%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC336+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 01:05:36 PM UTC 2026
% Result : Theorem 0.42s 0.30s
% Output : Refutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 94 ( 19 unt; 9 def)
% Number of atoms : 278 ( 37 equ)
% Maximal formula atoms : 21 ( 2 avg)
% Number of connectives : 319 ( 135 ~; 129 |; 30 &)
% ( 11 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 10 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 40 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax65) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax66) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| cons(X4,nil) != X2
| app(app(X5,X2),X6) != X3
| ? [X7] :
( ssItem(X7)
& memberP(X5,X7)
& lt(X4,X7) )
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X8,X4) ) ) ) )
& ( nil != X3
| nil != X2 ) )
| ( segmentP(X1,X0)
& totalorderedP(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] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| cons(X4,nil) != X2
| app(app(X5,X2),X6) != X3
| ? [X7] :
( ssItem(X7)
& memberP(X5,X7)
& lt(X4,X7) )
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X8,X4) ) ) ) )
& ( nil != X3
| nil != X2 ) )
| ( segmentP(X1,X0)
& totalorderedP(X0) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f175,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f180,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( ? [X4] :
( ? [X5] :
( ? [X6] :
( ssList(X6)
& cons(X4,nil) = X2
& app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ lt(X4,X7) )
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X8,X4) ) )
& ssList(X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ( ~ segmentP(X1,X0)
| ~ totalorderedP(X0) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f240,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f358,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
inference(cnf_transformation,[],[f175]) ).
fof(f367,plain,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f180]) ).
fof(f368,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f417,plain,
( nil = sK49
| sK50 = app(app(sK52,sK49),sK53) ),
inference(cnf_transformation,[],[f221]) ).
fof(f418,plain,
( nil = sK49
| sK49 = cons(sK51,nil) ),
inference(cnf_transformation,[],[f221]) ).
fof(f419,plain,
( nil = sK49
| ssList(sK53) ),
inference(cnf_transformation,[],[f221]) ).
fof(f420,plain,
( nil = sK49
| ssList(sK52) ),
inference(cnf_transformation,[],[f221]) ).
fof(f423,plain,
( nil = sK49
| ssItem(sK51) ),
inference(cnf_transformation,[],[f221]) ).
fof(f424,plain,
( ~ totalorderedP(sK47)
| ~ segmentP(sK48,sK47) ),
inference(cnf_transformation,[],[f221]) ).
fof(f425,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f221]) ).
fof(f426,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f221]) ).
fof(f427,plain,
ssList(sK50),
inference(cnf_transformation,[],[f221]) ).
fof(f428,plain,
ssList(sK49),
inference(cnf_transformation,[],[f221]) ).
fof(f433,plain,
( ~ totalorderedP(sK49)
| ~ segmentP(sK50,sK49) ),
inference(definition_unfolding,[],[f424,f425,f426,f425]) ).
fof(f439,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f240]) ).
fof(f476,plain,
! [X2,X3,X1] :
( ~ segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(consistent_polarity_flipping,[],[f439]) ).
fof(f573,plain,
! [X0] :
( ~ segmentP(X0,nil)
| ~ ssList(X0) ),
inference(consistent_polarity_flipping,[],[f358]) ).
fof(f582,plain,
! [X0] :
( ssItem(X0)
| ~ totalorderedP(cons(X0,nil)) ),
inference(consistent_polarity_flipping,[],[f367]) ).
fof(f583,plain,
~ totalorderedP(nil),
inference(consistent_polarity_flipping,[],[f368]) ).
fof(f610,plain,
( totalorderedP(sK49)
| segmentP(sK50,sK49) ),
inference(consistent_polarity_flipping,[],[f433]) ).
fof(f611,plain,
( nil = sK49
| ~ ssItem(sK51) ),
inference(consistent_polarity_flipping,[],[f423]) ).
fof(f628,definition,
( spl54_2
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl54_2])],[avatar_definition]) ).
fof(f630,plain,
( nil = sK49
| ~ spl54_2 ),
inference(avatar_component_clause,[],[f628]) ).
fof(f643,definition,
( spl54_5
<=> sK50 = app(app(sK52,sK49),sK53) ),
introduced(definition,[new_symbols(definition,[spl54_5])],[avatar_definition]) ).
fof(f645,plain,
( sK50 = app(app(sK52,sK49),sK53)
| ~ spl54_5 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f648,definition,
( spl54_6
<=> sK49 = cons(sK51,nil) ),
introduced(definition,[new_symbols(definition,[spl54_6])],[avatar_definition]) ).
fof(f650,plain,
( sK49 = cons(sK51,nil)
| ~ spl54_6 ),
inference(avatar_component_clause,[],[f648]) ).
fof(f653,definition,
( spl54_7
<=> ssList(sK53) ),
introduced(definition,[new_symbols(definition,[spl54_7])],[avatar_definition]) ).
fof(f655,plain,
( ssList(sK53)
| ~ spl54_7 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f657,plain,
( spl54_5
| spl54_2 ),
inference(avatar_split_clause,[],[f417,f628,f643]) ).
