%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC032+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 01:02:07 PM UTC 2026
% Result : Theorem 2.70s 1.34s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 11 unt; 4 def)
% Number of atoms : 232 ( 102 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 275 ( 99 ~; 97 |; 61 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 32 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ strictorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& lt(X7,X5) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ( nil != X1
| nil = X0 )
& ( nil != X0
| nil = X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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)
=> ( app(X2,X4) != X3
| ~ strictorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& lt(X7,X5) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ( nil != X1
| nil = X0 )
& ( nil != X0
| nil = X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( app(X2,X4) = X3
& strictorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ lt(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ( nil = X1
& nil != X0 )
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( app(X2,X4) = X3
& strictorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ lt(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ( nil = X1
& nil != X0 )
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f292,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f293,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f292]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& sK56 = app(sK55,sK57)
& strictorderedP(sK55)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != sK57
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != sK55
| ~ lt(X7,X5) ) ) ) )
& ssList(sK57)
& ( nil = sK56
| nil != sK55 )
& ( ( nil = sK54
& nil != sK53 )
| ( nil = sK53
& nil != sK54 ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57)],[f222]) ).
fof(f479,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( nil != sK53
| nil != sK54 ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( nil = sK54
| nil = sK53 ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil = sK56
| nil != sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
ssList(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK56 = app(sK55,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f546,definition,
( spl58_1
<=> nil = sK54 ),
introduced(definition,[new_symbols(definition,[spl58_1])],[avatar_definition]) ).
fof(f547,plain,
( nil = sK54
| ~ spl58_1 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f548,plain,
( nil != sK54
| spl58_1 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f550,definition,
( spl58_2
<=> nil = sK53 ),
introduced(definition,[new_symbols(definition,[spl58_2])],[avatar_definition]) ).
fof(f551,plain,
( nil = sK53
| ~ spl58_2 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f552,plain,
( nil != sK53
| spl58_2 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f553,plain,
( ~ spl58_1
| ~ spl58_2 ),
inference(avatar_split_clause,[],[f500,f550,f546]) ).
fof(f554,plain,
( spl58_2
| spl58_1 ),
inference(avatar_split_clause,[],[f503,f546,f550]) ).
fof(f556,definition,
( spl58_3
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl58_3])],[avatar_definition]) ).
fof(f558,plain,
( nil != sK55
| spl58_3 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f560,definition,
( spl58_4
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl58_4])],[avatar_definition]) ).
fof(f562,plain,
( nil = sK56
| ~ spl58_4 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f563,plain,
( ~ spl58_3
| spl58_4 ),
inference(avatar_split_clause,[],[f504,f560,f556]) ).
fof(f605,plain,
( nil != sK53
| spl58_3 ),
inference(forward_demodulation,[],[f558,f509]) ).
fof(f606,plain,
( $false
| ~ spl58_2
| spl58_3 ),
inference(forward_subsumption_resolution,[],[f605,f551]) ).
fof(f607,plain,
( ~ spl58_2
| spl58_3 ),
inference(avatar_contradiction_clause,[],[f606]) ).
fof(f611,plain,
sK56 = app(sK53,sK57),
inference(forward_demodulation,[],[f508,f509]) ).
fof(f612,plain,
sK54 = app(sK53,sK57),
inference(forward_demodulation,[],[f611,f510]) ).
fof(f613,plain,
( nil = app(sK53,sK57)
| ~ spl58_1 ),
inference(forward_demodulation,[],[f612,f547]) ).
fof(f696,plain,
( nil != nil
| nil = sK53
| ~ ssList(sK57)
| ~ ssList(sK53)
| ~ spl58_1 ),
inference(superposition,[],[f479,f613]) ).
fof(f699,plain,
( nil = sK53
| ~ ssList(sK57)
| ~ ssList(sK53)
| ~ spl58_1 ),
inference(trivial_inequality_removal,[],[f696]) ).
fof(f700,plain,
( ~ ssList(sK57)
| ~ ssList(sK53)
| ~ spl58_1
| spl58_2 ),
inference(forward_subsumption_resolution,[],[f699,f552]) ).
