%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC013+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 : n014.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 01:04:17 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 88 ( 18 unt; 7 def)
% Number of atoms : 325 ( 69 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 402 ( 165 ~; 174 |; 40 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 50 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
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
& ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X4
& hd(X3) = X5
& neq(nil,X3) ) )
| ? [X6] :
( ssList(X6)
& X0 = X6
& ? [X7] :
( ssItem(X7)
& cons(X7,nil) = X6
& hd(X1) = X7
& 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
& ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X4
& hd(X3) = X5
& neq(nil,X3) ) )
| ? [X6] :
( ssList(X6)
& X0 = X6
& ? [X7] :
( ssItem(X7)
& cons(X7,nil) = X6
& hd(X1) = X7
& neq(nil,X1) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f126,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f126]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X2 = X4
| ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X4
| hd(X3) != X5
| ~ neq(nil,X3) ) )
& ! [X6] :
( ~ ssList(X6)
| X0 != X6
| ! [X7] :
( ~ ssItem(X7)
| cons(X7,nil) != X6
| hd(X1) != X7
| ~ neq(nil,X1) ) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X2 = X4
| ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X4
| hd(X3) != X5
| ~ neq(nil,X3) ) )
& ! [X6] :
( ~ ssList(X6)
| X0 != X6
| ! [X7] :
( ~ ssItem(X7)
| cons(X7,nil) != X6
| hd(X1) != X7
| ~ neq(nil,X1) ) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f303,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f304,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 != X1
| ~ neq(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f305,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f306,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f314,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f412,plain,
! [X4,X5] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| hd(sK50) != X5
| cons(X5,nil) != X4
| ~ ssItem(X5)
| sK49 = X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f414,plain,
! [X6,X7] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK48)
| hd(sK48) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7)
| sK47 != X6
| ~ ssList(X6) ),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
ssList(sK50),
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f426,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f415,f419]) ).
fof(f427,plain,
! [X6,X7] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| hd(sK50) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7)
| sK49 != X6
| ~ ssList(X6) ),
inference(definition_unfolding,[],[f414,f419,f419,f418]) ).
fof(f444,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f304]) ).
fof(f455,plain,
! [X6] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| cons(hd(sK50),nil) != X6
| ~ ssItem(hd(sK50))
| sK49 != X6
| ~ ssList(X6) ),
inference(equality_resolution,[],[f427]) ).
fof(f456,plain,
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| ~ ssItem(hd(sK50))
| sK49 != cons(hd(sK50),nil)
| ~ ssList(cons(hd(sK50),nil)) ),
inference(equality_resolution,[],[f455]) ).
fof(f459,plain,
! [X4] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| cons(hd(sK50),nil) != X4
| ~ ssItem(hd(sK50))
| sK49 = X4
| ~ ssList(X4) ),
inference(equality_resolution,[],[f412]) ).
fof(f460,plain,
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| ~ ssItem(hd(sK50))
| sK49 = cons(hd(sK50),nil)
| ~ ssList(cons(hd(sK50),nil)) ),
inference(equality_resolution,[],[f459]) ).
fof(f520,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| neq(X1,X1) ),
inference(consistent_polarity_flipping,[],[f444]) ).
fof(f521,plain,
! [X0,X1] :
( ~ neq(X0,X1)
| ~ ssList(X1)
| X0 = X1
| ~ ssList(X0) ),
inference(consistent_polarity_flipping,[],[f303]) ).
fof(f522,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ssItem(X1)
| ~ ssList(X0) ),
inference(consistent_polarity_flipping,[],[f305]) ).
fof(f528,plain,
! [X0] :
( ~ ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(consistent_polarity_flipping,[],[f314]) ).
fof(f585,plain,
~ neq(sK50,nil),
inference(consistent_polarity_flipping,[],[f426]) ).
fof(f586,plain,
( neq(sK50,nil)
| neq(nil,sK50)
| ssItem(hd(sK50))
| sK49 != cons(hd(sK50),nil)
| ~ ssList(cons(hd(sK50),nil)) ),
inference(consistent_polarity_flipping,[],[f456]) ).
