%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC067-1 : 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 : 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 01:02:17 PM UTC 2026
% Result : Unsatisfiable 1.65s 1.13s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 24
% Syntax : Number of formulae : 95 ( 18 unt; 6 def)
% Number of atoms : 266 ( 45 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 340 ( 169 ~; 165 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f57,axiom,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
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(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(f123,axiom,
! [X0,X1] :
( app(X0,X1) != nil
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause119) ).
fof(f124,plain,
! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X1 ),
inference(reorient_equations,[],[f123]) ).
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,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
app(app(sk5,sk3),sk6) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,plain,
sk4 = app(app(sk5,sk3),sk6),
inference(reorient_equations,[],[f208]) ).
fof(f215,negated_conjecture,
( nil = sk4
| nil != sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f217,negated_conjecture,
! [X0] :
( nil = sk2
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk2,X0)
| ~ segmentP(sk1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f218,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f219,negated_conjecture,
! [X0] :
( nil != sk1
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk2,X0)
| ~ segmentP(sk1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f223,plain,
! [X0] :
( nil = sk4
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(definition_unfolding,[],[f217,f204,f204,f205]) ).
fof(f224,plain,
( nil != sk3
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f218,f205,f204]) ).
fof(f225,plain,
! [X0] :
( nil != sk3
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(definition_unfolding,[],[f219,f205,f204,f205]) ).
fof(f233,plain,
! [X2,X0,X1] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f187]) ).
fof(f240,definition,
( spl0_1
<=> ! [X0] :
( ~ ssList(X0)
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f241,plain,
( ! [X0] :
( ~ neq(X0,nil)
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ ssList(X0) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f243,definition,
( spl0_2
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f244,plain,
( nil = sk3
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f245,plain,
( nil != sk3
| spl0_2 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f246,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f225,f243,f240]) ).
fof(f248,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f250,plain,
( neq(sk4,nil)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f224,f243,f248]) ).
fof(f253,definition,
( spl0_4
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f255,plain,
( nil = sk4
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f256,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f223,f253,f240]) ).
fof(f258,plain,
( ~ spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f215,f253,f243]) ).
fof(f298,plain,
( nil != sk4
| ~ ssList(sk6)
| ~ ssList(app(sk5,sk3))
| nil = app(sk5,sk3) ),
inference(superposition,[],[f122,f209]) ).
fof(f302,plain,
( ~ ssList(sk6)
| ~ ssList(app(sk5,sk3))
| nil = app(sk5,sk3)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f298,f255]) ).
fof(f303,plain,
( ~ ssList(app(sk5,sk3))
| nil = app(sk5,sk3)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f302,f207]) ).
fof(f305,definition,
( spl0_5
<=> nil = app(sk5,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f307,plain,
( nil = app(sk5,sk3)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f309,definition,
( spl0_6
<=> ssList(app(sk5,sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f311,plain,
( ~ ssList(app(sk5,sk3))
| spl0_6 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f312,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f303,f253,f309,f305]) ).
fof(f313,plain,
( ~ ssList(sk5)
| ~ ssList(sk3)
| spl0_6 ),
inference(resolution,[],[f311,f85]) ).
fof(f314,plain,
( ~ ssList(sk3)
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f313,f206]) ).
fof(f315,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f314,f202]) ).
fof(f316,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f315]) ).
fof(f334,plain,
( nil != nil
| ~ ssList(sk3)
| ~ ssList(sk5)
| nil = sk3
| ~ spl0_5 ),
inference(superposition,[],[f124,f307]) ).
fof(f338,plain,
( ~ ssList(sk3)
| ~ ssList(sk5)
| nil = sk3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f334]) ).
fof(f340,plain,
( ~ ssList(sk5)
| nil = sk3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f338,f202]) ).
fof(f343,plain,
( nil = sk3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f340,f206]) ).
fof(f345,plain,
( $false
| spl0_2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f343,f245]) ).
fof(f346,plain,
( spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f345]) ).
fof(f348,plain,
( ! [X0] :
( ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0 )
| ~ spl0_1 ),
inference(resolution,[],[f241,f102]) ).
fof(f349,plain,
( ~ segmentP(sk3,sk4)
| ~ segmentP(sk4,sk4)
| ~ ssList(sk4)
| ~ spl0_1
| ~ spl0_3 ),
inference(resolution,[],[f241,f250]) ).
fof(f350,plain,
( ! [X0] :
( ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0 )
| ~ spl0_1 ),
inference(duplicate_literal_removal,[],[f348]) ).
fof(f351,plain,
( ~ segmentP(sk3,sk4)
| ~ ssList(sk4)
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f349,f57]) ).
fof(f352,plain,
( ! [X0] :
( ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f350,f8]) ).
fof(f361,plain,
( ~ segmentP(sk3,sk4)
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f351,f203]) ).
