%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC149-1 : 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 : n007.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 01:02:40 PM UTC 2026
% Result : Unsatisfiable 2.17s 1.15s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 70 ( 13 unt; 3 def)
% Number of atoms : 240 ( 53 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 349 ( 179 ~; 167 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f12,axiom,
! [X0] : ssItem(skaf83(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
fof(f112,axiom,
! [X0] :
( cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).
fof(f118,axiom,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
fof(f119,axiom,
! [X0,X1] :
( cons(X0,nil) != X1
| ~ ssItem(X0)
| ~ ssList(X1)
| singletonP(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
fof(f125,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
fof(f126,plain,
! [X0,X1] :
( cons(X0,X1) = app(cons(X0,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f125]) ).
fof(f161,axiom,
! [X2,X0,X1] :
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).
fof(f201,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f206,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2) ),
inference(reorient_equations,[],[f207]) ).
fof(f209,negated_conjecture,
~ singletonP(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f216,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f217,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(equality_resolution,[],[f119]) ).
fof(f238,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f216]) ).
fof(f245,definition,
( spl0_2
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f246,plain,
( ssList(nil)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f281,plain,
spl0_2,
inference(avatar_split_clause,[],[f8,f245]) ).
fof(f284,plain,
! [X2,X0,X1] :
( sk2 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(forward_demodulation,[],[f208,f204]) ).
fof(f543,plain,
! [X2,X0,X1] :
( sk2 != app(cons(X0,nil),app(cons(X1,nil),X2))
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| ~ ssList(cons(X0,nil))
| ~ ssList(X2) ),
inference(superposition,[],[f284,f161]) ).
fof(f567,plain,
! [X2,X0,X1] :
( ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| sk2 != app(cons(X0,nil),app(cons(X1,nil),X2)) ),
inference(duplicate_literal_removal,[],[f543]) ).
fof(f592,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| sk2 != app(cons(X0,nil),app(cons(X1,nil),X2))
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(resolution,[],[f567,f86]) ).
fof(f596,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| sk2 != app(cons(X0,nil),app(cons(X1,nil),X2))
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f592]) ).
fof(f597,plain,
( ! [X2,X0,X1] :
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| sk2 != app(cons(X0,nil),app(cons(X1,nil),X2)) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f596,f246]) ).
fof(f1086,plain,
( ! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssItem(X2)
| sk2 != app(cons(X2,nil),app(cons(X0,nil),X1))
| ~ ssList(nil)
| ~ ssItem(X0) )
| ~ spl0_2 ),
inference(resolution,[],[f597,f86]) ).
fof(f1088,plain,
( ! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssItem(X2)
| sk2 != app(cons(X2,nil),app(cons(X0,nil),X1))
| ~ ssList(nil) )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f1086]) ).
fof(f1089,plain,
( ! [X2,X0,X1] :
( sk2 != app(cons(X2,nil),app(cons(X0,nil),X1))
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X0) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1088,f246]) ).
fof(f1092,plain,
( ! [X2,X0,X1] :
( sk2 != app(cons(X2,nil),cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl0_2 ),
inference(superposition,[],[f1089,f126]) ).
fof(f1096,plain,
( ! [X2,X0,X1] :
( sk2 != app(cons(X2,nil),cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X0) )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f1092]) ).
fof(f1099,plain,
( ! [X2,X0,X1] :
( sk2 != cons(X0,cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(cons(X1,X2))
| ~ ssItem(X0) )
| ~ spl0_2 ),
inference(superposition,[],[f1096,f126]) ).
fof(f1100,plain,
( ! [X2,X0,X1] :
( sk2 != cons(X0,cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(cons(X1,X2)) )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f1099]) ).
fof(f1101,plain,
( ! [X2,X0,X1] :
( sk2 != cons(X0,cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X0)
| ~ ssItem(X1) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1100,f86]) ).
