%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC179+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 : n005.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 01:02:49 PM UTC 2026
% Result : Theorem 3.61s 1.51s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 8 unt; 1 def)
% Number of atoms : 175 ( 45 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 214 ( 66 ~; 55 |; 78 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 76 ( 45 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f71,axiom,
! [X0] :
( ssItem(X0)
=> duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| duplicatefreeP(X0)
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( cons(X4,nil) != X2
| app(app(X5,X2),X6) != X3
| ? [X7] :
( ssItem(X7)
& memberP(X5,X7)
& lt(X4,X7) )
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X8,X4) ) ) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
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(X0)
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( cons(X4,nil) != X2
| app(app(X5,X2),X6) != X3
| ? [X7] :
( ssItem(X7)
& memberP(X5,X7)
& lt(X4,X7) )
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X8,X4) ) ) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ~ duplicatefreeP(X0)
& ( ? [X4] :
( ? [X5] :
( ? [X6] :
( cons(X4,nil) = X2
& app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ lt(X4,X7) )
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X8,X4) )
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ( 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
& ~ duplicatefreeP(X0)
& ( ? [X4] :
( ? [X5] :
( ? [X6] :
( cons(X4,nil) = X2
& app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ lt(X4,X7) )
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X8,X4) )
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f132,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f140,definition,
! [X2,X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( cons(X4,nil) = X2
& app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ lt(X4,X7) )
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X8,X4) )
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ sP0(X2,X3) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f141,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ~ duplicatefreeP(X0)
& ( sP0(X2,X3)
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f99,f140]) ).
fof(f142,plain,
! [X2,X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( cons(X4,nil) = X2
& app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ lt(X4,X7) )
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X8,X4) )
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ sP0(X2,X3) ),
inference(nnf_transformation,[],[f140]) ).
fof(f143,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( cons(X2,nil) = X0
& app(app(X3,X0),X4) = X1
& ! [X5] :
( ~ ssItem(X5)
| ~ memberP(X3,X5)
| ~ lt(X2,X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ memberP(X4,X6)
| ~ lt(X6,X2) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f142]) ).
fof(f144,plain,
! [X0,X1] :
( ( cons(sK1(X0,X1),nil) = X0
& app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1
& ! [X5] :
( ~ ssItem(X5)
| ~ memberP(sK2(X0,X1),X5)
| ~ lt(sK1(X0,X1),X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ memberP(sK3(X0,X1),X6)
| ~ lt(X6,sK1(X0,X1)) )
& ssList(sK3(X0,X1))
& ssList(sK2(X0,X1))
& ssItem(sK1(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X3,sK2(X0,X1)),skolemize(X4,sK3(X0,X1))],[f143]) ).
fof(f145,plain,
( sK5 = sK7
& sK4 = sK6
& ~ duplicatefreeP(sK4)
& ( sP0(sK6,sK7)
| ( nil = sK7
& nil = sK6 ) )
& ssList(sK7)
& ssList(sK6)
& ssList(sK5)
& ssList(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f141]) ).
fof(f162,plain,
! [X0,X1] :
( ssItem(sK1(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
fof(f168,plain,
! [X0,X1] :
( cons(sK1(X0,X1),nil) = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
fof(f173,plain,
( sP0(sK6,sK7)
| nil = sK6 ),
inference(cnf_transformation,[],[f145]) ).
fof(f175,plain,
~ duplicatefreeP(sK4),
inference(cnf_transformation,[],[f145]) ).
fof(f176,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f145]) ).
fof(f220,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f221,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f233,plain,
~ duplicatefreeP(sK6),
inference(definition_unfolding,[],[f175,f176]) ).
fof(f253,plain,
! [X0,X1] :
( duplicatefreeP(X0)
| ~ ssItem(sK1(X0,X1))
| ~ sP0(X0,X1) ),
inference(superposition,[],[f221,f168]) ).
fof(f262,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| duplicatefreeP(X0) ),
inference(forward_subsumption_resolution,[],[f253,f162]) ).
fof(f268,plain,
( duplicatefreeP(sK6)
| nil = sK6 ),
inference(resolution,[],[f262,f173]) ).
fof(f269,plain,
nil = sK6,
inference(forward_subsumption_resolution,[],[f268,f233]) ).
