%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC076-1 : 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 : 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 01:02:19 PM UTC 2026
% Result : Unsatisfiable 3.07s 1.44s
% Output : Refutation 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 63 ( 19 unt; 5 def)
% Number of atoms : 148 ( 27 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 166 ( 81 ~; 80 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f57,axiom,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
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/sandbox/benchmark/theBenchmark.p',clause173) ).
fof(f201,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk2,X0)
| ~ segmentP(sk1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
app(app(sk5,sk3),sk6) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
sk4 = app(app(sk5,sk3),sk6),
inference(reorient_equations,[],[f209]) ).
fof(f216,negated_conjecture,
( nil = sk4
| nil != sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f217,negated_conjecture,
( nil != sk2
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f232,plain,
! [X2,X0,X1] :
( ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(app(X0,X1),X2),X1) ),
inference(equality_resolution,[],[f187]) ).
fof(f249,definition,
( spl0_1
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f251,plain,
( nil != sk1
| spl0_1 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f253,definition,
( spl0_2
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f255,plain,
( nil != sk2
| spl0_2 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f256,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f217,f253,f249]) ).
fof(f258,definition,
( spl0_3
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f260,plain,
( nil != sk3
| spl0_3 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f262,definition,
( spl0_4
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f264,plain,
( nil = sk4
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f265,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f216,f262,f258]) ).
fof(f271,definition,
( spl0_6
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f272,plain,
( ssList(nil)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f307,plain,
spl0_6,
inference(avatar_split_clause,[],[f8,f271]) ).
fof(f310,plain,
( nil != sk3
| spl0_1 ),
inference(forward_demodulation,[],[f251,f205]) ).
fof(f311,plain,
( ~ spl0_3
| spl0_1 ),
inference(avatar_split_clause,[],[f310,f249,f258]) ).
fof(f312,plain,
sk2 = app(app(sk5,sk3),sk6),
inference(forward_demodulation,[],[f210,f204]) ).
fof(f313,plain,
! [X0] :
( ~ neq(X0,nil)
| ~ ssList(X0)
| ~ segmentP(sk3,X0)
| ~ segmentP(sk2,X0) ),
inference(forward_demodulation,[],[f206,f205]) ).
fof(f364,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0)
| ~ segmentP(sk3,X0)
| ~ segmentP(sk2,X0) ),
inference(resolution,[],[f102,f313]) ).
fof(f367,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ segmentP(sk3,X0)
| ~ segmentP(sk2,X0) ),
inference(duplicate_literal_removal,[],[f364]) ).
fof(f368,plain,
( ! [X0] :
( ~ segmentP(sk3,X0)
| nil = X0
| ~ ssList(X0)
| ~ segmentP(sk2,X0) )
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f367,f272]) ).
fof(f370,plain,
( nil = sk3
| ~ ssList(sk3)
| ~ segmentP(sk2,sk3)
| ~ ssList(sk3)
| ~ spl0_6 ),
inference(resolution,[],[f368,f57]) ).
fof(f371,plain,
( nil = sk3
| ~ ssList(sk3)
| ~ segmentP(sk2,sk3)
| ~ spl0_6 ),
inference(duplicate_literal_removal,[],[f370]) ).
fof(f372,plain,
( ~ ssList(sk3)
| ~ segmentP(sk2,sk3)
| spl0_3
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f371,f260]) ).
fof(f373,plain,
( ~ segmentP(sk2,sk3)
| spl0_3
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f372,f202]) ).
fof(f1332,plain,
( ~ ssList(sk2)
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk6)
| segmentP(sk2,sk3) ),
inference(superposition,[],[f232,f312]) ).
fof(f1345,plain,
( ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk6)
| segmentP(sk2,sk3) ),
inference(forward_subsumption_resolution,[],[f1332,f201]) ).
fof(f1355,plain,
( ~ ssList(sk3)
| ~ ssList(sk6)
| segmentP(sk2,sk3) ),
inference(forward_subsumption_resolution,[],[f1345,f207]) ).