fof(f658,plain,
( spl54_6
| spl54_2 ),
inference(avatar_split_clause,[],[f418,f628,f648]) ).
fof(f659,plain,
( spl54_7
| spl54_2 ),
inference(avatar_split_clause,[],[f419,f628,f653]) ).
fof(f661,definition,
( spl54_8
<=> ssList(sK52) ),
introduced(definition,[new_symbols(definition,[spl54_8])],[avatar_definition]) ).
fof(f663,plain,
( ssList(sK52)
| ~ spl54_8 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f664,plain,
( spl54_8
| spl54_2 ),
inference(avatar_split_clause,[],[f420,f628,f661]) ).
fof(f667,definition,
( spl54_9
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl54_9])],[avatar_definition]) ).
fof(f669,plain,
( ~ ssItem(sK51)
| spl54_9 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f671,plain,
( ~ spl54_9
| spl54_2 ),
inference(avatar_split_clause,[],[f611,f628,f667]) ).
fof(f673,definition,
( spl54_10
<=> segmentP(sK50,sK49) ),
introduced(definition,[new_symbols(definition,[spl54_10])],[avatar_definition]) ).
fof(f675,plain,
( segmentP(sK50,sK49)
| ~ spl54_10 ),
inference(avatar_component_clause,[],[f673]) ).
fof(f677,definition,
( spl54_11
<=> totalorderedP(sK49) ),
introduced(definition,[new_symbols(definition,[spl54_11])],[avatar_definition]) ).
fof(f679,plain,
( totalorderedP(sK49)
| ~ spl54_11 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f680,plain,
( spl54_10
| spl54_11 ),
inference(avatar_split_clause,[],[f610,f677,f673]) ).
fof(f696,definition,
( spl54_15
<=> ! [X0] :
( ssItem(X0)
| ~ totalorderedP(cons(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[spl54_15])],[avatar_definition]) ).
fof(f697,plain,
( ! [X0] :
( ~ totalorderedP(cons(X0,nil))
| ssItem(X0) )
| ~ spl54_15 ),
inference(avatar_component_clause,[],[f696]) ).
fof(f699,plain,
spl54_15,
inference(avatar_split_clause,[],[f582,f696]) ).
fof(f720,plain,
( segmentP(sK50,nil)
| ~ spl54_2
| ~ spl54_10 ),
inference(forward_demodulation,[],[f675,f630]) ).
fof(f724,plain,
( totalorderedP(nil)
| ~ spl54_2
| ~ spl54_11 ),
inference(forward_demodulation,[],[f679,f630]) ).
fof(f727,plain,
( $false
| ~ spl54_2
| ~ spl54_11 ),
inference(forward_subsumption_resolution,[],[f583,f724]) ).
fof(f728,plain,
( ~ spl54_2
| ~ spl54_11 ),
inference(avatar_contradiction_clause,[],[f727]) ).
fof(f733,plain,
( ~ ssList(sK50)
| ~ spl54_2
| ~ spl54_10 ),
inference(resolution,[],[f573,f720]) ).
fof(f734,plain,
( $false
| ~ spl54_2
| ~ spl54_10 ),
inference(forward_subsumption_resolution,[],[f733,f427]) ).
fof(f735,plain,
( ~ spl54_2
| ~ spl54_10 ),
inference(avatar_contradiction_clause,[],[f734]) ).
fof(f748,plain,
( ~ totalorderedP(sK49)
| ssItem(sK51)
| ~ spl54_6
| ~ spl54_15 ),
inference(superposition,[],[f697,f650]) ).
fof(f2325,plain,
( ~ segmentP(sK50,sK49)
| ~ ssList(sK49)
| ~ ssList(sK53)
| ~ ssList(sK52)
| ~ ssList(sK50)
| ~ spl54_5 ),
inference(superposition,[],[f476,f645]) ).
fof(f2356,plain,
( ~ totalorderedP(sK49)
| ~ spl54_6
| spl54_9
| ~ spl54_15 ),
inference(forward_subsumption_resolution,[],[f748,f669]) ).
fof(f2358,plain,
( ~ segmentP(sK50,sK49)
| ~ ssList(sK53)
| ~ ssList(sK52)
| ~ ssList(sK50)
| ~ spl54_5 ),
inference(forward_subsumption_resolution,[],[f2325,f428]) ).
fof(f2359,plain,
( ~ spl54_11
| ~ spl54_6
| spl54_9
| ~ spl54_15 ),
inference(avatar_split_clause,[],[f2356,f696,f667,f648,f677]) ).
fof(f2360,plain,
( ~ segmentP(sK50,sK49)
| ~ ssList(sK52)
| ~ ssList(sK50)
| ~ spl54_5
| ~ spl54_7 ),
inference(forward_subsumption_resolution,[],[f2358,f655]) ).