fof(f750,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(sk6) ),
inference(superposition,[],[f233,f209]) ).
fof(f756,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(sk6) ),
inference(forward_subsumption_resolution,[],[f750,f206]) ).
fof(f763,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk6) ),
inference(forward_subsumption_resolution,[],[f756,f202]) ).
fof(f770,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk6) ),
inference(forward_subsumption_resolution,[],[f763,f203]) ).
fof(f774,plain,
segmentP(sk4,sk3),
inference(forward_subsumption_resolution,[],[f770,f207]) ).
fof(f800,plain,
( ~ segmentP(sk3,sk3)
| ~ ssList(sk3)
| nil = sk3
| ~ spl0_1 ),
inference(resolution,[],[f774,f352]) ).
fof(f804,plain,
( ~ ssList(sk3)
| nil = sk3
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f800,f57]) ).
fof(f806,plain,
( nil = sk3
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f804,f202]) ).
fof(f807,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f806,f245]) ).
fof(f808,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f807]) ).
fof(f842,plain,
( ~ segmentP(nil,sk4)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f361,f244]) ).
fof(f844,plain,
( segmentP(sk4,nil)
| ~ spl0_2 ),
inference(superposition,[],[f774,f244]) ).
fof(f845,plain,
( segmentP(nil,nil)
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f844,f255]) ).
fof(f847,plain,
( ~ segmentP(nil,nil)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f842,f255]) ).
fof(f851,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f847,f845]) ).
fof(f852,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f851]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f246]) ).
cnf(s2,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f251]) ).
cnf(s3,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f256]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f258]) ).
cnf(s6,plain,
( ~ spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f312]) ).
cnf(s7,plain,
spl0_6,
inference(sat_conversion,[],[f316]) ).
cnf(s8,plain,
( spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f346]) ).
cnf(s20,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f808]) ).
cnf(s25,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f852]) ).
cnf(s29,plain,
( ~ spl0_4
| spl0_5 ),
inference(rat,[],[s6,s7]) ).
cnf(s30,plain,
spl0_1,
inference(rat,[],[s8,s29,s1,s3]) ).
cnf(s31,plain,
spl0_2,
inference(rat,[],[s20,s30]) ).
cnf(s32,plain,
spl0_4,
inference(rat,[],[s5,s31]) ).
cnf(s33,plain,
spl0_3,
inference(rat,[],[s2,s31]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s25,s31,s30,s32,s33]) ).
fof(f857,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC067-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 07:40:41 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 1.65/1.13 % (2227345)Input is clausal, will run a generic CNF schedule.
% 1.65/1.13 % (2227353)lrs+10_1_sil=8000:sp=occurrence:random_seed=1100723750:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.65/1.13 % (2227353)First to succeed.
% 1.65/1.13 % (2227353)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2227345"
% 1.65/1.13 % (2227350)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=2463122597:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.65/1.13 % (2227355)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3617295113:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.65/1.13 % (2227354)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4206635882:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.65/1.13 % (2227356)dis-21_1_sil=8000:lcm=predicate:random_seed=359608761: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)
% 1.65/1.13 % (2227351)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1821587356:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.65/1.13 % (2227352)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1625886717:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.65/1.13 % (2227354)Also succeeded, but the first one will report.
% 1.65/1.13 % (2227355)Also succeeded, but the first one will report.
% 1.65/1.13 % (2227356)Instruction limit reached!
% 1.65/1.13 % (2227356)------------------------------
% 1.65/1.13 % (2227356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.65/1.13 % (2227356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/1.13 % (2227356)CaDiCaL version: 2.1.3
% 1.65/1.13 % (2227356)Termination reason: Instruction limit
% 1.65/1.13 % (2227356)Termination phase: Saturation
% 1.65/1.13 % (2227356)Time elapsed: 0.063 s
% 1.65/1.13 % (2227356)Peak memory usage: 90 MB
% 1.65/1.13 % (2227356)Instructions burned: 117 (million)
% 1.65/1.13 % (2227353)Refutation found. Thanks to Tanya!
% 1.65/1.13 % SZS status Unsatisfiable for theBenchmark
% 1.65/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/1.33 % (2227353)------------------------------
% 2.54/1.33 % (2227353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.33 % (2227353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.33 % (2227353)CaDiCaL version: 2.1.3
% 2.54/1.33 % (2227353)Termination reason: Refutation
% 2.54/1.33 % (2227353)Time elapsed: 0.009 s
% 2.54/1.33 % (2227353)Peak memory usage: 90 MB
% 2.54/1.33 % (2227353)Instructions burned: 22 (million)
% 2.54/1.33 % (2227353)------------------------------
% 2.54/1.33 % (2227353)------------------------------
% 2.54/1.33 % (2227345)Success in time 0.274 s
% 2.54/1.33 % Vampire exiting
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