fof(f1361,plain,
( ~ ssList(sk6)
| segmentP(sk2,sk3) ),
inference(forward_subsumption_resolution,[],[f1355,f202]) ).
fof(f1364,plain,
segmentP(sk2,sk3),
inference(forward_subsumption_resolution,[],[f1361,f208]) ).
fof(f1365,plain,
( $false
| spl0_3
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f1364,f373]) ).
fof(f1366,plain,
( spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f1365]) ).
fof(f1392,plain,
( nil = sk2
| ~ spl0_4 ),
inference(superposition,[],[f264,f204]) ).
fof(f1397,plain,
( $false
| spl0_2
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f1392,f255]) ).
fof(f1398,plain,
( spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f1397]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f256]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f265]) ).
cnf(s12,plain,
spl0_6,
inference(sat_conversion,[],[f307]) ).
cnf(s13,plain,
( spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f311]) ).
cnf(s36,plain,
( spl0_3
| ~ spl0_6 ),
inference(sat_conversion,[],[f1366]) ).
cnf(s41,plain,
( spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f1398]) ).
cnf(s53,plain,
spl0_3,
inference(rat,[],[s36,s12]) ).
cnf(s54,plain,
spl0_1,
inference(rat,[],[s13,s53]) ).
cnf(s59,plain,
spl0_4,
inference(rat,[],[s2,s53]) ).
cnf(s60,plain,
spl0_2,
inference(rat,[],[s41,s59]) ).
cnf(s62,plain,
$false,
inference(rat,[],[s1,s60,s54]) ).
fof(f1399,plain,
$false,
inference(avatar_sat_refutation,[],[s62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC076-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n004.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 07:44:22 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.07/1.44 % (188365)Input is clausal, will run a generic CNF schedule.
% 3.07/1.44 % (188476)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3341801327:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.07/1.44 % (188476)First to succeed.
% 3.07/1.44 % (188476)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-188365"
% 3.07/1.44 % (188472)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=799628793:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.07/1.44 % (188474)lrs+10_1_sil=8000:sp=occurrence:random_seed=541480305:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.07/1.44 % (188471)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=3366602127:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.07/1.44 % (188475)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2096433855:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.07/1.44 % (188473)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=393758595:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.07/1.44 % (188475)Also succeeded, but the first one will report.
% 3.07/1.44 % (188474)Also succeeded, but the first one will report.
% 3.07/1.44 % (188477)dis-21_1_sil=8000:lcm=predicate:random_seed=4035722133: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)
% 3.07/1.44 % (188477)Instruction limit reached!
% 3.07/1.44 % (188477)------------------------------
% 3.07/1.44 % (188477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.44 % (188477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.44 % (188477)CaDiCaL version: 2.1.3
% 3.07/1.44 % (188477)Termination reason: Instruction limit
% 3.07/1.44 % (188477)Termination phase: Saturation
% 3.07/1.44 % (188477)Time elapsed: 0.067 s
% 3.07/1.44 % (188477)Peak memory usage: 90 MB
% 3.07/1.44 % (188477)Instructions burned: 119 (million)
% 3.07/1.44 % (188476)Refutation found. Thanks to Tanya!
% 3.07/1.44 % SZS status Unsatisfiable for theBenchmark
% 3.07/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.07/1.44 % (188476)------------------------------
% 3.07/1.44 % (188476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.07/1.44 % (188476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.07/1.44 % (188476)CaDiCaL version: 2.1.3
% 3.07/1.44 % (188476)Termination reason: Refutation
% 3.07/1.44 % (188476)Time elapsed: 0.017 s
% 3.07/1.44 % (188476)Peak memory usage: 90 MB
% 3.07/1.44 % (188476)Instructions burned: 42 (million)
% 3.07/1.44 % (188476)------------------------------
% 3.07/1.44 % (188476)------------------------------
% 3.07/1.44 % (188365)Success in time 0.35 s
% 3.07/1.44 % Vampire exiting
%------------------------------------------------------------------------------