%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC406+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 01:03:50 PM UTC 2026
% Result : Theorem 3.47s 1.18s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 146 ( 26 equ)
% Maximal formula atoms : 22 ( 8 avg)
% Number of connectives : 186 ( 57 ~; 48 |; 63 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 43 ( 25 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X2,X4)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| ~ leq(X5,X4)
| X4 = X5 ) )
& memberP(X3,X4) )
| ( memberP(X2,X4)
& ( ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X5,X4) ) ) ) ) )
| ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X0,X6)
| memberP(X1,X6) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X2,X4)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| ~ leq(X5,X4)
| X4 = X5 ) )
& memberP(X3,X4) )
| ( memberP(X2,X4)
& ( ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X5,X4) ) ) ) ) )
| ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X0,X6)
| memberP(X1,X6) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X2,X4)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| ~ leq(X5,X4)
| X4 = X5 ) )
& memberP(X3,X4) )
| ( memberP(X2,X4)
& ( ~ memberP(X3,X4)
| ? [X6] :
( ssItem(X6)
& X4 != X6
& memberP(X3,X6)
& leq(X6,X4) ) ) ) ) )
| ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X0,X7)
| memberP(X1,X7) ) ) ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(X2,X4)
| ? [X5] :
( memberP(X3,X5)
& leq(X5,X4)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4) )
& ( ~ memberP(X2,X4)
| ( memberP(X3,X4)
& ! [X6] :
( ~ ssItem(X6)
| X4 = X6
| ~ memberP(X3,X6)
| ~ leq(X6,X4) ) ) ) ) )
& ? [X7] :
( memberP(X0,X7)
& ~ memberP(X1,X7)
& ssItem(X7) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(X2,X4)
| ? [X5] :
( memberP(X3,X5)
& leq(X5,X4)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4) )
& ( ~ memberP(X2,X4)
| ( memberP(X3,X4)
& ! [X6] :
( ~ ssItem(X6)
| X4 = X6
| ~ memberP(X3,X6)
| ~ leq(X6,X4) ) ) ) ) )
& ? [X7] :
( memberP(X0,X7)
& ~ memberP(X1,X7)
& ssItem(X7) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f128,plain,
( sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(sK2,X4)
| ( memberP(sK3,sK4(X4))
& leq(sK4(X4),X4)
& sK4(X4) != X4
& ssItem(sK4(X4)) )
| ~ memberP(sK3,X4) )
& ( ~ memberP(sK2,X4)
| ( memberP(sK3,X4)
& ! [X6] :
( ~ ssItem(X6)
| X4 = X6
| ~ memberP(sK3,X6)
| ~ leq(X6,X4) ) ) ) ) )
& memberP(sK0,sK5)
& ~ memberP(sK1,sK5)
& ssItem(sK5)
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X5,sK4(X4)),skolemize(X7,sK5)],[f100]) ).
fof(f144,plain,
ssItem(sK5),
inference(cnf_transformation,[],[f128]) ).
fof(f145,plain,
~ memberP(sK1,sK5),
inference(cnf_transformation,[],[f128]) ).
fof(f146,plain,
memberP(sK0,sK5),
inference(cnf_transformation,[],[f128]) ).
fof(f148,plain,
! [X4] :
( memberP(sK3,X4)
| ~ memberP(sK2,X4)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f128]) ).
fof(f153,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f128]) ).
fof(f154,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f128]) ).
fof(f192,plain,
memberP(sK2,sK5),
inference(definition_unfolding,[],[f146,f153]) ).
fof(f193,plain,
~ memberP(sK3,sK5),
inference(definition_unfolding,[],[f145,f154]) ).
fof(f202,plain,
( ~ memberP(sK2,sK5)
| ~ ssItem(sK5) ),
inference(resolution,[],[f148,f193]) ).
fof(f203,plain,
~ ssItem(sK5),
inference(forward_subsumption_resolution,[],[f202,f192]) ).
fof(f204,plain,
$false,
inference(forward_subsumption_resolution,[],[f203,f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC406+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 09:33:40 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 3.47/1.18 % (3251525)Detected formulas, will run a generic FOF schedule.
% 3.47/1.18 % (3251530)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=3071253402:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.47/1.18 % (3251534)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2946417226:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.47/1.18 % (3251533)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3222061078:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.47/1.18 % (3251535)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=212006657:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.47/1.18 % (3251536)dis-21_1_sil=8000:lcm=predicate:random_seed=750113396: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)
% 3.47/1.18 % (3251531)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=4042495520:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.47/1.18 % (3251532)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=43550441:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.47/1.18 % (3251534)First to succeed.
% 3.47/1.18 % (3251533)Also succeeded, but the first one will report.
% 3.47/1.18 % (3251534)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3251525"
% 3.47/1.18 % (3251536)Also succeeded, but the first one will report.
% 3.47/1.18 % (3251535)Also succeeded, but the first one will report.
% 3.47/1.18 % (3251534)Refutation found. Thanks to Tanya!
% 3.47/1.18 % SZS status Theorem for theBenchmark
% 3.47/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.18 % (3251534)------------------------------
% 3.47/1.18 % (3251534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.18 % (3251534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.18 % (3251534)CaDiCaL version: 2.1.3
% 3.47/1.18 % (3251534)Termination reason: Refutation
% 3.47/1.18 % (3251534)Time elapsed: 0.003 s
% 3.47/1.18 % (3251534)Peak memory usage: 88 MB
% 3.47/1.18 % (3251534)Instructions burned: 3 (million)
% 3.47/1.18 % (3251534)------------------------------
% 3.47/1.18 % (3251534)------------------------------
% 3.47/1.18 % (3251525)Success in time 0.416 s
% 3.47/1.18 % Vampire exiting
%------------------------------------------------------------------------------