%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC008+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 : n019.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 01:02:01 PM UTC 2026
% Result : Theorem 0.14s 1.51s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 9 unt; 0 def)
% Number of atoms : 207 ( 54 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 296 ( 125 ~; 107 |; 51 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 82 ( 62 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ frontsegP(X3,X2)
| ~ equalelemsP(X2)
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0 ) ) )
| ? [X7] :
( ssList(X7)
& neq(X2,X7)
& frontsegP(X3,X7)
& segmentP(X7,X2)
& equalelemsP(X7) ) ) ) ) ) ),
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
| ~ frontsegP(X3,X2)
| ~ equalelemsP(X2)
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0 ) ) )
| ? [X7] :
( ssList(X7)
& neq(X2,X7)
& frontsegP(X3,X7)
& segmentP(X7,X2)
& equalelemsP(X7) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& frontsegP(X3,X2)
& equalelemsP(X2)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0 ) ) )
& ! [X7] :
( ~ ssList(X7)
| ~ neq(X2,X7)
| ~ frontsegP(X3,X7)
| ~ segmentP(X7,X2)
| ~ equalelemsP(X7) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& frontsegP(X3,X2)
& equalelemsP(X2)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0 ) ) )
& ! [X7] :
( ~ ssList(X7)
| ~ neq(X2,X7)
| ~ frontsegP(X3,X7)
| ~ segmentP(X7,X2)
| ~ equalelemsP(X7) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f144,plain,
( sK1 = sK3
& sK0 = sK2
& frontsegP(sK3,sK2)
& equalelemsP(sK2)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != sK1
| app(X4,X6) != sK0 ) ) )
& ! [X7] :
( ~ ssList(X7)
| ~ neq(sK2,X7)
| ~ frontsegP(sK3,X7)
| ~ segmentP(X7,sK2)
| ~ equalelemsP(X7) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f152,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f123]) ).
fof(f153,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X3] :
( ssList(X3)
& app(X1,X3) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f152]) ).
fof(f154,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ( ssList(sK4(X0,X1))
& app(X1,sK4(X0,X1)) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1))],[f153]) ).
fof(f166,plain,
ssList(sK2),
inference(cnf_transformation,[],[f144]) ).
fof(f167,plain,
ssList(sK3),
inference(cnf_transformation,[],[f144]) ).
fof(f169,plain,
! [X6,X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,X5),X6) != sK1
| app(X4,X6) != sK0 ),
inference(cnf_transformation,[],[f144]) ).
fof(f171,plain,
frontsegP(sK3,sK2),
inference(cnf_transformation,[],[f144]) ).
fof(f172,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f144]) ).
fof(f173,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f144]) ).
fof(f174,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f199,plain,
! [X0,X1] :
( app(X1,sK4(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f200,plain,
! [X0,X1] :
( ssList(sK4(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f222,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f234,plain,
! [X6,X4,X5] :
( app(app(X4,X5),X6) != sK3
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssList(X4)
| app(X4,X6) != sK2 ),
inference(definition_unfolding,[],[f169,f173,f172]) ).
fof(f257,plain,
! [X0,X1] :
( app(X0,X1) != sK3
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| app(X0,nil) != sK2
| ~ ssList(app(X0,X1)) ),
inference(superposition,[],[f234,f174]) ).
fof(f259,plain,
! [X0,X1] :
( app(X0,nil) != sK2
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != sK3
| ~ ssList(app(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f257,f222]) ).
fof(f286,plain,
! [X0,X1] :
( sK2 != X0
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != sK3
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(superposition,[],[f259,f174]) ).
fof(f289,plain,
! [X0,X1] :
( app(X0,X1) != sK3
| ~ ssList(X1)
| ~ ssList(X0)
| sK2 != X0
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literal_removal,[],[f286]) ).
fof(f411,plain,
! [X0,X1] :
( sK3 != X0
| ~ ssList(sK4(X0,X1))
| ~ ssList(X1)
| sK2 != X1
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[],[f289,f199]) ).
fof(f421,plain,
! [X0,X1] :
( sK3 != X0
| ~ ssList(sK4(X0,X1))
| ~ ssList(X1)
| sK2 != X1
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(duplicate_literal_removal,[],[f411]) ).
fof(f435,plain,
! [X0,X1] :
( sK3 != X0
| ~ ssList(X1)
| sK2 != X1
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(forward_subsumption_resolution,[],[f421,f200]) ).
