%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC090-1 : 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 : n009.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 01:02:24 PM UTC 2026
% Result : Unsatisfiable 2.69s 1.34s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 78 ( 22 unt; 4 def)
% Number of atoms : 190 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 224 ( 112 ~; 108 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 28 !; 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(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
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(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,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X0] :
( ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| ~ segmentP(sk1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
app(sk5,sk6) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,plain,
sk4 = app(sk5,sk6),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
app(sk6,sk5) = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f213,plain,
sk3 = app(sk6,sk5),
inference(reorient_equations,[],[f212]) ).
fof(f228,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_2
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f250,plain,
( ssList(nil)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f285,plain,
spl0_2,
inference(avatar_split_clause,[],[f8,f249]) ).
fof(f288,plain,
sk2 = app(sk5,sk6),
inference(forward_demodulation,[],[f211,f204]) ).
fof(f289,plain,
sk1 = app(sk6,sk5),
inference(forward_demodulation,[],[f213,f205]) ).
fof(f305,plain,
( ~ ssList(sk2)
| ~ neq(sk2,nil)
| ~ ssList(sk2)
| ~ segmentP(sk1,sk2) ),
inference(resolution,[],[f57,f207]) ).
fof(f306,plain,
( ~ ssList(sk2)
| ~ neq(sk2,nil)
| ~ segmentP(sk1,sk2) ),
inference(duplicate_literal_removal,[],[f305]) ).
fof(f307,plain,
( ~ neq(sk2,nil)
| ~ segmentP(sk1,sk2) ),
inference(forward_subsumption_resolution,[],[f306,f201]) ).
fof(f308,plain,
~ segmentP(sk1,sk2),
inference(forward_subsumption_resolution,[],[f307,f206]) ).
fof(f351,definition,
( spl0_12
<=> nil = sk6 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f352,plain,
( nil != sk6
| spl0_12 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f353,plain,
( nil = sk6
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f530,plain,
( sk2 = app(sk5,nil)
| ~ spl0_12 ),
inference(superposition,[],[f288,f353]) ).
fof(f531,plain,
( sk1 = app(nil,sk5)
| ~ spl0_12 ),
inference(superposition,[],[f289,f353]) ).
fof(f686,plain,
( sk2 = sk5
| ~ ssList(sk5)
| ~ spl0_12 ),
inference(superposition,[],[f73,f530]) ).
fof(f702,plain,
( sk2 = sk5
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f686,f208]) ).
fof(f827,plain,
( sk1 = app(nil,sk2)
| ~ spl0_12 ),
inference(forward_demodulation,[],[f531,f702]) ).
fof(f863,plain,
( sk1 = sk2
| ~ ssList(sk2)
| ~ spl0_12 ),
inference(superposition,[],[f74,f827]) ).
fof(f878,plain,
( sk1 = sk2
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f863,f201]) ).
fof(f900,plain,
( ~ segmentP(sk2,sk2)
| ~ spl0_12 ),
inference(superposition,[],[f308,f878]) ).
fof(f912,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| segmentP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(superposition,[],[f228,f74]) ).
fof(f916,plain,
! [X0] :
( ~ ssList(app(sk2,X0))
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(X0)
| segmentP(app(sk2,X0),sk6) ),
inference(superposition,[],[f228,f288]) ).
fof(f925,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| segmentP(app(X0,X1),X0) ),
inference(duplicate_literal_removal,[],[f912]) ).
fof(f931,plain,
! [X0] :
( ~ ssList(app(sk2,X0))
| ~ ssList(sk6)
| ~ ssList(X0)
| segmentP(app(sk2,X0),sk6) ),
inference(forward_subsumption_resolution,[],[f916,f208]) ).
fof(f934,plain,
( ! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| segmentP(app(X0,X1),X0) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f925,f250]) ).
fof(f938,plain,
! [X0] :
( ~ ssList(app(sk2,X0))
| ~ ssList(X0)
| segmentP(app(sk2,X0),sk6) ),
inference(forward_subsumption_resolution,[],[f931,f209]) ).
fof(f940,plain,
( ! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f934,f85]) ).
fof(f971,plain,
( ~ ssList(sk2)
| ~ spl0_12 ),
inference(resolution,[],[f900,f57]) ).
fof(f975,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f971,f201]) ).
fof(f976,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[],[f975]) ).
fof(f1443,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| segmentP(sk2,sk6)
| ~ ssList(sk2) ),
inference(superposition,[],[f938,f73]) ).
fof(f1444,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| segmentP(sk2,sk6) ),
inference(duplicate_literal_removal,[],[f1443]) ).
fof(f1446,plain,
( ~ ssList(nil)
| segmentP(sk2,sk6) ),
inference(forward_subsumption_resolution,[],[f1444,f201]) ).
fof(f1448,plain,
( segmentP(sk2,sk6)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1446,f250]) ).
fof(f1449,plain,
( ~ neq(sk6,nil)
| ~ ssList(sk6)
| ~ segmentP(sk1,sk6)
| ~ spl0_2 ),
inference(resolution,[],[f1448,f207]) ).
fof(f1456,plain,
( ~ neq(sk6,nil)
| ~ segmentP(sk1,sk6)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1449,f209]) ).
