%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC076+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 01:04:33 PM UTC 2026
% Result : Theorem 0.18s 0.54s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 23 unt; 3 def)
% Number of atoms : 273 ( 68 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 305 ( 101 ~; 122 |; 58 &)
% ( 7 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 58 !; 30 ?)
% 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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,X2),X6) != X3
| ~ equalelemsP(X2)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssList(X9)
& app(cons(X7,nil),X9) = X2 ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X6
& ? [X12] :
( ssList(X12)
& app(X12,cons(X10,nil)) = X2 ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( nil = X1
& nil = X0 ) ) ) ) ) ),
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)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,X2),X6) != X3
| ~ equalelemsP(X2)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssList(X9)
& app(cons(X7,nil),X9) = X2 ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X6
& ? [X12] :
( ssList(X12)
& app(X12,cons(X10,nil)) = X2 ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( nil = X1
& nil = 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(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f172,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ? [X5] :
( ? [X6] :
( app(app(X5,X2),X6) = X3
& equalelemsP(X2)
& ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X5
| ! [X9] :
( ~ ssList(X9)
| app(cons(X7,nil),X9) != X2 ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X6
| ! [X12] :
( ~ ssList(X12)
| app(X12,cons(X10,nil)) != X2 ) ) )
& ssList(X6) )
& ssList(X5) )
& ( nil = X3
| nil != X2 )
& ( nil != X1
| nil != X0 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ? [X5] :
( ? [X6] :
( app(app(X5,X2),X6) = X3
& equalelemsP(X2)
& ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X5
| ! [X9] :
( ~ ssList(X9)
| app(cons(X7,nil),X9) != X2 ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X6
| ! [X12] :
( ~ ssList(X12)
| app(X12,cons(X10,nil)) != X2 ) ) )
& ssList(X6) )
& ssList(X5) )
& ( nil = X3
| nil != X2 )
& ( nil != X1
| nil != X0 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f241,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(f303,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f306,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f357,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f413,plain,
ssList(sK52),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
sK50 = app(app(sK51,sK49),sK52),
inference(cnf_transformation,[],[f222]) ).
fof(f416,plain,
! [X4] :
( ~ segmentP(sK47,X4)
| ~ segmentP(sK48,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
ssList(sK51),
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
( nil != sK49
| nil = sK50 ),
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
( nil != sK47
| nil != sK48 ),
inference(cnf_transformation,[],[f222]) ).
fof(f421,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f422,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f424,plain,
ssList(sK48),
inference(cnf_transformation,[],[f222]) ).
fof(f425,plain,
ssList(sK47),
inference(cnf_transformation,[],[f222]) ).
fof(f426,plain,
ssList(sK49),
inference(definition_unfolding,[],[f425,f421]) ).
fof(f427,plain,
ssList(sK50),
inference(definition_unfolding,[],[f424,f422]) ).
fof(f428,plain,
( nil != sK49
| nil != sK50 ),
inference(definition_unfolding,[],[f419,f421,f422]) ).
fof(f429,plain,
! [X4] :
( ~ segmentP(sK49,X4)
| ~ segmentP(sK50,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f416,f421,f422]) ).
fof(f435,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,[],[f241]) ).
fof(f475,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,[],[f435]) ).
fof(f535,plain,
! [X0,X1] :
( ~ neq(X0,X1)
| ssList(X1)
| X0 = X1
| ssList(X0) ),
inference(consistent_polarity_flipping,[],[f303]) ).
fof(f537,plain,
~ ssList(nil),
inference(consistent_polarity_flipping,[],[f306]) ).
fof(f588,plain,
! [X0] :
( ~ segmentP(X0,X0)
| ssList(X0) ),
inference(consistent_polarity_flipping,[],[f357]) ).
fof(f638,plain,
~ ssList(sK49),
inference(consistent_polarity_flipping,[],[f426]) ).
fof(f639,plain,
~ ssList(sK50),
inference(consistent_polarity_flipping,[],[f427]) ).
fof(f642,plain,
~ ssList(sK51),
inference(consistent_polarity_flipping,[],[f417]) ).
fof(f643,plain,
! [X4] :
( neq(X4,nil)
| segmentP(sK50,X4)
| segmentP(sK49,X4)
| ssList(X4) ),
inference(consistent_polarity_flipping,[],[f429]) ).
fof(f644,plain,
~ ssList(sK52),
inference(consistent_polarity_flipping,[],[f413]) ).
fof(f655,definition,
( spl53_1
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl53_1])],[avatar_definition]) ).
fof(f659,definition,
( spl53_2
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl53_2])],[avatar_definition]) ).
fof(f661,plain,
( nil != sK49
| spl53_2 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f662,plain,
( spl53_1
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f418,f659,f655]) ).
fof(f663,plain,
( ~ spl53_1
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f428,f659,f655]) ).
fof(f669,definition,
( spl53_4
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl53_4])],[avatar_definition]) ).
fof(f670,plain,
( ~ ssList(nil)
| spl53_4 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f698,plain,
~ spl53_4,
inference(avatar_split_clause,[],[f537,f669]) ).
fof(f813,plain,
! [X0] :
( ssList(nil)
| nil = X0
| ssList(X0)
| segmentP(sK50,X0)
| segmentP(sK49,X0)
| ssList(X0) ),
inference(resolution,[],[f535,f643]) ).
