%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC392+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 01:03:46 PM UTC 2026
% Result : Theorem 2.69s 1.15s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 15 unt; 0 def)
% Number of atoms : 221 ( 79 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 250 ( 82 ~; 97 |; 51 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 57 ( 43 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ( ~ memberP(X0,X4)
| memberP(X1,X4) ) )
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X2
| ~ memberP(X3,X5)
| ? [X6] :
( ssItem(X6)
& X5 != X6
& memberP(X3,X6)
& leq(X6,X5) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/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(X0,X4)
| memberP(X1,X4) ) )
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X2
| ~ memberP(X3,X5)
| ? [X6] :
( ssItem(X6)
& X5 != X6
& memberP(X3,X6)
& leq(X6,X5) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( memberP(X0,X4)
& ~ memberP(X1,X4)
& ssItem(X4) )
& ( ? [X5] :
( cons(X5,nil) = X2
& memberP(X3,X5)
& ! [X6] :
( ~ ssItem(X6)
| X5 = X6
| ~ memberP(X3,X6)
| ~ leq(X6,X5) )
& ssItem(X5) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( memberP(X0,X4)
& ~ memberP(X1,X4)
& ssItem(X4) )
& ( ? [X5] :
( cons(X5,nil) = X2
& memberP(X3,X5)
& ! [X6] :
( ~ ssItem(X6)
| X5 = X6
| ~ memberP(X3,X6)
| ~ leq(X6,X5) )
& ssItem(X5) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f107,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f127,plain,
( sK1 = sK3
& sK0 = sK2
& memberP(sK0,sK4)
& ~ memberP(sK1,sK4)
& ssItem(sK4)
& ( ( sK2 = cons(sK5,nil)
& memberP(sK3,sK5)
& ! [X6] :
( ~ ssItem(X6)
| sK5 = X6
| ~ memberP(sK3,X6)
| ~ leq(X6,sK5) )
& ssItem(sK5) )
| ( nil = sK3
& nil = sK2 ) )
& 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(X4,sK4),skolemize(X5,sK5)],[f99]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f108]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f130]) ).
fof(f143,plain,
( nil = sK2
| ssItem(sK5) ),
inference(cnf_transformation,[],[f127]) ).
fof(f144,plain,
( nil = sK3
| ssItem(sK5) ),
inference(cnf_transformation,[],[f127]) ).
fof(f147,plain,
( memberP(sK3,sK5)
| nil = sK2 ),
inference(cnf_transformation,[],[f127]) ).
fof(f148,plain,
( memberP(sK3,sK5)
| nil = sK3 ),
inference(cnf_transformation,[],[f127]) ).
fof(f149,plain,
( sK2 = cons(sK5,nil)
| nil = sK2 ),
inference(cnf_transformation,[],[f127]) ).
fof(f150,plain,
( sK2 = cons(sK5,nil)
| nil = sK3 ),
inference(cnf_transformation,[],[f127]) ).
fof(f151,plain,
ssItem(sK4),
inference(cnf_transformation,[],[f127]) ).
fof(f152,plain,
~ memberP(sK1,sK4),
inference(cnf_transformation,[],[f127]) ).
fof(f153,plain,
memberP(sK0,sK4),
inference(cnf_transformation,[],[f127]) ).
fof(f154,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f127]) ).
fof(f155,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f127]) ).
fof(f159,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f167,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f168,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f193,plain,
memberP(sK2,sK4),
inference(definition_unfolding,[],[f153,f154]) ).
fof(f194,plain,
~ memberP(sK3,sK4),
inference(definition_unfolding,[],[f152,f155]) ).
fof(f204,plain,
( sK2 = sK3
| ssItem(sK5)
| ssItem(sK5) ),
inference(superposition,[],[f143,f144]) ).
fof(f205,plain,
( sK2 = sK3
| ssItem(sK5) ),
inference(duplicate_literal_removal,[],[f204]) ).
fof(f207,plain,
( ~ memberP(sK2,sK4)
| ssItem(sK5) ),
inference(superposition,[],[f194,f205]) ).
fof(f209,plain,
ssItem(sK5),
inference(forward_subsumption_resolution,[],[f207,f193]) ).
fof(f232,plain,
( nil != sK2
| ~ ssItem(sK5)
| ~ ssList(nil)
| nil = sK3 ),
inference(superposition,[],[f159,f150]) ).
fof(f234,plain,
( nil != sK2
| ~ ssList(nil)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f232,f209]) ).
fof(f235,plain,
( nil != sK2
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f234,f167]) ).
fof(f415,plain,
! [X0] :
( ~ memberP(sK2,X0)
| memberP(nil,X0)
| sK5 = X0
| ~ ssList(nil)
| ~ ssItem(sK5)
| ~ ssItem(X0)
| nil = sK2 ),
inference(superposition,[],[f169,f149]) ).