fof(f1118,plain,
( ! [X0,X1] :
( cons(X1,X0) != sk2
| ~ ssList(skaf82(X0))
| ~ ssItem(X1)
| ~ ssItem(skaf83(X0))
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_2 ),
inference(superposition,[],[f1101,f112]) ).
fof(f1119,plain,
( ! [X0,X1] :
( cons(X1,X0) != sk2
| ~ ssItem(X1)
| ~ ssItem(skaf83(X0))
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1118,f13]) ).
fof(f1121,plain,
( ! [X0,X1] :
( cons(X1,X0) != sk2
| ~ ssItem(X1)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1119,f12]) ).
fof(f1124,plain,
( ! [X0] :
( sk2 != X0
| ~ ssItem(skaf83(X0))
| ~ ssList(skaf82(X0))
| nil = skaf82(X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_2 ),
inference(superposition,[],[f1121,f112]) ).
fof(f1125,plain,
( ! [X0] :
( sk2 != X0
| ~ ssList(skaf82(X0))
| nil = skaf82(X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1124,f12]) ).
fof(f1127,plain,
( ! [X0] :
( sk2 != X0
| nil = skaf82(X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1125,f13]) ).
fof(f1256,plain,
( nil = skaf82(sk2)
| ~ ssList(sk2)
| nil = sk2
| ~ spl0_2 ),
inference(equality_resolution,[],[f1127]) ).
fof(f1257,plain,
( nil = skaf82(sk2)
| nil = sk2
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1256,f201]) ).
fof(f1259,definition,
( spl0_21
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f1260,plain,
( nil != sk2
| spl0_21 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f1261,plain,
( nil = sk2
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f1263,definition,
( spl0_22
<=> nil = skaf82(sk2) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f1265,plain,
( nil = skaf82(sk2)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1263]) ).
fof(f1266,plain,
( spl0_21
| spl0_22
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f1257,f245,f1263,f1259]) ).
fof(f1268,plain,
( neq(nil,nil)
| ~ spl0_21 ),
inference(superposition,[],[f206,f1261]) ).
fof(f1271,plain,
( ~ ssList(nil)
| ~ spl0_21 ),
inference(resolution,[],[f1268,f238]) ).
fof(f1273,plain,
( $false
| ~ spl0_2
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1271,f246]) ).
fof(f1274,plain,
( ~ spl0_2
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f1273]) ).
fof(f1275,plain,
( sk2 = cons(skaf83(sk2),nil)
| ~ ssList(sk2)
| nil = sk2
| ~ spl0_22 ),
inference(superposition,[],[f112,f1265]) ).
fof(f1277,plain,
( sk2 = cons(skaf83(sk2),nil)
| nil = sk2
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1275,f201]) ).
fof(f1278,plain,
( sk2 = cons(skaf83(sk2),nil)
| spl0_21
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1277,f1260]) ).
fof(f1287,plain,
( singletonP(sk2)
| ~ ssList(sk2)
| ~ ssItem(skaf83(sk2))
| spl0_21
| ~ spl0_22 ),
inference(superposition,[],[f217,f1278]) ).
fof(f1381,plain,
( ~ ssList(sk2)
| ~ ssItem(skaf83(sk2))
| spl0_21
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1287,f209]) ).
fof(f1417,plain,
( ~ ssItem(skaf83(sk2))
| spl0_21
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1381,f201]) ).
fof(f1421,plain,
( $false
| spl0_21
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1417,f12]) ).
fof(f1422,plain,
( spl0_21
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1421]) ).
cnf(s10,plain,
spl0_2,
inference(sat_conversion,[],[f281]) ).
cnf(s53,plain,
( ~ spl0_2
| spl0_21
| spl0_22 ),
inference(sat_conversion,[],[f1266]) ).
cnf(s54,plain,
( ~ spl0_2
| ~ spl0_21 ),
inference(sat_conversion,[],[f1274]) ).
