%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC415+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 : n016.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 01:03:53 PM UTC 2026
% Result : Theorem 0.18s 1.31s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 183 ( 58 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 237 ( 95 ~; 86 |; 42 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 45 ( 33 !; 12 ?)
% 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(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& X2 != X4
& tl(X3) = X4
& neq(nil,X3) )
| ? [X5] :
( ssList(X5)
& tl(X1) = X5
& X0 = X5
& neq(nil,X1) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& X2 != X4
& tl(X3) = X4
& neq(nil,X3) )
| ? [X5] :
( ssList(X5)
& tl(X1) = X5
& X0 = X5
& neq(nil,X1) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X2 = X4
| tl(X3) != X4
| ~ neq(nil,X3) )
& ! [X5] :
( ~ ssList(X5)
| tl(X1) != X5
| X0 != X5
| ~ neq(nil,X1) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X2 = X4
| tl(X3) != X4
| ~ neq(nil,X3) )
& ! [X5] :
( ~ ssList(X5)
| tl(X1) != X5
| X0 != X5
| ~ neq(nil,X1) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f111,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f112,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f111]) ).
fof(f138,plain,
( sK1 = sK3
& sK0 = sK2
& ( ( neq(sK1,nil)
& ! [X4] :
( ~ ssList(X4)
| sK2 = X4
| tl(sK3) != X4
| ~ neq(nil,sK3) )
& ! [X5] :
( ~ ssList(X5)
| tl(sK1) != X5
| sK0 != X5
| ~ neq(nil,sK1) ) )
| ( neq(sK1,nil)
& ~ neq(sK3,nil) ) )
& 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(f139,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f150,plain,
ssList(sK3),
inference(cnf_transformation,[],[f138]) ).
fof(f151,plain,
! [X5] :
( ~ ssList(X5)
| tl(sK1) != X5
| sK0 != X5
| ~ neq(nil,sK1)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f138]) ).
fof(f153,plain,
! [X4] :
( ~ ssList(X4)
| sK2 = X4
| tl(sK3) != X4
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f138]) ).
fof(f156,plain,
( neq(sK1,nil)
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f138]) ).
fof(f157,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f138]) ).
fof(f158,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f138]) ).
fof(f159,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f160,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f163,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f170,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f198,plain,
( neq(sK3,nil)
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f156,f158,f158]) ).
fof(f202,plain,
! [X5] :
( ~ ssList(X5)
| tl(sK3) != X5
| sK2 != X5
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(definition_unfolding,[],[f151,f158,f157,f158]) ).
fof(f206,plain,
( ~ ssList(tl(sK3))
| sK2 = tl(sK3)
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(equality_resolution,[],[f153]) ).
fof(f208,plain,
( ~ ssList(tl(sK3))
| sK2 != tl(sK3)
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(equality_resolution,[],[f202]) ).
fof(f209,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f159]) ).
fof(f215,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f209]) ).
fof(f216,plain,
neq(sK3,nil),
inference(duplicate_literal_removal,[],[f198]) ).
fof(f217,plain,
( sK2 = tl(sK3)
| ~ ssList(tl(sK3))
| ~ neq(nil,sK3) ),
inference(forward_subsumption_resolution,[],[f206,f216]) ).
fof(f218,plain,
( ~ ssList(tl(sK3))
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f208,f217]) ).
fof(f219,plain,
( ~ ssList(tl(sK3))
| ~ neq(nil,sK3) ),
inference(forward_subsumption_resolution,[],[f218,f216]) ).
fof(f222,plain,
( nil = sK3
| ~ ssList(sK3)
| ~ neq(nil,sK3) ),
inference(resolution,[],[f170,f219]) ).
fof(f224,plain,
( ~ neq(nil,sK3)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f222,f150]) ).
fof(f231,plain,
( nil = sK3
| ~ ssList(sK3)
| ~ ssList(nil)
| nil = sK3 ),
inference(resolution,[],[f160,f224]) ).
fof(f232,plain,
( nil = sK3
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f231]) ).
fof(f235,plain,
( nil = sK3
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f232,f150]) ).
fof(f236,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f235,f163]) ).
fof(f240,plain,
neq(sK3,sK3),
inference(superposition,[],[f216,f236]) ).
fof(f247,plain,
~ ssList(sK3),
inference(resolution,[],[f240,f215]) ).
fof(f249,plain,
$false,
inference(forward_subsumption_resolution,[],[f247,f150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC415+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 : n016.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 09:37:18 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 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
% 0.18/1.31 % (3508397)Detected formulas, will run a generic FOF schedule.
% 0.18/1.31 % (3508402)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=4001572631:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/1.31 % (3508403)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=24323884:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/1.31 % (3508407)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2138786918:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/1.31 % (3508406)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=192579858:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/1.31 % (3508404)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=1794302302:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/1.31 % (3508408)dis-21_1_sil=8000:lcm=predicate:random_seed=340863908: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)
% 0.18/1.31 % (3508405)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2996556967:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/1.31 % (3508406)First to succeed.
% 0.18/1.31 % (3508406)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3508397"
% 0.18/1.31 % (3508405)Also succeeded, but the first one will report.
% 0.18/1.31 % (3508407)Also succeeded, but the first one will report.
% 0.18/1.31 % (3508408)Instruction limit reached!
% 0.18/1.31 % (3508408)------------------------------
% 0.18/1.31 % (3508408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.31 % (3508408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.31 % (3508408)CaDiCaL version: 2.1.3
% 0.18/1.31 % (3508408)Termination reason: Instruction limit
% 0.18/1.31 % (3508408)Termination phase: Saturation
% 0.18/1.31 % (3508408)Time elapsed: 0.075 s
% 0.18/1.31 % (3508408)Peak memory usage: 90 MB
% 0.18/1.31 % (3508408)Instructions burned: 130 (million)
% 0.18/1.31 % (3508416)lrs+10_1_sil=8000:sp=occurrence:random_seed=3117207293:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.18/1.31 % (3508416)Also succeeded, but the first one will report.
% 0.18/1.31 % (3508406)Refutation found. Thanks to Tanya!
% 0.18/1.31 % SZS status Theorem for theBenchmark
% 0.18/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.31 % (3508406)------------------------------
% 0.18/1.31 % (3508406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.31 % (3508406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.31 % (3508406)CaDiCaL version: 2.1.3
% 0.18/1.31 % (3508406)Termination reason: Refutation
% 0.18/1.31 % (3508406)Time elapsed: 0.004 s
% 0.18/1.31 % (3508406)Peak memory usage: 88 MB
% 0.18/1.31 % (3508406)Instructions burned: 4 (million)
% 0.18/1.31 % (3508406)------------------------------
% 0.18/1.31 % (3508406)------------------------------
% 0.18/1.31 % (3508397)Success in time 0.434 s
% 0.18/1.31 % Vampire exiting
%------------------------------------------------------------------------------