%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC025+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 : n019.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 01:02:05 PM UTC 2026
% Result : Theorem 2.68s 1.34s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 52 ( 9 unt; 0 def)
% Number of atoms : 225 ( 77 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 277 ( 104 ~; 105 |; 53 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 67 ( 51 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
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/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ duplicatefreeP(X2)
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X3,X4)
& memberP(X2,X4) )
| ( ~ memberP(X2,X4)
& memberP(X3,X4) ) ) )
| ( ( nil != X1
| nil = X0 )
& ( nil != X0
| nil = X1 ) ) ) ) ) ) ),
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
| ~ duplicatefreeP(X2)
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X3,X4)
& memberP(X2,X4) )
| ( ~ memberP(X2,X4)
& memberP(X3,X4) ) ) )
| ( ( nil != X1
| nil = X0 )
& ( nil != X0
| nil = X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& duplicatefreeP(X2)
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(X3,X4)
| ~ memberP(X2,X4) )
& ( memberP(X2,X4)
| ~ memberP(X3,X4) ) ) )
& ( ( nil = X1
& nil != X0 )
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& duplicatefreeP(X2)
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(X3,X4)
| ~ memberP(X2,X4) )
& ( memberP(X2,X4)
| ~ memberP(X3,X4) ) ) )
& ( ( nil = X1
& nil != X0 )
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f101,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(f108,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f109,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) )
| ~ ssList(X0) ),
inference(flattening,[],[f108]) ).
fof(f125,plain,
( sK1 = sK3
& sK0 = sK2
& duplicatefreeP(sK2)
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(sK3,X4)
| ~ memberP(sK2,X4) )
& ( memberP(sK2,X4)
| ~ memberP(sK3,X4) ) ) )
& ( ( nil = sK1
& nil != sK0 )
| ( nil = sK0
& nil != sK1 ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f127,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,[],[f101]) ).
fof(f128,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,[],[f127]) ).
fof(f137,plain,
! [X0] :
( nil = X0
| ( ssList(sK13(X0))
& ssItem(sK14(X0))
& cons(sK14(X0),sK13(X0)) = X0 )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X1,sK13(X0)),skolemize(X2,sK14(X0))],[f109]) ).
fof(f142,plain,
ssList(sK2),
inference(cnf_transformation,[],[f125]) ).
fof(f143,plain,
ssList(sK3),
inference(cnf_transformation,[],[f125]) ).
fof(f144,plain,
( nil != sK0
| nil != sK1 ),
inference(cnf_transformation,[],[f125]) ).
fof(f147,plain,
( nil = sK1
| nil = sK0 ),
inference(cnf_transformation,[],[f125]) ).
fof(f148,plain,
! [X4] :
( memberP(sK2,X4)
| ~ ssItem(X4)
| ~ memberP(sK3,X4) ),
inference(cnf_transformation,[],[f125]) ).
fof(f149,plain,
! [X4] :
( memberP(sK3,X4)
| ~ ssItem(X4)
| ~ memberP(sK2,X4) ),
inference(cnf_transformation,[],[f125]) ).
fof(f151,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f125]) ).
fof(f152,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f125]) ).
fof(f157,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f160,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f179,plain,
! [X0] :
( cons(sK14(X0),sK13(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f180,plain,
! [X0] :
( ssItem(sK14(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f181,plain,
! [X0] :
( ssList(sK13(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f197,plain,
( nil = sK3
| nil = sK2 ),
inference(definition_unfolding,[],[f147,f152,f151]) ).
fof(f200,plain,
( nil != sK3
| nil != sK2 ),
inference(definition_unfolding,[],[f144,f151,f152]) ).
fof(f203,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f160]) ).
fof(f211,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f203]) ).
fof(f223,plain,
! [X0] :
( ~ memberP(sK3,X0)
| ~ ssItem(X0)
| nil = sK2 ),
inference(superposition,[],[f157,f197]) ).
fof(f230,plain,
! [X0] :
( ~ ssItem(X0)
| nil = sK2
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(resolution,[],[f223,f149]) ).
fof(f231,plain,
! [X0] :
( ~ memberP(sK2,X0)
| nil = sK2
| ~ ssItem(X0) ),
inference(duplicate_literal_removal,[],[f230]) ).
fof(f264,plain,
! [X0] :
( memberP(X0,sK14(X0))
| ~ ssList(sK13(X0))
| ~ ssItem(sK14(X0))
| nil = X0
| ~ ssList(X0) ),
inference(superposition,[],[f211,f179]) ).
fof(f269,plain,
! [X0] :
( memberP(X0,sK14(X0))
| ~ ssItem(sK14(X0))
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f264,f181]) ).