cnf(s55,plain,
( spl0_21
| ~ spl0_22 ),
inference(sat_conversion,[],[f1422]) ).
cnf(s57,plain,
~ spl0_21,
inference(rat,[],[s54,s10]) ).
cnf(s58,plain,
~ spl0_22,
inference(rat,[],[s55,s57]) ).
cnf(s59,plain,
$false,
inference(rat,[],[s53,s10,s58,s57]) ).
fof(f1423,plain,
$false,
inference(avatar_sat_refutation,[],[s59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC149-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 08:07:56 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.17/1.15 % (2239578)Input is clausal, will run a generic CNF schedule.
% 2.17/1.15 % (2239588)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1733220334:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.17/1.15 % (2239588)First to succeed.
% 2.17/1.15 % (2239588)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2239578"
% 2.17/1.15 % (2239587)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3655760576:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.17/1.15 % (2239584)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1310780176:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.17/1.15 % (2239586)lrs+10_1_sil=8000:sp=occurrence:random_seed=616174338:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.17/1.15 % (2239585)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4272745814:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.17/1.15 % (2239583)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=318821765:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.17/1.15 % (2239589)dis-21_1_sil=8000:lcm=predicate:random_seed=790327915:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.17/1.15 % (2239587)Instruction limit reached!
% 2.17/1.15 % (2239587)------------------------------
% 2.17/1.15 % (2239587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.17/1.15 % (2239587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/1.15 % (2239587)CaDiCaL version: 2.1.3
% 2.17/1.15 % (2239587)Termination reason: Instruction limit
% 2.17/1.15 % (2239587)Termination phase: Saturation
% 2.17/1.15 % (2239587)Time elapsed: 0.051 s
% 2.17/1.15 % (2239587)Peak memory usage: 88 MB
% 2.17/1.15 % (2239587)Instructions burned: 114 (million)
% 2.17/1.15 % (2239589)Instruction limit reached!
% 2.17/1.15 % (2239589)------------------------------
% 2.17/1.15 % (2239589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.17/1.15 % (2239589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/1.15 % (2239589)CaDiCaL version: 2.1.3
% 2.17/1.15 % (2239589)Termination reason: Instruction limit
% 2.17/1.15 % (2239589)Termination phase: Saturation
% 2.17/1.15 % (2239589)Time elapsed: 0.050 s
% 2.17/1.15 % (2239589)Peak memory usage: 89 MB
% 2.17/1.15 % (2239589)Instructions burned: 119 (million)
% 2.17/1.15 % (2239586)Instruction limit reached!
% 2.17/1.15 % (2239586)------------------------------
% 2.17/1.15 % (2239586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.17/1.15 % (2239586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/1.15 % (2239586)CaDiCaL version: 2.1.3
% 2.17/1.15 % (2239586)Termination reason: Instruction limit
% 2.17/1.15 % (2239586)Termination phase: Saturation
% 2.17/1.15 % (2239586)Time elapsed: 0.064 s
% 2.17/1.15 % (2239586)Peak memory usage: 89 MB
% 2.17/1.15 % (2239586)Instructions burned: 108 (million)
% 2.17/1.15 % (2239588)Refutation found. Thanks to Tanya!
% 2.17/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.17/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.34 % (2239588)------------------------------
% 2.63/1.34 % (2239588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.34 % (2239588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.34 % (2239588)CaDiCaL version: 2.1.3
% 2.63/1.34 % (2239588)Termination reason: Refutation
% 2.63/1.34 % (2239588)Time elapsed: 0.021 s
% 2.63/1.34 % (2239588)Peak memory usage: 90 MB
% 2.63/1.34 % (2239588)Instructions burned: 55 (million)
% 2.63/1.34 % (2239588)------------------------------
% 2.63/1.34 % (2239588)------------------------------
% 2.63/1.34 % (2239578)Success in time 0.284 s
% 2.63/1.34 % Vampire exiting
%------------------------------------------------------------------------------