%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC118+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 : n009.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 01:02:32 PM UTC 2026
% Result : Theorem 5.30s 1.84s
% Output : Refutation 5.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 248 ( 71 equ)
% Maximal formula atoms : 30 ( 6 avg)
% Number of connectives : 337 ( 130 ~; 112 |; 73 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 95 ( 67 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
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 )
| ( nil = X1
& nil = X0 )
| ( neq(X0,nil)
& segmentP(X1,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 )
| ( nil = X1
& nil = X0 )
| ( neq(X0,nil)
& segmentP(X1,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 )
& ( nil != X1
| nil != X0 )
& ( ~ neq(X0,nil)
| ~ segmentP(X1,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 )
& ( nil != X1
| nil != X0 )
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f122,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(f123,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,[],[f122]) ).
fof(f124,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f146,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 )
& ( nil != sK1
| nil != sK0 )
& ( ~ neq(sK0,nil)
| ~ segmentP(sK1,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(f151,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f165,plain,
ssList(sK2),
inference(cnf_transformation,[],[f146]) ).
fof(f167,plain,
( ~ neq(sK0,nil)
| ~ segmentP(sK1,sK0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f168,plain,
( nil != sK1
| nil != sK0 ),
inference(cnf_transformation,[],[f146]) ).
fof(f169,plain,
( nil != sK2
| nil = sK3 ),
inference(cnf_transformation,[],[f146]) ).
fof(f170,plain,
ssList(sK4),
inference(cnf_transformation,[],[f146]) ).
fof(f171,plain,
ssList(sK5),
inference(cnf_transformation,[],[f146]) ).
fof(f175,plain,
sK3 = app(app(sK4,sK2),sK5),
inference(cnf_transformation,[],[f146]) ).
fof(f176,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f146]) ).
fof(f177,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f146]) ).
fof(f201,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f204,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f208,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,[],[f123]) ).
fof(f209,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f239,plain,
( nil != sK3
| nil != sK2 ),
inference(definition_unfolding,[],[f168,f177,f176]) ).
fof(f240,plain,
( ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(definition_unfolding,[],[f167,f176,f177,f176]) ).
fof(f255,plain,
nil != sK2,
inference(forward_subsumption_resolution,[],[f239,f169]) ).
fof(f654,plain,
! [X0] :
( segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(sK5)
| ~ ssList(sK4)
| ~ ssList(X0)
| ~ ssList(sK2) ),
inference(superposition,[],[f208,f175]) ).
fof(f665,plain,
! [X0] :
( segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(sK4)
| ~ ssList(X0)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f654,f171]) ).
fof(f673,plain,
! [X0] :
( segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(X0)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f665,f170]) ).
fof(f674,plain,
! [X0] :
( segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f673,f165]) ).
fof(f675,plain,
( ~ segmentP(sK2,sK2)
| ~ ssList(sK2)
| ~ neq(sK2,nil) ),
inference(resolution,[],[f674,f240]) ).
fof(f681,plain,
( ~ ssList(sK2)
| ~ neq(sK2,nil) ),
inference(forward_subsumption_resolution,[],[f675,f209]) ).
fof(f682,plain,
~ neq(sK2,nil),
inference(forward_subsumption_resolution,[],[f681,f165]) ).
fof(f716,plain,
( nil = sK2
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(resolution,[],[f682,f201]) ).
fof(f717,plain,
( ~ ssList(nil)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f716,f255]) ).
fof(f719,plain,
~ ssList(sK2),
inference(forward_subsumption_resolution,[],[f717,f204]) ).
fof(f720,plain,
$false,
inference(forward_subsumption_resolution,[],[f719,f165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC118+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.41 % Computer : n009.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Mon Sep 28 07:59:30 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.47 Running first-order theorem proving
% 0.22/0.47 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
% 5.30/1.84 % (2874294)Detected formulas, will run a generic FOF schedule.
% 5.30/1.84 % (2874310)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=1056181623:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.30/1.84 % (2874314)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4066410504:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.30/1.84 % (2874311)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=1855689626:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.30/1.84 % (2874315)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1627537378:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.30/1.84 % (2874313)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3931682255:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.30/1.84 % (2874317)dis-21_1_sil=8000:lcm=predicate:random_seed=1874956616: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)
% 5.30/1.84 % (2874312)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=1151226960:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.30/1.84 % (2874314)First to succeed.
% 5.30/1.84 % (2874314)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2874294"
% 5.30/1.84 % (2874313)Also succeeded, but the first one will report.
% 5.30/1.84 % (2874315)Also succeeded, but the first one will report.
% 5.30/1.84 % (2874317)Instruction limit reached!
% 5.30/1.84 % (2874317)------------------------------
% 5.30/1.84 % (2874317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.30/1.84 % (2874317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.30/1.84 % (2874317)CaDiCaL version: 2.1.3
% 5.30/1.84 % (2874317)Termination reason: Instruction limit
% 5.30/1.84 % (2874317)Termination phase: Saturation
% 5.30/1.84 % (2874317)Time elapsed: 0.123 s
% 5.30/1.84 % (2874317)Peak memory usage: 90 MB
% 5.30/1.84 % (2874317)Instructions burned: 130 (million)
% 5.30/1.84 % (2874327)lrs+10_1_sil=8000:sp=occurrence:random_seed=273884095:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.30/1.84 % (2874327)Also succeeded, but the first one will report.
% 5.30/1.84 % (2874314)Refutation found. Thanks to Tanya!
% 5.30/1.84 % SZS status Theorem for theBenchmark
% 5.30/1.84 % SZS output start Proof for theBenchmark
% See solution above
% 5.30/1.84 % (2874314)------------------------------
% 5.30/1.84 % (2874314)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.30/1.84 % (2874314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.30/1.84 % (2874314)CaDiCaL version: 2.1.3
% 5.30/1.84 % (2874314)Termination reason: Refutation
% 5.30/1.84 % (2874314)Time elapsed: 0.024 s
% 5.30/1.84 % (2874314)Peak memory usage: 88 MB
% 5.30/1.84 % (2874314)Instructions burned: 22 (million)
% 5.30/1.84 % (2874314)------------------------------
% 5.30/1.84 % (2874314)------------------------------
% 5.30/1.84 % (2874294)Success in time 0.649 s
% 5.30/1.84 % Vampire exiting
%------------------------------------------------------------------------------