%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC110-1 : 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 : n001.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 01:02:29 PM UTC 2026
% Result : Unsatisfiable 5.52s 1.79s
% Output : Refutation 5.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 72 ( 15 unt; 5 def)
% Number of atoms : 178 ( 32 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 207 ( 101 ~; 101 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f118,axiom,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
fof(f121,axiom,
! [X0,X1] :
( app(X0,X1) != nil
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause118) ).
fof(f122,plain,
! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
inference(reorient_equations,[],[f121]) ).
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/sandbox2/benchmark/theBenchmark.p',clause149) ).
fof(f187,axiom,
! [X2,X3,X0,X1] :
( app(app(X0,X1),X2) != X3
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| segmentP(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause173) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,plain,
sk4 = app(sk3,sk5),
inference(reorient_equations,[],[f207]) ).
fof(f212,negated_conjecture,
( nil = sk4
| nil != sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f214,negated_conjecture,
( nil = sk2
| ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f215,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f220,plain,
( nil = sk4
| ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3) ),
inference(definition_unfolding,[],[f214,f204,f205,f204,f205]) ).
fof(f221,plain,
( nil != sk3
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f215,f205,f204]) ).
fof(f225,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f226,plain,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2))
| segmentP(app(app(X0,X1),X2),X1) ),
inference(equality_resolution,[],[f187]) ).
fof(f228,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f225]) ).
fof(f242,definition,
( spl0_4
<=> segmentP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f243,plain,
( ~ segmentP(sk4,sk3)
| spl0_4 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f245,definition,
( spl0_5
<=> neq(sk3,nil) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f246,plain,
( ~ neq(sk3,nil)
| spl0_5 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f248,definition,
( spl0_6
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f252,definition,
( spl0_7
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f253,plain,
( neq(sk4,nil)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f254,plain,
( spl0_7
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f221,f248,f252]) ).
fof(f256,definition,
( spl0_8
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f257,plain,
( nil = sk4
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f258,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_8 ),
inference(avatar_split_clause,[],[f220,f256,f245,f242]) ).
fof(f260,plain,
( ~ spl0_6
| spl0_8 ),
inference(avatar_split_clause,[],[f212,f256,f248]) ).
fof(f277,plain,
( nil != sk4
| ~ ssList(sk5)
| ~ ssList(sk3)
| nil = sk3 ),
inference(superposition,[],[f122,f208]) ).
fof(f280,plain,
( nil != sk4
| ~ ssList(sk3)
| nil = sk3 ),
inference(forward_subsumption_resolution,[],[f277,f206]) ).
fof(f281,plain,
( nil != sk4
| nil = sk3 ),
inference(forward_subsumption_resolution,[],[f280,f202]) ).
fof(f450,plain,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(X0,app(X1,X2)))
| segmentP(app(app(X0,X1),X2),X1) ),
inference(forward_subsumption_demodulation,[],[f226,f161]) ).
fof(f451,plain,
! [X2,X0,X1] :
( segmentP(app(X0,app(X1,X2)),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(X0,app(X1,X2)))
| ~ ssList(X2) ),
inference(forward_subsumption_demodulation,[],[f450,f161]) ).
fof(f457,plain,
! [X0] :
( segmentP(app(X0,sk4),sk3)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(app(X0,sk4))
| ~ ssList(sk5) ),
inference(superposition,[],[f451,f208]) ).
fof(f468,plain,
! [X0] :
( segmentP(app(X0,sk4),sk3)
| ~ ssList(X0)
| ~ ssList(app(X0,sk4))
| ~ ssList(sk5) ),
inference(forward_subsumption_resolution,[],[f457,f202]) ).
fof(f473,plain,
! [X0] :
( segmentP(app(X0,sk4),sk3)
| ~ ssList(X0)
| ~ ssList(app(X0,sk4)) ),
inference(forward_subsumption_resolution,[],[f468,f206]) ).
fof(f551,plain,
( segmentP(sk4,sk3)
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssList(sk4) ),
inference(superposition,[],[f473,f74]) ).
fof(f553,plain,
( segmentP(sk4,sk3)
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(duplicate_literal_removal,[],[f551]) ).
fof(f556,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f553,f243]) ).
fof(f559,plain,
( ~ ssList(sk4)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f556,f8]) ).