fof(f818,plain,
! [X0] :
( ssList(nil)
| nil = X0
| ssList(X0)
| segmentP(sK50,X0)
| segmentP(sK49,X0) ),
inference(duplicate_literal_removal,[],[f813]) ).
fof(f819,plain,
( ! [X0] :
( segmentP(sK50,X0)
| ssList(X0)
| nil = X0
| segmentP(sK49,X0) )
| spl53_4 ),
inference(forward_subsumption_resolution,[],[f818,f670]) ).
fof(f2543,plain,
( ~ segmentP(sK50,sK49)
| ssList(sK49)
| ssList(sK52)
| ssList(sK51)
| ssList(sK50) ),
inference(superposition,[],[f475,f415]) ).
fof(f2548,plain,
( ~ segmentP(sK50,sK49)
| ssList(sK52)
| ssList(sK51)
| ssList(sK50) ),
inference(forward_subsumption_resolution,[],[f2543,f638]) ).
fof(f2555,plain,
( ~ segmentP(sK50,sK49)
| ssList(sK51)
| ssList(sK50) ),
inference(forward_subsumption_resolution,[],[f2548,f644]) ).
fof(f2562,plain,
( ~ segmentP(sK50,sK49)
| ssList(sK50) ),
inference(forward_subsumption_resolution,[],[f2555,f642]) ).
fof(f2565,plain,
~ segmentP(sK50,sK49),
inference(forward_subsumption_resolution,[],[f2562,f639]) ).
fof(f2568,plain,
( ssList(sK49)
| nil = sK49
| segmentP(sK49,sK49)
| spl53_4 ),
inference(resolution,[],[f2565,f819]) ).
fof(f2573,plain,
( nil = sK49
| segmentP(sK49,sK49)
| spl53_4 ),
inference(forward_subsumption_resolution,[],[f2568,f638]) ).
fof(f2575,plain,
( segmentP(sK49,sK49)
| spl53_2
| spl53_4 ),
inference(forward_subsumption_resolution,[],[f2573,f661]) ).
fof(f2657,plain,
( ssList(sK49)
| spl53_2
| spl53_4 ),
inference(resolution,[],[f2575,f588]) ).
fof(f2661,plain,
( $false
| spl53_2
| spl53_4 ),
inference(forward_subsumption_resolution,[],[f2657,f638]) ).
fof(f2662,plain,
( spl53_2
| spl53_4 ),
inference(avatar_contradiction_clause,[],[f2661]) ).
cnf(s1,plain,
( spl53_1
| ~ spl53_2 ),
inference(sat_conversion,[],[f662]) ).
cnf(s2,plain,
( ~ spl53_1
| ~ spl53_2 ),
inference(sat_conversion,[],[f663]) ).
cnf(s11,plain,
~ spl53_4,
inference(sat_conversion,[],[f698]) ).
cnf(s75,plain,
( spl53_2
| spl53_4 ),
inference(sat_conversion,[],[f2662]) ).
cnf(s76,plain,
spl53_2,
inference(rat,[],[s75,s11]) ).
cnf(s81,plain,
~ spl53_1,
inference(rat,[],[s2,s76]) ).
cnf(s97,plain,
$false,
inference(rat,[],[s1,s76,s81]) ).
fof(f2663,plain,
$false,
inference(avatar_sat_refutation,[],[s97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC076+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 07:44:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.42 Running first-order model finding
% 0.14/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.54 % (188493)Will run a generic schedule for satisfiability detection.
% 0.18/0.54 % (188505)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=36510611:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.54 % (188500)% WARNING: option uhcvi not known.
% 0.18/0.54 % (188499)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4191398671_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.54 % (188501)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=857307909:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.54 % (188502)dis+10_1_sil=32000:sp=arity:random_seed=868350990:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.54 % (188503)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=653980707:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.54 % (188500)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3989500555:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.54 % (188504)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3112726305:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.54 % TRYING [1]
% 0.18/0.54 % TRYING [2]
% 0.18/0.54 % TRYING [3]
% 0.18/0.54 % TRYING [4]
% 0.18/0.54 % (188505)Instruction limit reached!
% 0.18/0.54 % (188505)------------------------------
% 0.18/0.54 % (188505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.54 % (188505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.54 % (188505)CaDiCaL version: 2.1.3
% 0.18/0.54 % (188505)Termination reason: Instruction limit
% 0.18/0.54 % (188505)Termination phase: Saturation
% 0.18/0.54 % (188505)Time elapsed: 0.073 s
% 0.18/0.54 % (188505)Peak memory usage: 14 MB
% 0.18/0.54 % (188505)Instructions burned: 163 (million)
% 0.18/0.54 % (188500) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-188493-188500"...
% 0.18/0.54 % (188500)...printing done.
% 0.18/0.54 % (188513)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1149889188:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.54 % (188500)Refutation found. Thanks to Tanya!
% 0.18/0.54 % SZS status Theorem for theBenchmark
% 0.18/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.55 % (188500)------------------------------
% 0.18/0.55 % (188500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.55 % (188500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.55 % (188500)CaDiCaL version: 2.1.3
% 0.18/0.55 % (188500)Termination reason: Refutation
% 0.18/0.55 % (188500)Time elapsed: 0.067 s
% 0.18/0.55 % (188500)Peak memory usage: 14 MB
% 0.18/0.55 % (188500)Instructions burned: 88 (million)
% 0.18/0.55 % (188493)Success in time 0.113 s
% 0.18/0.55 % Vampire exiting
%------------------------------------------------------------------------------