%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC042+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 : n006.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 01:02:10 PM UTC 2026
% Result : Theorem 2.66s 1.36s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 154 ( 77 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 197 ( 68 ~; 59 |; 56 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 52 ( 34 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ totalorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& leq(X7,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)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ totalorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& leq(X7,X5) ) ) ) ) ) )
| ( nil != X3
& nil = X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ? [X4] :
( app(X2,X4) = X3
& totalorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ leq(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ? [X4] :
( app(X2,X4) = X3
& totalorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ leq(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f134,plain,
( nil = sK1
& sK1 = sK3
& sK0 = sK2
& nil != sK0
& sK3 = app(sK2,sK4)
& totalorderedP(sK2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != sK4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != sK2
| ~ leq(X7,X5) ) ) ) )
& ssList(sK4)
& ( nil = sK3
| nil != sK2 )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f99]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f108]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f137]) ).
fof(f147,plain,
ssList(sK2),
inference(cnf_transformation,[],[f134]) ).
fof(f150,plain,
ssList(sK4),
inference(cnf_transformation,[],[f134]) ).
fof(f153,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f134]) ).
fof(f154,plain,
nil != sK0,
inference(cnf_transformation,[],[f134]) ).
fof(f155,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f134]) ).
fof(f156,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f134]) ).
fof(f157,plain,
nil = sK1,
inference(cnf_transformation,[],[f134]) ).
fof(f170,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f204,plain,
nil = sK3,
inference(definition_unfolding,[],[f157,f156]) ).
fof(f205,plain,
sK2 != sK3,
inference(definition_unfolding,[],[f154,f204,f155]) ).
fof(f217,plain,
! [X0,X1] :
( app(X0,X1) != sK3
| sK3 = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f170,f204,f204]) ).
fof(f247,plain,
( sK3 != sK3
| sK2 = sK3
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[],[f217,f153]) ).
fof(f250,plain,
( sK2 = sK3
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(trivial_inequality_removal,[],[f247]) ).
fof(f251,plain,
( ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f250,f205]) ).
fof(f252,plain,
~ ssList(sK2),
inference(forward_subsumption_resolution,[],[f251,f150]) ).
fof(f253,plain,
$false,
inference(forward_subsumption_resolution,[],[f252,f147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC042+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n006.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 07:34:25 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.66/1.36 % (3800145)Detected formulas, will run a generic FOF schedule.
% 2.66/1.36 % (3800154)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4082457928:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.36 % (3800154)First to succeed.
% 2.66/1.36 % (3800154)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3800145"
% 2.66/1.36 % (3800156)dis-21_1_sil=8000:lcm=predicate:random_seed=3757559147: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)
% 2.66/1.36 % (3800153)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=304387243:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.36 % (3800150)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=96574257:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.36 % (3800151)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=1386395728:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.36 % (3800152)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=659811324:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.36 % (3800155)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=935155305:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.36 % (3800153)Also succeeded, but the first one will report.
% 2.66/1.36 % (3800156)Also succeeded, but the first one will report.
% 2.66/1.36 % (3800155)Also succeeded, but the first one will report.
% 2.66/1.36 % (3800154)Refutation found. Thanks to Tanya!
% 2.66/1.36 % SZS status Theorem for theBenchmark
% 2.66/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.36 % (3800154)------------------------------
% 2.66/1.36 % (3800154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.36 % (3800154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.36 % (3800154)CaDiCaL version: 2.1.3
% 2.66/1.36 % (3800154)Termination reason: Refutation
% 2.66/1.36 % (3800154)Time elapsed: 0.002 s
% 2.66/1.36 % (3800154)Peak memory usage: 88 MB
% 2.66/1.36 % (3800154)Instructions burned: 4 (million)
% 2.66/1.36 % (3800154)------------------------------
% 2.66/1.36 % (3800154)------------------------------
% 2.66/1.36 % (3800145)Success in time 0.291 s
% 2.66/1.36 % Vampire exiting
%------------------------------------------------------------------------------