%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC076+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 : n006.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 01:02:19 PM UTC 2026
% Result : Theorem 2.75s 1.36s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 12 unt; 0 def)
% Number of atoms : 250 ( 71 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 343 ( 136 ~; 116 |; 69 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 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 : 94 ( 68 !; 26 ?)
% 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)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,X2),X6) != X3
| ~ equalelemsP(X2)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssList(X9)
& app(cons(X7,nil),X9) = X2 ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X6
& ? [X12] :
( ssList(X12)
& app(X12,cons(X10,nil)) = X2 ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( nil = X1
& nil = 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)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,X2),X6) != X3
| ~ equalelemsP(X2)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssList(X9)
& app(cons(X7,nil),X9) = X2 ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X6
& ? [X12] :
( ssList(X12)
& app(X12,cons(X10,nil)) = X2 ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( nil = X1
& nil = X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ? [X5] :
( ? [X6] :
( app(app(X5,X2),X6) = X3
& equalelemsP(X2)
& ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X5
| ! [X9] :
( ~ ssList(X9)
| app(cons(X7,nil),X9) != X2 ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X6
| ! [X12] :
( ~ ssList(X12)
| app(X12,cons(X10,nil)) != X2 ) ) )
& ssList(X6) )
& ssList(X5) )
& ( nil = X3
| nil != X2 )
& ( nil != X1
| nil != 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] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ? [X5] :
( ? [X6] :
( app(app(X5,X2),X6) = X3
& equalelemsP(X2)
& ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X5
| ! [X9] :
( ~ ssList(X9)
| app(cons(X7,nil),X9) != X2 ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X6
| ! [X12] :
( ~ ssList(X12)
| app(X12,cons(X10,nil)) != X2 ) ) )
& ssList(X6) )
& ssList(X5) )
& ( nil = X3
| nil != X2 )
& ( nil != X1
| nil != 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(f133,plain,
( sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK1,X4)
| ~ segmentP(sK0,X4) )
& sK3 = app(app(sK4,sK2),sK5)
& equalelemsP(sK2)
& ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != sK4
| ! [X9] :
( ~ ssList(X9)
| app(cons(X7,nil),X9) != sK2 ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != sK5
| ! [X12] :
( ~ ssList(X12)
| app(X12,cons(X10,nil)) != sK2 ) ) )
& ssList(sK5)
& ssList(sK4)
& ( nil = sK3
| nil != sK2 )
& ( nil != sK1
| nil != 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(X5,sK4),skolemize(X6,sK5)],[f99]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f149,plain,
ssList(sK2),
inference(cnf_transformation,[],[f133]) ).
fof(f151,plain,
( nil != sK1
| nil != sK0 ),
inference(cnf_transformation,[],[f133]) ).
fof(f152,plain,
( nil != sK2
| nil = sK3 ),
inference(cnf_transformation,[],[f133]) ).
fof(f153,plain,
ssList(sK4),
inference(cnf_transformation,[],[f133]) ).
fof(f154,plain,
ssList(sK5),
inference(cnf_transformation,[],[f133]) ).
fof(f158,plain,
sK3 = app(app(sK4,sK2),sK5),
inference(cnf_transformation,[],[f133]) ).
fof(f159,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK1,X4)
| ~ segmentP(sK0,X4) ),
inference(cnf_transformation,[],[f133]) ).
fof(f160,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f133]) ).
fof(f161,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f133]) ).
fof(f185,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f188,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f192,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(f193,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f209,plain,
! [X4] :
( ~ segmentP(sK3,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| ~ segmentP(sK2,X4) ),
inference(definition_unfolding,[],[f159,f161,f160]) ).
fof(f210,plain,
( nil != sK3
| nil != sK2 ),
inference(definition_unfolding,[],[f151,f161,f160]) ).
fof(f223,plain,
nil != sK2,
inference(forward_subsumption_resolution,[],[f210,f152]) ).
fof(f580,plain,
! [X0] :
( segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(sK5)
| ~ ssList(sK4)
| ~ ssList(X0)
| ~ ssList(sK2) ),
inference(superposition,[],[f192,f158]) ).