fof(f2361,plain,
( ~ segmentP(sK50,sK49)
| ~ ssList(sK50)
| ~ spl54_5
| ~ spl54_7
| ~ spl54_8 ),
inference(forward_subsumption_resolution,[],[f2360,f663]) ).
fof(f2362,plain,
( ~ segmentP(sK50,sK49)
| ~ spl54_5
| ~ spl54_7
| ~ spl54_8 ),
inference(forward_subsumption_resolution,[],[f2361,f427]) ).
fof(f2363,plain,
( ~ spl54_10
| ~ spl54_5
| ~ spl54_7
| ~ spl54_8 ),
inference(avatar_split_clause,[],[f2362,f661,f653,f643,f673]) ).
cnf(s8,plain,
( spl54_2
| spl54_5 ),
inference(sat_conversion,[],[f657]) ).
cnf(s9,plain,
( spl54_2
| spl54_6 ),
inference(sat_conversion,[],[f658]) ).
cnf(s10,plain,
( spl54_2
| spl54_7 ),
inference(sat_conversion,[],[f659]) ).
cnf(s11,plain,
( spl54_2
| spl54_8 ),
inference(sat_conversion,[],[f664]) ).
cnf(s14,plain,
( spl54_2
| ~ spl54_9 ),
inference(sat_conversion,[],[f671]) ).
cnf(s15,plain,
( spl54_10
| spl54_11 ),
inference(sat_conversion,[],[f680]) ).
cnf(s20,plain,
spl54_15,
inference(sat_conversion,[],[f699]) ).
cnf(s29,plain,
( ~ spl54_2
| ~ spl54_11 ),
inference(sat_conversion,[],[f728]) ).
cnf(s30,plain,
( ~ spl54_2
| ~ spl54_10 ),
inference(sat_conversion,[],[f735]) ).
cnf(s86,plain,
( ~ spl54_6
| spl54_9
| ~ spl54_11
| ~ spl54_15 ),
inference(sat_conversion,[],[f2359]) ).
cnf(s87,plain,
( ~ spl54_5
| ~ spl54_7
| ~ spl54_8
| ~ spl54_10 ),
inference(sat_conversion,[],[f2363]) ).
cnf(s96,plain,
~ spl54_2,
inference(rat,[],[s15,s29,s30]) ).
cnf(s97,plain,
~ spl54_9,
inference(rat,[],[s14,s96]) ).
cnf(s98,plain,
spl54_8,
inference(rat,[],[s11,s96]) ).
cnf(s99,plain,
spl54_7,
inference(rat,[],[s10,s96]) ).
cnf(s100,plain,
spl54_6,
inference(rat,[],[s9,s96]) ).
cnf(s101,plain,
spl54_5,
inference(rat,[],[s8,s96]) ).
cnf(s105,plain,
~ spl54_11,
inference(rat,[],[s86,s20,s97,s100]) ).
cnf(s108,plain,
~ spl54_10,
inference(rat,[],[s87,s99,s98,s101]) ).
cnf(s111,plain,
$false,
inference(rat,[],[s15,s105,s108]) ).
fof(f2364,plain,
$false,
inference(avatar_sat_refutation,[],[s111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC336+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.16 % Computer : n009.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Mon Sep 28 09:09:45 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 Running first-order model finding
% 0.10/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.30 % (2903590)Will run a generic schedule for satisfiability detection.
% 0.42/0.30 % (2903595)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2257455889_2999 on theBenchmark for (2999ds/0Mi)
% 0.42/0.30 % (2903597)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3963677274:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.42/0.30 % (2903598)dis+10_1_sil=32000:sp=arity:random_seed=571864060:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.42/0.30 % (2903599)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4281470426:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.42/0.30 % (2903600)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3882303676:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.42/0.30 % (2903601)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4021159232:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.42/0.30 % TRYING [1]
% 0.42/0.30 % TRYING [2]
% 0.42/0.30 % (2903596)% WARNING: option uhcvi not known.
% 0.42/0.30 % TRYING [3]
% 0.42/0.30 % (2903596)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2197672123:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.42/0.30 % TRYING [4]
% 0.42/0.30 % TRYING [5]
% 0.42/0.30 % (2903596) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2903590-2903596"...
% 0.42/0.30 % (2903596)...printing done.
% 0.42/0.30 % (2903596)Refutation found. Thanks to Tanya!
% 0.42/0.30 % SZS status Theorem for theBenchmark
% 0.42/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.42/0.30 % (2903596)------------------------------
% 0.42/0.30 % (2903596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.42/0.30 % (2903596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.30 % (2903596)CaDiCaL version: 2.1.3
% 0.42/0.30 % (2903596)Termination reason: Refutation
% 0.42/0.30 % (2903596)Time elapsed: 0.050 s
% 0.42/0.30 % (2903596)Peak memory usage: 14 MB
% 0.42/0.30 % (2903596)Instructions burned: 75 (million)
% 0.42/0.30 % (2903590)Success in time 0.097 s
% 0.42/0.30 % Vampire exiting
%------------------------------------------------------------------------------