fof(f422,plain,
! [X0] :
( ~ memberP(sK2,X0)
| memberP(nil,X0)
| sK5 = X0
| ~ ssItem(sK5)
| ~ ssItem(X0)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f415,f167]) ).
fof(f427,plain,
! [X0] :
( ~ memberP(sK2,X0)
| memberP(nil,X0)
| sK5 = X0
| ~ ssItem(X0)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f422,f209]) ).
fof(f430,plain,
! [X0] :
( ~ memberP(sK2,X0)
| sK5 = X0
| ~ ssItem(X0)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f427,f168]) ).
fof(f433,plain,
( sK4 = sK5
| ~ ssItem(sK4)
| nil = sK2 ),
inference(resolution,[],[f430,f193]) ).
fof(f440,plain,
( sK4 = sK5
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f433,f151]) ).
fof(f463,plain,
( memberP(sK3,sK4)
| nil = sK2
| nil = sK2 ),
inference(superposition,[],[f147,f440]) ).
fof(f464,plain,
( memberP(sK3,sK4)
| nil = sK3
| nil = sK2 ),
inference(superposition,[],[f148,f440]) ).
fof(f482,plain,
( memberP(sK3,sK4)
| nil = sK2 ),
inference(duplicate_literal_removal,[],[f463]) ).
fof(f487,plain,
( memberP(sK3,sK4)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f464,f235]) ).
fof(f488,plain,
nil = sK2,
inference(forward_subsumption_resolution,[],[f482,f194]) ).
fof(f490,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f487,f194]) ).
fof(f564,plain,
sK2 = sK3,
inference(forward_demodulation,[],[f490,f488]) ).
fof(f630,plain,
~ memberP(sK2,sK4),
inference(superposition,[],[f194,f564]) ).
fof(f632,plain,
$false,
inference(forward_subsumption_resolution,[],[f630,f193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC392+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n003.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 09:27:57 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.69/1.15 % (1457217)Detected formulas, will run a generic FOF schedule.
% 2.69/1.15 % (1457226)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3601150231:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.15 % (1457226)First to succeed.
% 2.69/1.15 % (1457226)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1457217"
% 2.69/1.15 % (1457227)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=816923147:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.15 % (1457225)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2422706440:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.15 % (1457228)dis-21_1_sil=8000:lcm=predicate:random_seed=573950032: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)
% 2.69/1.15 % (1457222)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=3141779099:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.15 % (1457224)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=716507896:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.15 % (1457223)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=797186938:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.15 % (1457225)Also succeeded, but the first one will report.
% 2.69/1.15 % (1457228)Instruction limit reached!
% 2.69/1.15 % (1457228)------------------------------
% 2.69/1.15 % (1457228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.15 % (1457228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.15 % (1457228)CaDiCaL version: 2.1.3
% 2.69/1.15 % (1457228)Termination reason: Instruction limit
% 2.69/1.15 % (1457228)Termination phase: Saturation
% 2.69/1.15 % (1457228)Time elapsed: 0.070 s
% 2.69/1.15 % (1457228)Peak memory usage: 90 MB
% 2.69/1.15 % (1457228)Instructions burned: 129 (million)
% 2.69/1.15 % (1457227)Instruction limit reached!
% 2.69/1.15 % (1457227)------------------------------
% 2.69/1.15 % (1457227)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.15 % (1457227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.15 % (1457227)CaDiCaL version: 2.1.3
% 2.69/1.15 % (1457227)Termination reason: Instruction limit
% 2.69/1.15 % (1457227)Termination phase: Saturation
% 2.69/1.15 % (1457227)Time elapsed: 0.094 s
% 2.69/1.15 % (1457227)Peak memory usage: 90 MB
% 2.69/1.15 % (1457227)Instructions burned: 139 (million)
% 2.69/1.15 % (1457226)Refutation found. Thanks to Tanya!
% 2.69/1.15 % SZS status Theorem for theBenchmark
% 2.69/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.15 % (1457226)------------------------------
% 2.69/1.15 % (1457226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.15 % (1457226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.15 % (1457226)CaDiCaL version: 2.1.3
% 2.69/1.15 % (1457226)Termination reason: Refutation
% 2.69/1.15 % (1457226)Time elapsed: 0.006 s
% 2.69/1.15 % (1457226)Peak memory usage: 88 MB
% 2.69/1.15 % (1457226)Instructions burned: 16 (million)
% 2.69/1.15 % (1457226)------------------------------
% 2.69/1.15 % (1457226)------------------------------
% 2.69/1.15 % (1457217)Success in time 0.29 s
% 2.69/1.15 % Vampire exiting
%------------------------------------------------------------------------------