fof(f1461,definition,
( spl0_49
<=> segmentP(sk1,sk6) ),
introduced(definition,[new_symbols(definition,[spl0_49])],[avatar_definition]) ).
fof(f1465,definition,
( spl0_50
<=> neq(sk6,nil) ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f1467,plain,
( ~ neq(sk6,nil)
| spl0_50 ),
inference(avatar_component_clause,[],[f1465]) ).
fof(f1468,plain,
( ~ spl0_49
| ~ spl0_50
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f1456,f249,f1465,f1461]) ).
fof(f2076,plain,
( segmentP(sk1,sk6)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ spl0_2 ),
inference(superposition,[],[f940,f289]) ).
fof(f2117,plain,
( segmentP(sk1,sk6)
| ~ ssList(sk6)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f2076,f208]) ).
fof(f2118,plain,
( segmentP(sk1,sk6)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f2117,f209]) ).
fof(f2119,plain,
( spl0_49
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f2118,f249,f1461]) ).
fof(f2441,plain,
( ~ ssList(sk6)
| ~ ssList(nil)
| nil = sk6
| spl0_50 ),
inference(resolution,[],[f1467,f102]) ).
fof(f2442,plain,
( ~ ssList(nil)
| nil = sk6
| spl0_50 ),
inference(forward_subsumption_resolution,[],[f2441,f209]) ).
fof(f2443,plain,
( nil = sk6
| ~ spl0_2
| spl0_50 ),
inference(forward_subsumption_resolution,[],[f2442,f250]) ).
fof(f2444,plain,
( $false
| ~ spl0_2
| spl0_12
| spl0_50 ),
inference(forward_subsumption_resolution,[],[f2443,f352]) ).
fof(f2445,plain,
( ~ spl0_2
| spl0_12
| spl0_50 ),
inference(avatar_contradiction_clause,[],[f2444]) ).
cnf(s10,plain,
spl0_2,
inference(sat_conversion,[],[f285]) ).
cnf(s22,plain,
~ spl0_12,
inference(sat_conversion,[],[f976]) ).
cnf(s56,plain,
( ~ spl0_2
| ~ spl0_49
| ~ spl0_50 ),
inference(sat_conversion,[],[f1468]) ).
cnf(s63,plain,
( ~ spl0_2
| spl0_49 ),
inference(sat_conversion,[],[f2119]) ).
cnf(s78,plain,
( ~ spl0_2
| spl0_12
| spl0_50 ),
inference(sat_conversion,[],[f2445]) ).
cnf(s98,plain,
spl0_50,
inference(rat,[],[s78,s22,s10]) ).
cnf(s99,plain,
spl0_49,
inference(rat,[],[s63,s10]) ).
cnf(s100,plain,
$false,
inference(rat,[],[s56,s98,s99,s10]) ).
fof(f2446,plain,
$false,
inference(avatar_sat_refutation,[],[s100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC090-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 07:49:00 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.69/1.34 % (2870115)Input is clausal, will run a generic CNF schedule.
% 2.69/1.34 % (2870125)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3348021575:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.69/1.34 % (2870125)First to succeed.
% 2.69/1.34 % (2870125)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2870115"
% 2.69/1.34 % (2870124)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1651118050:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.69/1.34 % (2870120)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=1384753356:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.69/1.34 % (2870123)lrs+10_1_sil=8000:sp=occurrence:random_seed=601671513:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.69/1.34 % (2870121)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3435492901:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.69/1.34 % (2870122)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3168498120:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.69/1.34 % (2870123)Also succeeded, but the first one will report.
% 2.69/1.34 % (2870126)dis-21_1_sil=8000:lcm=predicate:random_seed=2742640639: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)
% 2.69/1.34 % (2870124)Also succeeded, but the first one will report.
% 2.69/1.34 % (2870126)Instruction limit reached!
% 2.69/1.34 % (2870126)------------------------------
% 2.69/1.34 % (2870126)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.34 % (2870126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.34 % (2870126)CaDiCaL version: 2.1.3
% 2.69/1.34 % (2870126)Termination reason: Instruction limit
% 2.69/1.34 % (2870126)Termination phase: Saturation
% 2.69/1.34 % (2870126)Time elapsed: 0.061 s
% 2.69/1.34 % (2870126)Peak memory usage: 89 MB
% 2.69/1.34 % (2870126)Instructions burned: 118 (million)
% 2.69/1.34 % (2870125)Refutation found. Thanks to Tanya!
% 2.69/1.34 % SZS status Unsatisfiable for theBenchmark
% 2.69/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.34 % (2870125)------------------------------
% 2.69/1.34 % (2870125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.34 % (2870125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.34 % (2870125)CaDiCaL version: 2.1.3
% 2.69/1.34 % (2870125)Termination reason: Refutation
% 2.69/1.34 % (2870125)Time elapsed: 0.027 s
% 2.69/1.34 % (2870125)Peak memory usage: 90 MB
% 2.69/1.34 % (2870125)Instructions burned: 70 (million)
% 2.69/1.34 % (2870125)------------------------------
% 2.69/1.34 % (2870125)------------------------------
% 2.69/1.34 % (2870115)Success in time 0.3 s
% 2.69/1.34 % Vampire exiting
%------------------------------------------------------------------------------