%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC371+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 : n002.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 01:03:40 PM UTC 2026
% Result : Theorem 3.53s 1.10s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 197 ( 50 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 256 ( 94 ~; 85 |; 60 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 88 ( 62 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
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
| ~ 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) ) ) ) ) ) )
| segmentP(X1,X0)
| ( 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
| ~ 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) ) ) ) ) ) )
| segmentP(X1,X0)
| ( 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
& 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) )
& ~ segmentP(X1,X0)
& ( 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
& 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) )
& ~ segmentP(X1,X0)
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f115,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f144,plain,
( sK1 = sK3
& sK0 = sK2
& 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)
& ~ segmentP(sK1,sK0)
& ( 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(f150,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f127]) ).
fof(f151,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X4,X1),X5) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f150]) ).
fof(f152,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK9(X0,X1))
& ssList(sK10(X0,X1))
& app(app(sK9(X0,X1),X1),sK10(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f151]) ).
fof(f161,plain,
ssList(sK2),
inference(cnf_transformation,[],[f144]) ).
fof(f164,plain,
~ segmentP(sK1,sK0),
inference(cnf_transformation,[],[f144]) ).
fof(f165,plain,
ssList(sK4),
inference(cnf_transformation,[],[f144]) ).
fof(f168,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f144]) ).
fof(f169,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f144]) ).
fof(f170,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f144]) ).
fof(f190,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f192,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f193,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f204,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f228,plain,
~ segmentP(sK3,sK2),
inference(definition_unfolding,[],[f164,f170,f169]) ).
fof(f234,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f204]) ).
fof(f699,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(superposition,[],[f234,f190]) ).
fof(f707,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literal_removal,[],[f699]) ).
fof(f715,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f707,f193]) ).
fof(f721,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f715,f192]) ).
fof(f924,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[],[f721,f168]) ).
fof(f934,plain,
( ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f924,f228]) ).
fof(f939,plain,
~ ssList(sK2),
inference(forward_subsumption_resolution,[],[f934,f165]) ).
fof(f940,plain,
$false,
inference(forward_subsumption_resolution,[],[f939,f161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC371+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n002.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 09:23:22 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running first-order theorem proving
% 0.10/0.24 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
% 3.53/1.10 % (230430)Detected formulas, will run a generic FOF schedule.
% 3.53/1.10 % (230441)dis-21_1_sil=8000:lcm=predicate:random_seed=1278551548: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)
% 3.53/1.10 % (230440)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3356245874:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.10 % (230435)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=2151857644:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.10 % (230439)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3062300887:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.10 % (230438)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3859194536:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.10 % (230436)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=452485749:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.10 % (230437)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=270807963:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.10 % (230441)Instruction limit reached!
% 3.53/1.10 % (230441)------------------------------
% 3.53/1.10 % (230441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.10 % (230441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.10 % (230441)CaDiCaL version: 2.1.3
% 3.53/1.10 % (230441)Termination reason: Instruction limit
% 3.53/1.10 % (230441)Termination phase: Saturation
% 3.53/1.10 % (230441)Time elapsed: 0.041 s
% 3.53/1.10 % (230441)Peak memory usage: 91 MB
% 3.53/1.10 % (230441)Instructions burned: 131 (million)
% 3.53/1.10 % (230439)First to succeed.
% 3.53/1.10 % (230439)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-230430"
% 3.53/1.10 % (230440)Also succeeded, but the first one will report.
% 3.53/1.10 % (230438)Instruction limit reached!
% 3.53/1.10 % (230438)------------------------------
% 3.53/1.10 % (230438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.10 % (230438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.10 % (230438)CaDiCaL version: 2.1.3
% 3.53/1.10 % (230438)Termination reason: Instruction limit
% 3.53/1.10 % (230438)Termination phase: Saturation
% 3.53/1.10 % (230438)Time elapsed: 0.069 s
% 3.53/1.10 % (230438)Peak memory usage: 89 MB
% 3.53/1.10 % (230438)Instructions burned: 109 (million)
% 3.53/1.10 % (230449)lrs+10_1_sil=8000:sp=occurrence:random_seed=2153288139:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.53/1.10 % (230449)Instruction limit reached!
% 3.53/1.10 % (230449)------------------------------
% 3.53/1.10 % (230449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.10 % (230449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.10 % (230449)CaDiCaL version: 2.1.3
% 3.53/1.10 % (230449)Termination reason: Instruction limit
% 3.53/1.10 % (230449)Termination phase: Saturation
% 3.53/1.10 % (230449)Time elapsed: 0.088 s
% 3.53/1.10 % (230449)Peak memory usage: 93 MB
% 3.53/1.10 % (230449)Instructions burned: 286 (million)
% 3.53/1.10 % (230450)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2334574305:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.53/1.10 % (230439)Refutation found. Thanks to Tanya!
% 3.53/1.10 % SZS status Theorem for theBenchmark
% 3.53/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.10 % (230439)------------------------------
% 3.53/1.10 % (230439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.10 % (230439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.10 % (230439)CaDiCaL version: 2.1.3
% 3.53/1.10 % (230439)Termination reason: Refutation
% 3.53/1.10 % (230439)Time elapsed: 0.018 s
% 3.53/1.10 % (230439)Peak memory usage: 88 MB
% 3.53/1.10 % (230439)Instructions burned: 28 (million)
% 3.53/1.10 % (230439)------------------------------
% 3.53/1.10 % (230439)------------------------------
% 3.53/1.10 % (230430)Success in time 0.439 s
% 3.53/1.10 % Vampire exiting
%------------------------------------------------------------------------------