fof(f588,plain,
( neq(sK50,nil)
| neq(nil,sK50)
| ssItem(hd(sK50))
| sK49 = cons(hd(sK50),nil)
| ~ ssList(cons(hd(sK50),nil)) ),
inference(consistent_polarity_flipping,[],[f460]) ).
fof(f594,plain,
! [X1] :
( neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f520]) ).
fof(f598,definition,
( spl51_1
<=> ssList(cons(hd(sK50),nil)) ),
introduced(definition,[new_symbols(definition,[spl51_1])],[avatar_definition]) ).
fof(f600,plain,
( ~ ssList(cons(hd(sK50),nil))
| spl51_1 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f602,definition,
( spl51_2
<=> sK49 = cons(hd(sK50),nil) ),
introduced(definition,[new_symbols(definition,[spl51_2])],[avatar_definition]) ).
fof(f606,definition,
( spl51_3
<=> ssItem(hd(sK50)) ),
introduced(definition,[new_symbols(definition,[spl51_3])],[avatar_definition]) ).
fof(f608,plain,
( ssItem(hd(sK50))
| ~ spl51_3 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f610,definition,
( spl51_4
<=> neq(nil,sK50) ),
introduced(definition,[new_symbols(definition,[spl51_4])],[avatar_definition]) ).
fof(f612,plain,
( neq(nil,sK50)
| ~ spl51_4 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f614,definition,
( spl51_5
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl51_5])],[avatar_definition]) ).
fof(f616,plain,
( ~ neq(sK50,nil)
| spl51_5 ),
inference(avatar_component_clause,[],[f614]) ).
fof(f618,plain,
( ~ spl51_1
| spl51_2
| spl51_3
| spl51_4
| spl51_5 ),
inference(avatar_split_clause,[],[f588,f614,f610,f606,f602,f598]) ).
fof(f620,plain,
( ~ spl51_1
| ~ spl51_2
| spl51_3
| spl51_4
| spl51_5 ),
inference(avatar_split_clause,[],[f586,f614,f610,f606,f602,f598]) ).
fof(f621,plain,
~ spl51_5,
inference(avatar_split_clause,[],[f585,f614]) ).
fof(f627,definition,
( spl51_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl51_7])],[avatar_definition]) ).
fof(f628,plain,
( ssList(nil)
| ~ spl51_7 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f656,plain,
spl51_7,
inference(avatar_split_clause,[],[f306,f627]) ).
fof(f710,plain,
( ssItem(hd(sK50))
| ~ ssList(nil)
| spl51_1 ),
inference(resolution,[],[f522,f600]) ).
fof(f713,plain,
( ssItem(hd(sK50))
| spl51_1
| ~ spl51_7 ),
inference(forward_subsumption_resolution,[],[f710,f628]) ).
fof(f714,plain,
( spl51_3
| spl51_1
| ~ spl51_7 ),
inference(avatar_split_clause,[],[f713,f627,f598,f606]) ).
fof(f715,plain,
( nil = sK50
| ~ ssList(sK50)
| ~ spl51_3 ),
inference(resolution,[],[f528,f608]) ).
fof(f716,plain,
( nil = sK50
| ~ spl51_3 ),
inference(forward_subsumption_resolution,[],[f715,f417]) ).
fof(f720,plain,
( ~ neq(nil,nil)
| ~ spl51_3
| spl51_5 ),
inference(superposition,[],[f616,f716]) ).
fof(f725,plain,
( ~ ssList(nil)
| ~ spl51_3
| spl51_5 ),
inference(resolution,[],[f720,f594]) ).
fof(f726,plain,
( $false
| ~ spl51_3
| spl51_5
| ~ spl51_7 ),
inference(forward_subsumption_resolution,[],[f725,f628]) ).
fof(f727,plain,
( ~ spl51_3
| spl51_5
| ~ spl51_7 ),
inference(avatar_contradiction_clause,[],[f726]) ).
fof(f755,definition,
( spl51_14
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl51_14])],[avatar_definition]) ).
fof(f757,plain,
( nil = sK50
| ~ spl51_14 ),
inference(avatar_component_clause,[],[f755]) ).
fof(f818,plain,
( neq(nil,nil)
| ~ spl51_4
| ~ spl51_14 ),
inference(superposition,[],[f612,f757]) ).
