X0)
| ~ member(sK6,X0)
| ~ member(sK5,X0) )
| ~ spl7_4 ),
inference(forward_subsumption_resolution,[],[f170,f40]) ).
fof(f185,plain,
( ~ member(sK4,sK0)
| ~ member(sK6,sK0)
| ~ member(sK5,sK0)
| ~ spl7_4 ),
inference(resolution,[],[f176,f32]) ).
fof(f186,plain,
( ~ member(sK6,sK0)
| ~ member(sK5,sK0)
| ~ spl7_4 ),
inference(forward_subsumption_resolution,[],[f185,f35]) ).
fof(f187,plain,
( ~ member(sK5,sK0)
| ~ spl7_4 ),
inference(forward_subsumption_resolution,[],[f186,f33]) ).
fof(f188,plain,
( $false
| ~ spl7_4 ),
inference(forward_subsumption_resolution,[],[f187,f34]) ).
fof(f189,plain,
~ spl7_4,
inference(avatar_contradiction_clause,[],[f188]) ).
cnf(s2,plain,
( spl7_3
| spl7_4 ),
inference(sat_conversion,[],[f119]) ).
cnf(s3,plain,
~ spl7_3,
inference(sat_conversion,[],[f124]) ).
cnf(s6,plain,
~ spl7_4,
inference(sat_conversion,[],[f189]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s3]) ).
fof(f190,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET776+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 02:46:31 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.66/1.32 % (2972198)Detected formulas, will run a generic FOF schedule.
% 2.66/1.32 % (2972206)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2985612776:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.32 % (2972206)First to succeed.
% 2.66/1.32 % (2972206)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2972198"
% 2.66/1.32 % (2972208)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1132713685:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.32 % (2972203)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=2411830631:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.32 % (2972207)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2035310369:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.32 % (2972205)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=2718637451:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.32 % (2972204)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=2104625759:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.32 % (2972207)Also succeeded, but the first one will report.
% 2.66/1.32 % (2972208)Also succeeded, but the first one will report.
% 2.66/1.32 % (2972209)dis-21_1_sil=8000:lcm=predicate:random_seed=628315581: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)
% 2.66/1.32 % (2972209)Also succeeded, but the first one will report.
% 2.66/1.32 % (2972206)Refutation found. Thanks to Tanya!
% 2.66/1.32 % SZS status Theorem for theBenchmark
% 2.66/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.32 % (2972206)------------------------------
% 2.66/1.32 % (2972206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.32 % (2972206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.32 % (2972206)CaDiCaL version: 2.1.3
% 2.66/1.32 % (2972206)Termination reason: Refutation
% 2.66/1.32 % (2972206)Time elapsed: 0.003 s
% 2.66/1.32 % (2972206)Peak memory usage: 89 MB
% 2.66/1.32 % (2972206)Instructions burned: 5 (million)
% 2.66/1.32 % (2972206)------------------------------
% 2.66/1.32 % (2972206)------------------------------
% 2.66/1.32 % (2972198)Success in time 0.291 s
% 2.66/1.32 % Vampire exiting
%------------------------------------------------------------------------------