fof(f701,plain,
( ~ ssList(sK53)
| ~ spl58_1
| spl58_2 ),
inference(forward_subsumption_resolution,[],[f700,f505]) ).
fof(f702,plain,
( $false
| ~ spl58_1
| spl58_2 ),
inference(forward_subsumption_resolution,[],[f701,f496]) ).
fof(f703,plain,
( ~ spl58_1
| spl58_2 ),
inference(avatar_contradiction_clause,[],[f702]) ).
fof(f710,plain,
( nil = sK54
| ~ spl58_4 ),
inference(superposition,[],[f562,f510]) ).
fof(f715,plain,
( $false
| spl58_1
| ~ spl58_4 ),
inference(forward_subsumption_resolution,[],[f710,f548]) ).
fof(f716,plain,
( spl58_1
| ~ spl58_4 ),
inference(avatar_contradiction_clause,[],[f715]) ).
cnf(s1,plain,
( ~ spl58_1
| ~ spl58_2 ),
inference(sat_conversion,[],[f553]) ).
cnf(s2,plain,
( spl58_1
| spl58_2 ),
inference(sat_conversion,[],[f554]) ).
cnf(s3,plain,
( ~ spl58_3
| spl58_4 ),
inference(sat_conversion,[],[f563]) ).
cnf(s14,plain,
( ~ spl58_2
| spl58_3 ),
inference(sat_conversion,[],[f607]) ).
cnf(s17,plain,
( ~ spl58_1
| spl58_2 ),
inference(sat_conversion,[],[f703]) ).
cnf(s19,plain,
( spl58_1
| ~ spl58_4 ),
inference(sat_conversion,[],[f716]) ).
cnf(s24,plain,
spl58_1,
inference(rat,[],[s14,s3,s2,s19]) ).
cnf(s25,plain,
spl58_2,
inference(rat,[],[s17,s24]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s1,s25,s24]) ).
fof(f717,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC032+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 07:31:22 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.70/1.34 % (181246)Detected formulas, will run a generic FOF schedule.
% 2.70/1.34 % (181256)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2811091201:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.70/1.34 % (181256)First to succeed.
% 2.70/1.34 % (181256)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-181246"
% 2.70/1.34 % (181251)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=3066014656:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.70/1.34 % (181252)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=2253236754:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.70/1.34 % (181253)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=190409240:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.70/1.34 % (181254)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=153868256:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.70/1.34 % (181255)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=416808725:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.70/1.34 % (181255)Also succeeded, but the first one will report.
% 2.70/1.34 % (181254)Also succeeded, but the first one will report.
% 2.70/1.34 % (181257)dis-21_1_sil=8000:lcm=predicate:random_seed=2637369385: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)
% 2.70/1.34 % (181257)Instruction limit reached!
% 2.70/1.34 % (181257)------------------------------
% 2.70/1.34 % (181257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.34 % (181257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.34 % (181257)CaDiCaL version: 2.1.3
% 2.70/1.34 % (181257)Termination reason: Instruction limit
% 2.70/1.34 % (181257)Termination phase: Saturation
% 2.70/1.34 % (181257)Time elapsed: 0.071 s
% 2.70/1.34 % (181257)Peak memory usage: 91 MB
% 2.70/1.34 % (181257)Instructions burned: 129 (million)
% 2.70/1.34 % (181256)Refutation found. Thanks to Tanya!
% 2.70/1.34 % SZS status Theorem for theBenchmark
% 2.70/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/1.34 % (181256)------------------------------
% 2.70/1.34 % (181256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.34 % (181256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.34 % (181256)CaDiCaL version: 2.1.3
% 2.70/1.34 % (181256)Termination reason: Refutation
% 2.70/1.34 % (181256)Time elapsed: 0.008 s
% 2.70/1.34 % (181256)Peak memory usage: 90 MB
% 2.70/1.34 % (181256)Instructions burned: 20 (million)
% 2.70/1.34 % (181256)------------------------------
% 2.70/1.34 % (181256)------------------------------
% 2.70/1.34 % (181246)Success in time 0.301 s
% 2.70/1.34 % Vampire exiting
%------------------------------------------------------------------------------