%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n017.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 12:44:35 PM UTC 2026
% Result : Theorem 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 174 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 207 ( 72 ~; 61 |; 50 &)
% ( 6 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 84 ( 70 !; 14 ?)
% 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/Axioms/SET006+2.ax',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(f21,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(f22,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,[],[f21]) ).
fof(f25,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,[],[f22]) ).
fof(f26,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,[],[f25]) ).
fof(f27,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(f28,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,[],[f27]) ).
fof(f59,plain,
! [X3,X0,X1,X4,X5] :
( ~ pre_order(X0,X1)
| ~ member(X5,X1)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X4)
| apply(X0,X3,X5) ),
inference(cnf_transformation,[],[f26]) ).
fof(f60,plain,
! [X3,X4] :
( ~ apply(sK5,X3,X4)
| ~ member(X3,sK3)
| apply(sK4,X4,X3)
| ~ member(X4,sK3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f61,plain,
! [X3,X4] :
( ~ apply(sK5,X3,X4)
| ~ member(X3,sK3)
| apply(sK4,X3,X4)
| ~ member(X4,sK3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f63,plain,
member(sK9,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f64,plain,
member(sK8,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f65,plain,
member(sK7,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f66,plain,
member(sK6,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f67,plain,
apply(sK4,sK6,sK7),
inference(cnf_transformation,[],[f28]) ).
fof(f68,plain,
apply(sK5,sK7,sK9),
inference(cnf_transformation,[],[f28]) ).
fof(f69,plain,
apply(sK5,sK6,sK8),
inference(cnf_transformation,[],[f28]) ).
fof(f70,plain,
~ apply(sK4,sK8,sK9),
inference(cnf_transformation,[],[f28]) ).
fof(f71,plain,
pre_order(sK4,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f76,plain,
( ~ member(sK6,sK3)
| apply(sK4,sK8,sK6)
| ~ member(sK8,sK3) ),
inference(resolution,[],[f60,f69]) ).
fof(f77,plain,
( apply(sK4,sK8,sK6)
| ~ member(sK8,sK3) ),
inference(forward_subsumption_resolution,[],[f76,f66]) ).
fof(f79,plain,
apply(sK4,sK8,sK6),
inference(forward_subsumption_resolution,[],[f77,f64]) ).
fof(f81,plain,
( ~ member(sK7,sK3)
| apply(sK4,sK7,sK9)
| ~ member(sK9,sK3) ),
inference(resolution,[],[f61,f68]) ).
fof(f84,plain,
( apply(sK4,sK7,sK9)
| ~ member(sK9,sK3) ),
inference(forward_subsumption_resolution,[],[f81,f65]) ).
fof(f86,plain,
apply(sK4,sK7,sK9),
inference(forward_subsumption_resolution,[],[f84,f63]) ).
fof(f222,plain,
! [X2,X0,X1] :
( ~ apply(sK4,X1,X0)
| ~ apply(sK4,X2,X1)
| apply(sK4,X2,X0)
| ~ member(X0,sK3)
| ~ member(X1,sK3)
| ~ member(X2,sK3) ),
inference(resolution,[],[f59,f71]) ).
fof(f232,plain,
! [X0] :
( ~ apply(sK4,X0,sK7)
| apply(sK4,X0,sK9)
| ~ member(sK9,sK3)
| ~ member(sK7,sK3)
| ~ member(X0,sK3) ),
inference(resolution,[],[f222,f86]) ).
fof(f243,plain,
! [X0] :
( ~ apply(sK4,X0,sK9)
| ~ apply(sK4,sK8,X0)
| ~ member(sK9,sK3)
| ~ member(X0,sK3)
| ~ member(sK8,sK3) ),
inference(resolution,[],[f222,f70]) ).
fof(f257,plain,
! [X0] :
( ~ apply(sK4,X0,sK9)
| ~ apply(sK4,sK8,X0)
| ~ member(X0,sK3)
| ~ member(sK8,sK3) ),
inference(forward_subsumption_resolution,[],[f243,f63]) ).
fof(f262,plain,
! [X0] :
( ~ apply(sK4,X0,sK7)
| apply(sK4,X0,sK9)
| ~ member(sK7,sK3)
| ~ member(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f232,f63]) ).
fof(f265,plain,
! [X0] :
( ~ apply(sK4,X0,sK9)
| ~ apply(sK4,sK8,X0)
| ~ member(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f257,f64]) ).
fof(f270,plain,
! [X0] :
( apply(sK4,X0,sK9)
| ~ apply(sK4,X0,sK7)
| ~ member(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f262,f65]) ).
fof(f354,plain,
( ~ apply(sK4,sK6,sK9)
| ~ member(sK6,sK3) ),
inference(resolution,[],[f265,f79]) ).
fof(f369,plain,
~ apply(sK4,sK6,sK9),
inference(forward_subsumption_resolution,[],[f354,f66]) ).
fof(f779,plain,
( ~ apply(sK4,sK6,sK7)
| ~ member(sK6,sK3) ),
inference(resolution,[],[f270,f369]) ).
fof(f789,plain,
~ member(sK6,sK3),
inference(forward_subsumption_resolution,[],[f779,f67]) ).
fof(f794,plain,
$false,
inference(forward_subsumption_resolution,[],[f789,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET776+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 02:43:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.49 % (3164214)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (3164222)dis+10_1_sil=32000:sp=arity:random_seed=1813897535:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (3164220)% WARNING: option uhcvi not known.
% 0.17/0.49 % (3164219)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=547581953_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % (3164223)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1542001747:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (3164220)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=995279347:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (3164224)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2840463073:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (3164221)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4140151257:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (3164225)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2470118010:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % TRYING [4]
% 0.17/0.49 % TRYING [5]
% 0.17/0.49 % (3164222)Instruction limit reached!
% 0.17/0.49 % (3164222)------------------------------
% 0.17/0.49 % (3164222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (3164222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (3164222)CaDiCaL version: 2.1.3
% 0.17/0.49 % (3164222)Termination reason: Instruction limit
% 0.17/0.49 % (3164222)Termination phase: Saturation
% 0.17/0.49 % (3164223) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3164214-3164223"...
% 0.17/0.49 % (3164222)Time elapsed: 0.035 s
% 0.17/0.49 % (3164222)Peak memory usage: 12 MB
% 0.17/0.49 % (3164222)Instructions burned: 105 (million)
% 0.17/0.49 % (3164223)...printing done.
% 0.17/0.49 % (3164223)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (3164223)------------------------------
% 0.17/0.49 % (3164223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (3164223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (3164223)CaDiCaL version: 2.1.3
% 0.17/0.49 % (3164223)Termination reason: Refutation
% 0.17/0.49 % (3164223)Time elapsed: 0.028 s
% 0.17/0.49 % (3164223)Peak memory usage: 12 MB
% 0.17/0.49 % (3164223)Instructions burned: 44 (million)
% 0.17/0.49 % (3164214)Success in time 0.066 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------