fof(f448,plain,
! [X0] :
( ~ ssList(X0)
| sK2 != X0
| ~ ssList(sK3)
| ~ frontsegP(sK3,X0) ),
inference(equality_resolution,[],[f435]) ).
fof(f449,plain,
! [X0] :
( sK2 != X0
| ~ ssList(X0)
| ~ frontsegP(sK3,X0) ),
inference(forward_subsumption_resolution,[],[f448,f167]) ).
fof(f450,plain,
( ~ ssList(sK2)
| ~ frontsegP(sK3,sK2) ),
inference(equality_resolution,[],[f449]) ).
fof(f451,plain,
~ frontsegP(sK3,sK2),
inference(forward_subsumption_resolution,[],[f450,f166]) ).
fof(f452,plain,
$false,
inference(forward_subsumption_resolution,[],[f451,f171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC008+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 07:24:34 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
% 0.14/1.51 % (3825846)Detected formulas, will run a generic FOF schedule.
% 0.14/1.51 % (3825854)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1143136008:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.14/1.51 % (3825854)Instruction limit reached!
% 0.14/1.51 % (3825854)------------------------------
% 0.14/1.51 % (3825854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.51 % (3825854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.51 % (3825854)CaDiCaL version: 2.1.3
% 0.14/1.51 % (3825854)Termination reason: Instruction limit
% 0.14/1.51 % (3825854)Termination phase: Saturation
% 0.14/1.51 % (3825854)Time elapsed: 0.036 s
% 0.14/1.51 % (3825854)Peak memory usage: 89 MB
% 0.14/1.51 % (3825854)Instructions burned: 110 (million)
% 0.14/1.51 % (3825852)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=1782473834:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.14/1.51 % (3825857)dis-21_1_sil=8000:lcm=predicate:random_seed=2293895916: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)
% 0.14/1.51 % (3825855)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1996530620:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.14/1.51 % (3825851)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=2215452045:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.14/1.51 % (3825853)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=680187144:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.14/1.51 % (3825856)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3588858003:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.14/1.51 % (3825855)First to succeed.
% 0.14/1.51 % (3825855)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3825846"
% 0.14/1.51 % (3825856)Also succeeded, but the first one will report.
% 0.14/1.51 % (3825857)Instruction limit reached!
% 0.14/1.51 % (3825857)------------------------------
% 0.14/1.51 % (3825857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.51 % (3825857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.51 % (3825857)CaDiCaL version: 2.1.3
% 0.14/1.51 % (3825857)Termination reason: Instruction limit
% 0.14/1.51 % (3825857)Termination phase: Saturation
% 0.14/1.51 % (3825857)Time elapsed: 0.075 s
% 0.14/1.51 % (3825857)Peak memory usage: 90 MB
% 0.14/1.51 % (3825857)Instructions burned: 130 (million)
% 0.14/1.51 % (3825859)lrs+10_1_sil=8000:sp=occurrence:random_seed=4063866492:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.14/1.51 % (3825859)Instruction limit reached!
% 0.14/1.51 % (3825859)------------------------------
% 0.14/1.51 % (3825859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.51 % (3825859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.51 % (3825859)CaDiCaL version: 2.1.3
% 0.14/1.51 % (3825859)Termination reason: Instruction limit
% 0.14/1.51 % (3825859)Termination phase: Saturation
% 0.14/1.51 % (3825859)Time elapsed: 0.094 s
% 0.14/1.51 % (3825859)Peak memory usage: 93 MB
% 0.14/1.51 % (3825859)Instructions burned: 288 (million)
% 0.14/1.51 % (3825866)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1461768265:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.14/1.51 % (3825855)Refutation found. Thanks to Tanya!
% 0.14/1.51 % SZS status Theorem for theBenchmark
% 0.14/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/1.51 % (3825855)------------------------------
% 0.14/1.51 % (3825855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.51 % (3825855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.51 % (3825855)CaDiCaL version: 2.1.3
% 0.14/1.51 % (3825855)Termination reason: Refutation
% 0.14/1.51 % (3825855)Time elapsed: 0.009 s
% 0.14/1.51 % (3825855)Peak memory usage: 88 MB
% 0.14/1.51 % (3825855)Instructions burned: 11 (million)
% 0.14/1.51 % (3825855)------------------------------
% 0.14/1.51 % (3825855)------------------------------
% 0.14/1.51 % (3825846)Success in time 0.455 s
% 0.14/1.51 % Vampire exiting
%------------------------------------------------------------------------------