%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC352+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 : n004.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 01:03:35 PM UTC 2026
% Result : Theorem 0.18s 0.90s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 18 unt; 6 def)
% Number of atoms : 189 ( 41 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 206 ( 79 ~; 73 |; 33 &)
% ( 10 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 28 ( 0 sgn 20 !; 8 ?)
% 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(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| frontsegP(X1,X0)
| ( nil != X2
& nil = X3 )
| ( neq(X3,nil)
& ( ~ neq(X2,nil)
| ~ frontsegP(X3,X2) ) ) ) ) ) ) ),
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(X1,X0)
| ( nil != X2
& nil = X3 )
| ( neq(X3,nil)
& ( ~ neq(X2,nil)
| ~ frontsegP(X3,X2) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f158,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ~ frontsegP(X1,X0)
& ( nil = X2
| nil != X3 )
& ( ~ neq(X3,nil)
| ( neq(X2,nil)
& frontsegP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ~ frontsegP(X1,X0)
& ( nil = X2
| nil != X3 )
& ( ~ neq(X3,nil)
| ( neq(X2,nil)
& frontsegP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f283,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f158]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ~ frontsegP(sK54,sK53)
& ( nil = sK55
| nil != sK56 )
& ( ~ neq(sK56,nil)
| ( neq(sK55,nil)
& frontsegP(sK56,sK55) ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f387,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f430,plain,
! [X0] :
( frontsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f499,plain,
ssList(sK56),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ neq(sK56,nil)
| frontsegP(sK56,sK55) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( nil = sK55
| nil != sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
~ frontsegP(sK54,sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f523,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f430]) ).
fof(f541,definition,
( spl57_1
<=> frontsegP(sK56,sK55) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f542,plain,
( ~ frontsegP(sK56,sK55)
| spl57_1 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f545,definition,
( spl57_2
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f547,plain,
( ~ neq(sK56,nil)
| spl57_2 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f548,plain,
( spl57_1
| ~ spl57_2 ),
inference(avatar_split_clause,[],[f500,f545,f541]) ).
fof(f555,definition,
( spl57_4
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_4])],[avatar_definition]) ).
fof(f556,plain,
( nil = sK56
| ~ spl57_4 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f559,definition,
( spl57_5
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl57_5])],[avatar_definition]) ).
fof(f561,plain,
( nil = sK55
| ~ spl57_5 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f562,plain,
( ~ spl57_4
| spl57_5 ),
inference(avatar_split_clause,[],[f502,f559,f555]) ).
fof(f564,definition,
( spl57_6
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_6])],[avatar_definition]) ).
fof(f565,plain,
( ssList(nil)
| ~ spl57_6 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f593,definition,
( spl57_12
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[spl57_12])],[avatar_definition]) ).
fof(f595,plain,
( frontsegP(nil,nil)
| ~ spl57_12 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f596,plain,
( ~ spl57_6
| spl57_12 ),
inference(avatar_split_clause,[],[f523,f593,f564]) ).
fof(f597,plain,
spl57_6,
inference(avatar_split_clause,[],[f389,f564]) ).
fof(f600,plain,
~ frontsegP(sK56,sK53),
inference(superposition,[],[f503,f505]) ).
fof(f602,plain,
~ frontsegP(sK56,sK55),
inference(forward_demodulation,[],[f600,f504]) ).
fof(f603,plain,
~ spl57_1,
inference(avatar_split_clause,[],[f602,f541]) ).
fof(f641,plain,
( nil = sK56
| ~ ssList(nil)
| ~ ssList(sK56)
| spl57_2 ),
inference(resolution,[],[f387,f547]) ).
fof(f650,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_2
| ~ spl57_6 ),
inference(forward_subsumption_resolution,[],[f641,f565]) ).
fof(f651,plain,
( nil = sK56
| spl57_2
| ~ spl57_6 ),
inference(forward_subsumption_resolution,[],[f650,f499]) ).
fof(f652,plain,
( spl57_4
| spl57_2
| ~ spl57_6 ),
inference(avatar_split_clause,[],[f651,f564,f545,f555]) ).
fof(f658,plain,
( ~ frontsegP(sK56,nil)
| spl57_1
| ~ spl57_5 ),
inference(superposition,[],[f542,f561]) ).
