%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC339+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 : n015.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 01:03:31 PM UTC 2026
% Result : Theorem 2.86s 1.18s
% Output : Refutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 204 ( 48 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 276 ( 101 ~; 90 |; 67 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 87 ( 59 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
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)
=> ( app(app(X4,X2),X5) != X3
| ~ totalorderedP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X2
& leq(X6,X8) ) ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X5
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(X13,cons(X12,nil)) = X2
& leq(X12,X10) ) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( segmentP(X1,X0)
& totalorderedP(X0) ) ) ) ) ) ),
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)
=> ( app(app(X4,X2),X5) != X3
| ~ totalorderedP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X2
& leq(X6,X8) ) ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X5
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(X13,cons(X12,nil)) = X2
& leq(X12,X10) ) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( segmentP(X1,X0)
& totalorderedP(X0) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& totalorderedP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X2
| ~ leq(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != X2
| ~ leq(X12,X10) ) ) ) )
& ssList(X5) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ~ segmentP(X1,X0)
| ~ totalorderedP(X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& totalorderedP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X2
| ~ leq(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != X2
| ~ leq(X12,X10) ) ) ) )
& ssList(X5) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ~ segmentP(X1,X0)
| ~ totalorderedP(X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f120]) ).
fof(f122,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f144,plain,
( sK1 = sK3
& sK0 = sK2
& sK3 = app(app(sK4,sK2),sK5)
& totalorderedP(sK2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != sK4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != sK2
| ~ leq(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != sK5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != sK2
| ~ leq(X12,X10) ) ) ) )
& ssList(sK5)
& ssList(sK4)
& ( nil = sK3
| nil != sK2 )
& ( ~ segmentP(sK1,sK0)
| ~ totalorderedP(sK0) )
& 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(X5,sK5)],[f99]) ).
fof(f161,plain,
ssList(sK2),
inference(cnf_transformation,[],[f144]) ).
fof(f163,plain,
( ~ segmentP(sK1,sK0)
| ~ totalorderedP(sK0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f165,plain,
ssList(sK4),
inference(cnf_transformation,[],[f144]) ).
fof(f166,plain,
ssList(sK5),
inference(cnf_transformation,[],[f144]) ).
fof(f169,plain,
totalorderedP(sK2),
inference(cnf_transformation,[],[f144]) ).
fof(f170,plain,
sK3 = app(app(sK4,sK2),sK5),
inference(cnf_transformation,[],[f144]) ).
fof(f171,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f144]) ).
fof(f172,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f144]) ).
fof(f199,plain,
! [X2,X3,X0,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f200,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f230,plain,
( ~ segmentP(sK3,sK2)
| ~ totalorderedP(sK2) ),
inference(definition_unfolding,[],[f163,f172,f171,f171]) ).
fof(f241,plain,
~ segmentP(sK3,sK2),
inference(forward_subsumption_resolution,[],[f230,f169]) ).
fof(f632,plain,
! [X0] :
( segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(sK5)
| ~ ssList(sK4)
| ~ ssList(X0)
| ~ ssList(sK2) ),
inference(superposition,[],[f199,f170]) ).
fof(f643,plain,
! [X0] :
( segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(sK4)
| ~ ssList(X0)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f632,f166]) ).
fof(f651,plain,
! [X0] :
( segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(X0)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f643,f165]) ).
fof(f652,plain,
! [X0] :
( segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f651,f161]) ).
fof(f653,plain,
( ~ segmentP(sK2,sK2)
| ~ ssList(sK2) ),
inference(resolution,[],[f652,f241]) ).
fof(f659,plain,
~ ssList(sK2),
inference(forward_subsumption_resolution,[],[f653,f200]) ).
fof(f660,plain,
$false,
inference(forward_subsumption_resolution,[],[f659,f161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC339+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 09:14:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.86/1.18 % (2489876)Detected formulas, will run a generic FOF schedule.
% 2.86/1.18 % (2489885)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1608351904:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.86/1.18 % (2489885)First to succeed.
% 2.86/1.18 % (2489885)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2489876"
% 2.86/1.18 % (2489882)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=1922290653:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.86/1.18 % (2489887)dis-21_1_sil=8000:lcm=predicate:random_seed=3848646756: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)
% 2.86/1.18 % (2489883)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=2259546551:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.86/1.18 % (2489881)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=293874177:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.86/1.18 % (2489886)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3212090185:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.86/1.18 % (2489884)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3740501337:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.86/1.18 % (2489884)Also succeeded, but the first one will report.
% 2.86/1.18 % (2489886)Also succeeded, but the first one will report.
% 2.86/1.18 % (2489887)Instruction limit reached!
% 2.86/1.18 % (2489887)------------------------------
% 2.86/1.18 % (2489887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.18 % (2489887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.18 % (2489887)CaDiCaL version: 2.1.3
% 2.86/1.18 % (2489887)Termination reason: Instruction limit
% 2.86/1.18 % (2489887)Termination phase: Saturation
% 2.86/1.18 % (2489887)Time elapsed: 0.074 s
% 2.86/1.18 % (2489887)Peak memory usage: 90 MB
% 2.86/1.18 % (2489887)Instructions burned: 130 (million)
% 2.86/1.18 % (2489885)Refutation found. Thanks to Tanya!
% 2.86/1.18 % SZS status Theorem for theBenchmark
% 2.86/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.86/1.18 % (2489885)------------------------------
% 2.86/1.18 % (2489885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.18 % (2489885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.18 % (2489885)CaDiCaL version: 2.1.3
% 2.86/1.18 % (2489885)Termination reason: Refutation
% 2.86/1.18 % (2489885)Time elapsed: 0.008 s
% 2.86/1.18 % (2489885)Peak memory usage: 88 MB
% 2.86/1.18 % (2489885)Instructions burned: 20 (million)
% 2.86/1.18 % (2489885)------------------------------
% 2.86/1.18 % (2489885)------------------------------
% 2.86/1.18 % (2489876)Success in time 0.318 s
% 2.86/1.18 % Vampire exiting
%------------------------------------------------------------------------------