fof(f591,plain,
! [X0] :
( segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(sK4)
| ~ ssList(X0)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f580,f154]) ).
fof(f600,plain,
! [X0] :
( segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(X0)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f591,f153]) ).
fof(f601,plain,
! [X0] :
( segmentP(sK3,X0)
| ~ segmentP(sK2,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f600,f149]) ).
fof(f603,plain,
! [X0] :
( ~ segmentP(sK2,X0)
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| ~ segmentP(sK2,X0) ),
inference(resolution,[],[f601,f209]) ).
fof(f606,plain,
! [X0] :
( ~ segmentP(sK2,X0)
| ~ ssList(X0)
| ~ neq(X0,nil) ),
inference(duplicate_literal_removal,[],[f603]) ).
fof(f640,plain,
( ~ ssList(sK2)
| ~ neq(sK2,nil)
| ~ ssList(sK2) ),
inference(resolution,[],[f606,f193]) ).
fof(f643,plain,
( ~ ssList(sK2)
| ~ neq(sK2,nil) ),
inference(duplicate_literal_removal,[],[f640]) ).
fof(f645,plain,
~ neq(sK2,nil),
inference(forward_subsumption_resolution,[],[f643,f149]) ).
fof(f647,plain,
( nil = sK2
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(resolution,[],[f645,f185]) ).
fof(f648,plain,
( ~ ssList(nil)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f647,f223]) ).
fof(f650,plain,
~ ssList(sK2),
inference(forward_subsumption_resolution,[],[f648,f188]) ).
fof(f651,plain,
$false,
inference(forward_subsumption_resolution,[],[f650,f149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC076+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 07:44:10 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.75/1.36 % (3807020)Detected formulas, will run a generic FOF schedule.
% 2.75/1.36 % (3807029)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=364553576:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.75/1.36 % (3807029)First to succeed.
% 2.75/1.36 % (3807029)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3807020"
% 2.75/1.36 % (3807028)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=195815257:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.75/1.36 % (3807025)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=1546750275:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.75/1.36 % (3807031)dis-21_1_sil=8000:lcm=predicate:random_seed=1416121907: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)
% 2.75/1.36 % (3807026)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=2695912814:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.75/1.36 % (3807027)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=4222197935:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.75/1.36 % (3807030)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=84321466:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.75/1.36 % (3807028)Also succeeded, but the first one will report.
% 2.75/1.36 % (3807030)Also succeeded, but the first one will report.
% 2.75/1.36 % (3807031)Instruction limit reached!
% 2.75/1.36 % (3807031)------------------------------
% 2.75/1.36 % (3807031)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.36 % (3807031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.36 % (3807031)CaDiCaL version: 2.1.3
% 2.75/1.36 % (3807031)Termination reason: Instruction limit
% 2.75/1.36 % (3807031)Termination phase: Saturation
% 2.75/1.36 % (3807031)Time elapsed: 0.077 s
% 2.75/1.36 % (3807031)Peak memory usage: 90 MB
% 2.75/1.36 % (3807031)Instructions burned: 129 (million)
% 2.75/1.36 % (3807029)Refutation found. Thanks to Tanya!
% 2.75/1.36 % SZS status Theorem for theBenchmark
% 2.75/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/1.36 % (3807029)------------------------------
% 2.75/1.36 % (3807029)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.36 % (3807029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.36 % (3807029)CaDiCaL version: 2.1.3
% 2.75/1.36 % (3807029)Termination reason: Refutation
% 2.75/1.36 % (3807029)Time elapsed: 0.007 s
% 2.75/1.36 % (3807029)Peak memory usage: 89 MB
% 2.75/1.36 % (3807029)Instructions burned: 18 (million)
% 2.75/1.36 % (3807029)------------------------------
% 2.75/1.36 % (3807029)------------------------------
% 2.75/1.36 % (3807020)Success in time 0.307 s
% 2.75/1.36 % Vampire exiting
%------------------------------------------------------------------------------