fof(f271,plain,
! [X0] :
( memberP(X0,sK14(X0))
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f269,f180]) ).
fof(f273,plain,
( nil = sK2
| ~ ssList(sK2)
| nil = sK2
| ~ ssItem(sK14(sK2)) ),
inference(resolution,[],[f271,f231]) ).
fof(f277,plain,
( nil = sK2
| ~ ssList(sK2)
| ~ ssItem(sK14(sK2)) ),
inference(duplicate_literal_removal,[],[f273]) ).
fof(f279,plain,
( nil = sK2
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f277,f180]) ).
fof(f281,plain,
nil = sK2,
inference(forward_subsumption_resolution,[],[f279,f142]) ).
fof(f294,plain,
! [X0] :
( ~ memberP(sK2,X0)
| ~ ssItem(X0) ),
inference(superposition,[],[f157,f281]) ).
fof(f299,plain,
( sK2 != sK3
| sK2 != sK2 ),
inference(superposition,[],[f200,f281]) ).
fof(f300,plain,
sK2 != sK3,
inference(trivial_inequality_removal,[],[f299]) ).
fof(f316,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssItem(X0)
| ~ memberP(sK3,X0) ),
inference(resolution,[],[f294,f148]) ).
fof(f318,plain,
! [X0] :
( ~ memberP(sK3,X0)
| ~ ssItem(X0) ),
inference(duplicate_literal_removal,[],[f316]) ).
fof(f320,plain,
( ~ ssItem(sK14(sK3))
| nil = sK3
| ~ ssList(sK3) ),
inference(resolution,[],[f318,f271]) ).
fof(f322,plain,
( nil = sK3
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f320,f180]) ).
fof(f323,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f322,f143]) ).
fof(f346,plain,
sK2 = sK3,
inference(superposition,[],[f281,f323]) ).
fof(f348,plain,
$false,
inference(forward_subsumption_resolution,[],[f346,f300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC025+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n019.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 07:29:48 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
% 2.68/1.34 % (3829162)Detected formulas, will run a generic FOF schedule.
% 2.68/1.34 % (3829171)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2547172052:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.34 % (3829171)First to succeed.
% 2.68/1.34 % (3829171)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3829162"
% 2.68/1.34 % (3829169)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=260090822:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.34 % (3829168)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=1633346928:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.34 % (3829170)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1252194938:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.34 % (3829167)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=1261526245:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.34 % (3829173)dis-21_1_sil=8000:lcm=predicate:random_seed=2792598058: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)
% 2.68/1.34 % (3829172)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3701568829:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.34 % (3829170)Refutation not found, incomplete strategy
% 2.68/1.34 % (3829170)------------------------------
% 2.68/1.34 % (3829170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.34 % (3829170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.34 % (3829170)CaDiCaL version: 2.1.3
% 2.68/1.34 % (3829170)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.34 % (3829170)Time elapsed: 0.003 s
% 2.68/1.34 % (3829170)Peak memory usage: 88 MB
% 2.68/1.34 % (3829170)Instructions burned: 3 (million)
% 2.68/1.34 % (3829172)Also succeeded, but the first one will report.
% 2.68/1.34 % (3829173)Instruction limit reached!
% 2.68/1.34 % (3829173)------------------------------
% 2.68/1.34 % (3829173)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.34 % (3829173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.34 % (3829173)CaDiCaL version: 2.1.3
% 2.68/1.34 % (3829173)Termination reason: Instruction limit
% 2.68/1.34 % (3829173)Termination phase: Saturation
% 2.68/1.34 % (3829173)Time elapsed: 0.072 s
% 2.68/1.34 % (3829173)Peak memory usage: 90 MB
% 2.68/1.34 % (3829173)Instructions burned: 131 (million)
% 2.68/1.34 % (3829171)Refutation found. Thanks to Tanya!
% 2.68/1.34 % SZS status Theorem for theBenchmark
% 2.68/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.34 % (3829171)------------------------------
% 2.68/1.34 % (3829171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.34 % (3829171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.34 % (3829171)CaDiCaL version: 2.1.3
% 2.68/1.34 % (3829171)Termination reason: Refutation
% 2.68/1.34 % (3829171)Time elapsed: 0.004 s
% 2.68/1.34 % (3829171)Peak memory usage: 88 MB
% 2.68/1.34 % (3829171)Instructions burned: 8 (million)
% 2.68/1.34 % (3829171)------------------------------
% 2.68/1.34 % (3829171)------------------------------
% 2.68/1.34 % (3829162)Success in time 0.295 s
% 2.68/1.34 % Vampire exiting
%------------------------------------------------------------------------------