fof(f560,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f559,f203]) ).
fof(f561,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f560]) ).
fof(f573,plain,
( spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f281,f256,f248]) ).
fof(f587,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| nil = sk3
| spl0_5 ),
inference(resolution,[],[f246,f102]) ).
fof(f588,plain,
( ~ ssList(nil)
| nil = sk3
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f587,f202]) ).
fof(f589,plain,
( nil = sk3
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f588,f8]) ).
fof(f590,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f589,f245,f248]) ).
fof(f592,plain,
( neq(nil,nil)
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f253,f257]) ).
fof(f605,plain,
( ~ ssList(nil)
| ~ spl0_7
| ~ spl0_8 ),
inference(resolution,[],[f592,f228]) ).
fof(f606,plain,
( $false
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f605,f8]) ).
fof(f607,plain,
( ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f606]) ).
cnf(s4,plain,
( ~ spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f254]) ).
cnf(s5,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f258]) ).
cnf(s7,plain,
( ~ spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f260]) ).
cnf(s11,plain,
spl0_4,
inference(sat_conversion,[],[f561]) ).
cnf(s14,plain,
( spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f573]) ).
cnf(s19,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f590]) ).
cnf(s21,plain,
( ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f607]) ).
cnf(s22,plain,
( ~ spl0_5
| spl0_8 ),
inference(rat,[],[s5,s11]) ).
cnf(s26,plain,
~ spl0_6,
inference(rat,[],[s21,s4,s7]) ).
cnf(s27,plain,
spl0_5,
inference(rat,[],[s19,s26]) ).
cnf(s31,plain,
~ spl0_8,
inference(rat,[],[s14,s26]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s22,s31,s27]) ).
fof(f608,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC110-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.43 % Computer : n001.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Mon Sep 28 08:00:32 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 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
% 5.52/1.79 % (198833)Input is clausal, will run a generic CNF schedule.
% 5.52/1.79 % (198840)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3714883597:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.52/1.79 % (198838)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=2668378731:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.52/1.79 % (198841)lrs+10_1_sil=8000:sp=occurrence:random_seed=3769520713:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.52/1.79 % (198842)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3534961592:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.52/1.79 % (198839)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2956631824:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.52/1.79 % (198843)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1428957793:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.52/1.79 % (198844)dis-21_1_sil=8000:lcm=predicate:random_seed=513769321: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)
% 5.52/1.79 % (198842)First to succeed.
% 5.52/1.79 % (198842)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-198833"
% 5.52/1.79 % (198841)Also succeeded, but the first one will report.
% 5.52/1.79 % (198843)Also succeeded, but the first one will report.
% 5.52/1.79 % (198844)Instruction limit reached!
% 5.52/1.79 % (198844)------------------------------
% 5.52/1.79 % (198844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.79 % (198844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.79 % (198844)CaDiCaL version: 2.1.3
% 5.52/1.79 % (198844)Termination reason: Instruction limit
% 5.52/1.79 % (198844)Termination phase: Saturation
% 5.52/1.79 % (198844)Time elapsed: 0.104 s
% 5.52/1.79 % (198844)Peak memory usage: 89 MB
% 5.52/1.79 % (198844)Instructions burned: 118 (million)
% 5.52/1.79 % (198852)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2827021004:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 5.52/1.79 % (198852)Also succeeded, but the first one will report.
% 5.52/1.79 % (198842)Refutation found. Thanks to Tanya!
% 5.52/1.79 % SZS status Unsatisfiable for theBenchmark
% 5.52/1.79 % SZS output start Proof for theBenchmark
% See solution above
% 5.52/1.79 % (198842)------------------------------
% 5.52/1.79 % (198842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.79 % (198842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.79 % (198842)CaDiCaL version: 2.1.3
% 5.52/1.79 % (198842)Termination reason: Refutation
% 5.52/1.79 % (198842)Time elapsed: 0.021 s
% 5.52/1.79 % (198842)Peak memory usage: 89 MB
% 5.52/1.79 % (198842)Instructions burned: 18 (million)
% 5.52/1.79 % (198842)------------------------------
% 5.52/1.79 % (198842)------------------------------
% 5.52/1.79 % (198833)Success in time 0.696 s
% 5.52/1.79 % Vampire exiting
%------------------------------------------------------------------------------