fof(f276,plain,
duplicatefreeP(sK6),
inference(superposition,[],[f220,f269]) ).
fof(f278,plain,
$false,
inference(forward_subsumption_resolution,[],[f276,f233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC179+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 % Computer : n005.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8046.5625MB
% 0.12/0.42 % OS : Linux 6.8.0-71-generic
% 0.12/0.42 % CPULimit : 300
% 0.12/0.42 % WCLimit : 300
% 0.12/0.42 % DateTime : Mon Sep 28 08:19:17 UTC 2026
% 0.12/0.42 % CPUTime :
% 0.12/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.46 Running first-order theorem proving
% 0.12/0.46 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
% 3.61/1.51 % (638250)Detected formulas, will run a generic FOF schedule.
% 3.61/1.51 % (638258)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2255026718:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.61/1.51 % (638258)Refutation not found, incomplete strategy
% 3.61/1.51 % (638258)------------------------------
% 3.61/1.51 % (638258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.51 % (638258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.51 % (638258)CaDiCaL version: 2.1.3
% 3.61/1.51 % (638258)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.51 % (638258)Time elapsed: 0.002 s
% 3.61/1.51 % (638258)Peak memory usage: 88 MB
% 3.61/1.51 % (638258)Instructions burned: 5 (million)
% 3.61/1.51 % (638257)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=1229623697:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.61/1.51 % (638256)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=1432438148:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.61/1.51 % (638255)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=1813793330:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.61/1.51 % (638261)dis-21_1_sil=8000:lcm=predicate:random_seed=95895042: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)
% 3.61/1.51 % (638259)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3348303398:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.61/1.51 % (638259)First to succeed.
% 3.61/1.51 % (638259)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-638250"
% 3.61/1.51 % (638260)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1306985659:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.61/1.51 % (638260)Also succeeded, but the first one will report.
% 3.61/1.51 % (638261)Instruction limit reached!
% 3.61/1.51 % (638261)------------------------------
% 3.61/1.51 % (638261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.51 % (638261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.51 % (638261)CaDiCaL version: 2.1.3
% 3.61/1.51 % (638261)Termination reason: Instruction limit
% 3.61/1.51 % (638261)Termination phase: Saturation
% 3.61/1.51 % (638261)Time elapsed: 0.070 s
% 3.61/1.51 % (638261)Peak memory usage: 91 MB
% 3.61/1.51 % (638261)Instructions burned: 129 (million)
% 3.61/1.51 % (638258)------------------------------
% 3.61/1.51 % (638258)------------------------------
% 3.61/1.51 % (638270)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1841620062:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.61/1.51 % (638269)lrs+10_1_sil=8000:sp=occurrence:random_seed=3230752938:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.61/1.51 % (638269)Also succeeded, but the first one will report.
% 3.61/1.51 % (638270)Instruction limit reached!
% 3.61/1.51 % (638270)------------------------------
% 3.61/1.51 % (638270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.51 % (638270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.51 % (638270)CaDiCaL version: 2.1.3
% 3.61/1.51 % (638270)Termination reason: Instruction limit
% 3.61/1.51 % (638270)Termination phase: Saturation
% 3.61/1.51 % (638270)Time elapsed: 0.041 s
% 3.61/1.51 % (638270)Peak memory usage: 92 MB
% 3.61/1.51 % (638270)Instructions burned: 158 (million)
% 3.61/1.51 % (638259)Refutation found. Thanks to Tanya!
% 3.61/1.51 % SZS status Theorem for theBenchmark
% 3.61/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.51 % (638259)------------------------------
% 3.61/1.51 % (638259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.51 % (638259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.51 % (638259)CaDiCaL version: 2.1.3
% 3.61/1.51 % (638259)Termination reason: Refutation
% 3.61/1.51 % (638259)Time elapsed: 0.005 s
% 3.61/1.51 % (638259)Peak memory usage: 88 MB
% 3.61/1.51 % (638259)Instructions burned: 5 (million)
% 3.61/1.51 % (638259)------------------------------
% 3.61/1.51 % (638259)------------------------------
% 3.61/1.51 % (638250)Success in time 0.422 s
% 3.61/1.51 % Vampire exiting
%------------------------------------------------------------------------------