fof(f819,plain,
( ~ neq(nil,nil)
| spl51_5
| ~ spl51_14 ),
inference(superposition,[],[f616,f757]) ).
fof(f841,plain,
( ~ ssList(sK50)
| nil = sK50
| ~ ssList(nil)
| ~ spl51_4 ),
inference(resolution,[],[f521,f612]) ).
fof(f890,plain,
( $false
| ~ spl51_4
| spl51_5
| ~ spl51_14 ),
inference(forward_subsumption_resolution,[],[f819,f818]) ).
fof(f891,plain,
( ~ spl51_4
| spl51_5
| ~ spl51_14 ),
inference(avatar_contradiction_clause,[],[f890]) ).
fof(f901,plain,
( nil = sK50
| ~ ssList(nil)
| ~ spl51_4 ),
inference(forward_subsumption_resolution,[],[f841,f417]) ).
fof(f902,plain,
( nil = sK50
| ~ spl51_4
| ~ spl51_7 ),
inference(forward_subsumption_resolution,[],[f901,f628]) ).
fof(f903,plain,
( spl51_14
| ~ spl51_4
| ~ spl51_7 ),
inference(avatar_split_clause,[],[f902,f627,f610,f755]) ).
cnf(s2,plain,
( ~ spl51_1
| spl51_2
| spl51_3
| spl51_4
| spl51_5 ),
inference(sat_conversion,[],[f618]) ).
cnf(s4,plain,
( ~ spl51_1
| ~ spl51_2
| spl51_3
| spl51_4
| spl51_5 ),
inference(sat_conversion,[],[f620]) ).
cnf(s5,plain,
~ spl51_5,
inference(sat_conversion,[],[f621]) ).
cnf(s14,plain,
spl51_7,
inference(sat_conversion,[],[f656]) ).
cnf(s15,plain,
( spl51_1
| spl51_3
| ~ spl51_7 ),
inference(sat_conversion,[],[f714]) ).
cnf(s16,plain,
( ~ spl51_3
| spl51_5
| ~ spl51_7 ),
inference(sat_conversion,[],[f727]) ).
cnf(s23,plain,
( ~ spl51_4
| spl51_5
| ~ spl51_14 ),
inference(sat_conversion,[],[f891]) ).
cnf(s25,plain,
( ~ spl51_4
| ~ spl51_7
| spl51_14 ),
inference(sat_conversion,[],[f903]) ).
cnf(s30,plain,
~ spl51_3,
inference(rat,[],[s16,s14,s5]) ).
cnf(s31,plain,
spl51_1,
inference(rat,[],[s15,s14,s30]) ).
cnf(s32,plain,
( ~ spl51_2
| spl51_4 ),
inference(rat,[],[s4,s5,s30,s31]) ).
cnf(s33,plain,
( spl51_2
| spl51_4 ),
inference(rat,[],[s2,s5,s30,s31]) ).
cnf(s34,plain,
~ spl51_4,
inference(rat,[],[s23,s25,s5,s14]) ).
cnf(s35,plain,
~ spl51_2,
inference(rat,[],[s32,s34]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s33,s34,s35]) ).
fof(f904,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC013+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 % Computer : n014.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 07:25:31 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.17/0.47 % (1607870)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (1607876)% WARNING: option uhcvi not known.
% 0.17/0.47 % (1607876)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1257461653:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (1607875)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3457227311_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (1607877)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2862223855:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (1607878)dis+10_1_sil=32000:sp=arity:random_seed=1193584684:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (1607879)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=960407200:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (1607880)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2545857423:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (1607881)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4179751504:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (1607876) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1607870-1607876"...
% 0.17/0.47 % (1607876)...printing done.
% 0.17/0.47 % (1607876)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1607876)------------------------------
% 0.17/0.47 % (1607876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1607876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1607876)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1607876)Termination reason: Refutation
% 0.17/0.47 % (1607876)Time elapsed: 0.009 s
% 0.17/0.47 % (1607876)Peak memory usage: 13 MB
% 0.17/0.47 % (1607876)Instructions burned: 23 (million)
% 0.17/0.47 % (1607870)Success in time 0.036 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------