%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC398+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 : 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 01:03:48 PM UTC 2026
% Result : Theorem 3.42s 1.16s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 12 unt; 0 def)
% Number of atoms : 156 ( 38 equ)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 197 ( 67 ~; 60 |; 53 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 57 ( 39 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ equalelemsP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssList(X7)
& app(X7,cons(X5,nil)) = X2 ) ) ) ) )
| ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X0,X8)
| memberP(X1,X8) ) )
| ( 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] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ equalelemsP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssList(X7)
& app(X7,cons(X5,nil)) = X2 ) ) ) ) )
| ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X0,X8)
| memberP(X1,X8) ) )
| ( nil != X3
& nil = X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( app(X2,X4) = X3
& equalelemsP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != X2 ) ) )
& ssList(X4) )
& ? [X8] :
( memberP(X0,X8)
& ~ memberP(X1,X8)
& ssItem(X8) )
& ( 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] :
( app(X2,X4) = X3
& equalelemsP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != X2 ) ) )
& ssList(X4) )
& ? [X8] :
( memberP(X0,X8)
& ~ memberP(X1,X8)
& ssItem(X8) )
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f125,plain,
( sK1 = sK3
& sK0 = sK2
& sK3 = app(sK2,sK4)
& equalelemsP(sK2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != sK4
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != sK2 ) ) )
& ssList(sK4)
& memberP(sK0,sK5)
& ~ memberP(sK1,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(X8,sK5)],[f99]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f120]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f132]) ).
fof(f142,plain,
ssList(sK2),
inference(cnf_transformation,[],[f125]) ).
fof(f145,plain,
ssItem(sK5),
inference(cnf_transformation,[],[f125]) ).
fof(f146,plain,
~ memberP(sK1,sK5),
inference(cnf_transformation,[],[f125]) ).
fof(f147,plain,
memberP(sK0,sK5),
inference(cnf_transformation,[],[f125]) ).
fof(f148,plain,
ssList(sK4),
inference(cnf_transformation,[],[f125]) ).
fof(f151,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f125]) ).
fof(f152,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f125]) ).
fof(f153,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f125]) ).
fof(f183,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f197,plain,
memberP(sK2,sK5),
inference(definition_unfolding,[],[f147,f152]) ).
fof(f198,plain,
~ memberP(sK3,sK5),
inference(definition_unfolding,[],[f146,f153]) ).
fof(f267,plain,
! [X0] :
( memberP(sK3,X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK4)
| ~ ssList(sK2)
| ~ ssItem(X0) ),
inference(superposition,[],[f183,f151]) ).
fof(f271,plain,
! [X0] :
( memberP(sK3,X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK2)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f267,f148]) ).
fof(f272,plain,
! [X0] :
( memberP(sK3,X0)
| ~ memberP(sK2,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f271,f142]) ).
fof(f273,plain,
( ~ memberP(sK2,sK5)
| ~ ssItem(sK5) ),
inference(resolution,[],[f272,f198]) ).
fof(f274,plain,
~ ssItem(sK5),
inference(forward_subsumption_resolution,[],[f273,f197]) ).
fof(f275,plain,
$false,
inference(forward_subsumption_resolution,[],[f274,f145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC398+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n019.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 09:27:34 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 3.42/1.16 % (3873742)Detected formulas, will run a generic FOF schedule.
% 3.42/1.16 % (3873747)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=4292567057:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.42/1.16 % (3873752)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2311571825:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.42/1.16 % (3873753)dis-21_1_sil=8000:lcm=predicate:random_seed=1989634690: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)
% 3.42/1.16 % (3873750)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1089206550:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.42/1.16 % (3873749)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=125274995:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.42/1.16 % (3873748)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=658853208:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.42/1.16 % (3873751)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3439846947:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.42/1.16 % (3873751)First to succeed.
% 3.42/1.16 % (3873751)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3873742"
% 3.42/1.16 % (3873750)Also succeeded, but the first one will report.
% 3.42/1.16 % (3873753)Instruction limit reached!
% 3.42/1.16 % (3873753)------------------------------
% 3.42/1.16 % (3873753)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.16 % (3873753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.16 % (3873753)CaDiCaL version: 2.1.3
% 3.42/1.16 % (3873753)Termination reason: Instruction limit
% 3.42/1.16 % (3873753)Termination phase: Saturation
% 3.42/1.16 % (3873753)Time elapsed: 0.070 s
% 3.42/1.16 % (3873753)Peak memory usage: 90 MB
% 3.42/1.16 % (3873753)Instructions burned: 130 (million)
% 3.42/1.16 % (3873752)Instruction limit reached!
% 3.42/1.16 % (3873752)------------------------------
% 3.42/1.16 % (3873752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.16 % (3873752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.16 % (3873752)CaDiCaL version: 2.1.3
% 3.42/1.16 % (3873752)Termination reason: Instruction limit
% 3.42/1.16 % (3873752)Termination phase: Saturation
% 3.42/1.16 % (3873752)Time elapsed: 0.092 s
% 3.42/1.16 % (3873752)Peak memory usage: 90 MB
% 3.42/1.16 % (3873752)Instructions burned: 139 (million)
% 3.42/1.16 % (3873762)lrs+10_1_sil=8000:sp=occurrence:random_seed=1569239746:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.42/1.16 % (3873762)Also succeeded, but the first one will report.
% 3.42/1.16 % (3873763)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3833341174:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.42/1.16 % (3873763)Also succeeded, but the first one will report.
% 3.42/1.16 % (3873751)Refutation found. Thanks to Tanya!
% 3.42/1.16 % SZS status Theorem for theBenchmark
% 3.42/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.16 % (3873751)------------------------------
% 3.42/1.16 % (3873751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.16 % (3873751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.16 % (3873751)CaDiCaL version: 2.1.3
% 3.42/1.16 % (3873751)Termination reason: Refutation
% 3.42/1.16 % (3873751)Time elapsed: 0.005 s
% 3.42/1.16 % (3873751)Peak memory usage: 88 MB
% 3.42/1.16 % (3873751)Instructions burned: 6 (million)
% 3.42/1.16 % (3873751)------------------------------
% 3.42/1.16 % (3873751)------------------------------
% 3.42/1.16 % (3873742)Success in time 0.41 s
% 3.42/1.16 % Vampire exiting
%------------------------------------------------------------------------------