%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC009+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 : n007.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 01:02:01 PM UTC 2026
% Result : Theorem 2.69s 1.29s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 165 ( 67 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 224 ( 87 ~; 71 |; 55 &)
% ( 0 <=>; 11 =>; 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 : 67 ( 43 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0 ) ) )
| ! [X7] :
( ssList(X7)
=> ( app(X2,X7) != X3
| ~ strictorderedP(X2)
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X7
& ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(X11,cons(X10,nil)) = X2
& lt(X10,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)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0 ) ) )
| ! [X7] :
( ssList(X7)
=> ( app(X2,X7) != X3
| ~ strictorderedP(X2)
| ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X7
& ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(X11,cons(X10,nil)) = X2
& lt(X10,X8) ) ) ) ) ) )
| ( nil != X3
& nil = X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0 ) ) )
& ? [X7] :
( app(X2,X7) = X3
& strictorderedP(X2)
& ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X7
| ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X10,nil)) != X2
| ~ lt(X10,X8) ) ) ) )
& ssList(X7) )
& ( 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] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0 ) ) )
& ? [X7] :
( app(X2,X7) = X3
& strictorderedP(X2)
& ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X7
| ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X10,nil)) != X2
| ~ lt(X10,X8) ) ) ) )
& ssList(X7) )
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f107,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f144,plain,
( sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != sK1
| app(X4,X6) != sK0 ) ) )
& sK3 = app(sK2,sK4)
& strictorderedP(sK2)
& ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != sK4
| ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X10,nil)) != sK2
| ~ lt(X10,X8) ) ) ) )
& 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(X7,sK4)],[f99]) ).
fof(f159,plain,
ssList(sK2),
inference(cnf_transformation,[],[f144]) ).
fof(f160,plain,
ssList(sK3),
inference(cnf_transformation,[],[f144]) ).
fof(f162,plain,
ssList(sK4),
inference(cnf_transformation,[],[f144]) ).
fof(f165,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f144]) ).
fof(f166,plain,
! [X6,X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,X5),X6) != sK1
| app(X4,X6) != sK0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f167,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f144]) ).
fof(f168,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f144]) ).
fof(f180,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f191,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f223,plain,
! [X6,X4,X5] :
( app(app(X4,X5),X6) != sK3
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssList(X4)
| app(X4,X6) != sK2 ),
inference(definition_unfolding,[],[f166,f168,f167]) ).
fof(f234,plain,
! [X0] :
( sK3 != app(sK3,X0)
| ~ ssList(sK4)
| ~ ssList(X0)
| ~ ssList(sK2)
| sK2 != app(sK2,X0) ),
inference(superposition,[],[f223,f165]) ).
fof(f235,plain,
! [X0] :
( sK3 != app(sK3,X0)
| ~ ssList(X0)
| ~ ssList(sK2)
| sK2 != app(sK2,X0) ),
inference(forward_subsumption_resolution,[],[f234,f162]) ).
fof(f236,plain,
! [X0] :
( sK3 != app(sK3,X0)
| ~ ssList(X0)
| sK2 != app(sK2,X0) ),
inference(forward_subsumption_resolution,[],[f235,f159]) ).
fof(f240,plain,
( sK3 != sK3
| ~ ssList(nil)
| sK2 != app(sK2,nil)
| ~ ssList(sK3) ),
inference(superposition,[],[f236,f180]) ).
fof(f241,plain,
( ~ ssList(nil)
| sK2 != app(sK2,nil)
| ~ ssList(sK3) ),
inference(trivial_inequality_removal,[],[f240]) ).
fof(f243,plain,
( sK2 != app(sK2,nil)
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f241,f191]) ).
fof(f247,plain,
sK2 != app(sK2,nil),
inference(forward_subsumption_resolution,[],[f243,f160]) ).
fof(f251,plain,
( sK2 != sK2
| ~ ssList(sK2) ),
inference(superposition,[],[f247,f180]) ).
fof(f252,plain,
~ ssList(sK2),
inference(trivial_inequality_removal,[],[f251]) ).
fof(f253,plain,
$false,
inference(forward_subsumption_resolution,[],[f252,f159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC009+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 07:23:25 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 2.69/1.29 % (2220160)Detected formulas, will run a generic FOF schedule.
% 2.69/1.29 % (2220187)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=688757882:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.29 % (2220187)First to succeed.
% 2.69/1.29 % (2220187)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2220160"
% 2.69/1.29 % (2220185)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=3067374793:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.29 % (2220189)dis-21_1_sil=8000:lcm=predicate:random_seed=2247549307: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)
% 2.69/1.29 % (2220183)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=1822868537:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.29 % (2220188)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=454099189:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.29 % (2220184)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=429551382:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.29 % (2220186)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1824299693:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.29 % (2220188)Also succeeded, but the first one will report.
% 2.69/1.29 % (2220186)Also succeeded, but the first one will report.
% 2.69/1.29 % (2220189)Instruction limit reached!
% 2.69/1.29 % (2220189)------------------------------
% 2.69/1.29 % (2220189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.29 % (2220189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.29 % (2220189)CaDiCaL version: 2.1.3
% 2.69/1.29 % (2220189)Termination reason: Instruction limit
% 2.69/1.29 % (2220189)Termination phase: Saturation
% 2.69/1.29 % (2220189)Time elapsed: 0.072 s
% 2.69/1.29 % (2220189)Peak memory usage: 90 MB
% 2.69/1.29 % (2220189)Instructions burned: 130 (million)
% 2.69/1.29 % (2220187)Refutation found. Thanks to Tanya!
% 2.69/1.29 % SZS status Theorem for theBenchmark
% 2.69/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.29 % (2220187)------------------------------
% 2.69/1.29 % (2220187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.29 % (2220187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.29 % (2220187)CaDiCaL version: 2.1.3
% 2.69/1.29 % (2220187)Termination reason: Refutation
% 2.69/1.29 % (2220187)Time elapsed: 0.003 s
% 2.69/1.29 % (2220187)Peak memory usage: 88 MB
% 2.69/1.29 % (2220187)Instructions burned: 5 (million)
% 2.69/1.29 % (2220187)------------------------------
% 2.69/1.29 % (2220187)------------------------------
% 2.69/1.29 % (2220160)Success in time 0.314 s
% 2.69/1.29 % Vampire exiting
%------------------------------------------------------------------------------