fof(f660,plain,
( ~ frontsegP(nil,nil)
| spl57_1
| ~ spl57_4
| ~ spl57_5 ),
inference(forward_demodulation,[],[f658,f556]) ).
fof(f661,plain,
( $false
| spl57_1
| ~ spl57_4
| ~ spl57_5
| ~ spl57_12 ),
inference(forward_subsumption_resolution,[],[f660,f595]) ).
fof(f662,plain,
( spl57_1
| ~ spl57_4
| ~ spl57_5
| ~ spl57_12 ),
inference(avatar_contradiction_clause,[],[f661]) ).
cnf(s1,plain,
( spl57_1
| ~ spl57_2 ),
inference(sat_conversion,[],[f548]) ).
cnf(s3,plain,
( ~ spl57_4
| spl57_5 ),
inference(sat_conversion,[],[f562]) ).
cnf(s11,plain,
( ~ spl57_6
| spl57_12 ),
inference(sat_conversion,[],[f596]) ).
cnf(s12,plain,
spl57_6,
inference(sat_conversion,[],[f597]) ).
cnf(s13,plain,
~ spl57_1,
inference(sat_conversion,[],[f603]) ).
cnf(s16,plain,
( spl57_2
| spl57_4
| ~ spl57_6 ),
inference(sat_conversion,[],[f652]) ).
cnf(s18,plain,
( spl57_1
| ~ spl57_4
| ~ spl57_5
| ~ spl57_12 ),
inference(sat_conversion,[],[f662]) ).
cnf(s19,plain,
spl57_12,
inference(rat,[],[s11,s12]) ).
cnf(s23,plain,
~ spl57_2,
inference(rat,[],[s1,s13]) ).
cnf(s24,plain,
spl57_4,
inference(rat,[],[s16,s12,s23]) ).
cnf(s25,plain,
~ spl57_5,
inference(rat,[],[s18,s19,s13,s24]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s3,s25,s24]) ).
fof(f663,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC352+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 09:12:37 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 0.18/0.90 % (223602)Detected formulas, will run a generic FOF schedule.
% 0.18/0.90 % (223612)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3723072407:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/0.90 % (223613)dis-21_1_sil=8000:lcm=predicate:random_seed=4010386552: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)
% 0.18/0.90 % (223611)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=94965843:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/0.90 % (223610)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=576233827:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/0.90 % (223607)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=2822013642:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/0.90 % (223609)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=1676456487:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/0.90 % (223608)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=2358762082:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/0.90 % (223612)First to succeed.
% 0.18/0.90 % (223612)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-223602"
% 0.18/0.90 % (223610)Also succeeded, but the first one will report.
% 0.18/0.90 % (223611)Also succeeded, but the first one will report.
% 0.18/0.90 % (223613)Instruction limit reached!
% 0.18/0.90 % (223613)------------------------------
% 0.18/0.90 % (223613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/0.90 % (223613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.90 % (223613)CaDiCaL version: 2.1.3
% 0.18/0.90 % (223613)Termination reason: Instruction limit
% 0.18/0.90 % (223613)Termination phase: Saturation
% 0.18/0.90 % (223613)Time elapsed: 0.075 s
% 0.18/0.90 % (223613)Peak memory usage: 90 MB
% 0.18/0.90 % (223613)Instructions burned: 129 (million)
% 0.18/0.90 % (223612)Refutation found. Thanks to Tanya!
% 0.18/0.90 % SZS status Theorem for theBenchmark
% 0.18/0.90 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.91 % (223612)------------------------------
% 0.18/0.91 % (223612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/0.91 % (223612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.91 % (223612)CaDiCaL version: 2.1.3
% 0.18/0.91 % (223612)Termination reason: Refutation
% 0.18/0.91 % (223612)Time elapsed: 0.006 s
% 0.18/0.91 % (223612)Peak memory usage: 90 MB
% 0.18/0.91 % (223612)Instructions burned: 15 (million)
% 0.18/0.91 % (223612)------------------------------
% 0.18/0.91 % (223612)------------------------------
% 0.18/0.91 % (223602)Success in time 0.301 s
% 0.18/0.91 % Vampire exiting
%------------------------------------------------------------------------------