%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC003-1 : 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 : n003.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 01:01:59 PM UTC 2026
% Result : Unsatisfiable 2.36s 1.18s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 24
% Syntax : Number of formulae : 93 ( 19 unt; 11 def)
% Number of atoms : 272 ( 46 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 355 ( 176 ~; 168 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
fof(f98,axiom,
! [X0,X1] :
( cons(X0,X1) != nil
| ~ ssItem(X0)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
fof(f99,plain,
! [X0,X1] :
( nil != cons(X0,X1)
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(reorient_equations,[],[f98]) ).
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(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)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f217,negated_conjecture,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X0,X1),X2) != sk2
| app(X0,X2) != sk1
| ~ neq(X1,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
fof(f218,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
fof(f219,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f220,negated_conjecture,
( ssList(sk7)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
fof(f221,negated_conjecture,
( app(app(sk6,cons(sk5,nil)),sk7) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_20) ).
fof(f222,plain,
( sk4 = app(app(sk6,cons(sk5,nil)),sk7)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f221]) ).
fof(f223,negated_conjecture,
( app(sk6,sk7) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_21) ).
fof(f224,plain,
( sk3 = app(sk6,sk7)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f223]) ).
fof(f250,plain,
neq(sk2,nil),
inference(duplicate_literal_removal,[],[f206]) ).
fof(f258,definition,
( spl0_1
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f260,plain,
( ~ neq(sk4,nil)
| spl0_1 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f266,definition,
( spl0_3
<=> sk3 = app(sk6,sk7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f268,plain,
( sk3 = app(sk6,sk7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f269,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f224,f266,f258]) ).
fof(f271,definition,
( spl0_4
<=> sk4 = app(app(sk6,cons(sk5,nil)),sk7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f273,plain,
( sk4 = app(app(sk6,cons(sk5,nil)),sk7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f274,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f222,f271,f258]) ).
fof(f276,definition,
( spl0_5
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f278,plain,
( ssList(sk7)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f279,plain,
( ~ spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f220,f276,f258]) ).
fof(f281,definition,
( spl0_6
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f283,plain,
( ssList(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f284,plain,
( ~ spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f219,f281,f258]) ).
fof(f286,definition,
( spl0_7
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f288,plain,
( ssItem(sk5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f289,plain,
( ~ spl0_1
| spl0_7 ),
inference(avatar_split_clause,[],[f218,f286,f258]) ).
fof(f291,definition,
( spl0_8
<=> ! [X2,X0,X1] :
( ~ ssList(X0)
| ~ neq(X1,nil)
| app(X0,X2) != sk1
| app(app(X0,X1),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f292,plain,
( ! [X2,X0,X1] :
( ~ neq(X1,nil)
| ~ ssList(X0)
| app(X0,X2) != sk1
| app(app(X0,X1),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f293,plain,
( ~ spl0_1
| spl0_8 ),
inference(avatar_split_clause,[],[f217,f291,f258]) ).
fof(f295,definition,
( spl0_9
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f306,plain,
spl0_9,
inference(avatar_split_clause,[],[f250,f295]) ).
fof(f312,definition,
( spl0_11
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f313,plain,
( ssList(nil)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f348,plain,
spl0_11,
inference(avatar_split_clause,[],[f8,f312]) ).
fof(f351,plain,
( ~ neq(sk2,nil)
| spl0_1 ),
inference(forward_demodulation,[],[f260,f204]) ).
fof(f352,plain,
( ~ spl0_9
| spl0_1 ),
inference(avatar_split_clause,[],[f351,f258,f295]) ).
fof(f355,plain,
( sk1 = app(sk6,sk7)
| ~ spl0_3 ),
inference(forward_demodulation,[],[f268,f205]) ).
fof(f356,plain,
( sk2 = app(app(sk6,cons(sk5,nil)),sk7)
| ~ spl0_4 ),
inference(forward_demodulation,[],[f273,f204]) ).
fof(f418,plain,
( ! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X1)
| app(X1,X2) != sk1
| sk2 != app(app(X1,X0),X2)
| ~ ssList(X2)
| ~ ssList(X0) )
| ~ spl0_8 ),
inference(resolution,[],[f102,f292]) ).
fof(f421,plain,
( ! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X1)
| app(X1,X2) != sk1
| sk2 != app(app(X1,X0),X2)
| ~ ssList(X2) )
| ~ spl0_8 ),
inference(duplicate_literal_removal,[],[f418]) ).
fof(f422,plain,
( ! [X2,X0,X1] :
( app(X1,X2) != sk1
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0)
| sk2 != app(app(X1,X0),X2)
| ~ ssList(X2) )
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f421,f313]) ).
fof(f423,plain,
( ! [X0] :
( sk1 != sk1
| nil = X0
| ~ ssList(sk6)
| ~ ssList(X0)
| sk2 != app(app(sk6,X0),sk7)
| ~ ssList(sk7) )
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f422,f355]) ).
fof(f431,plain,
( ! [X0] :
( nil = X0
| ~ ssList(sk6)
| ~ ssList(X0)
| sk2 != app(app(sk6,X0),sk7)
| ~ ssList(sk7) )
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f423]) ).
fof(f435,plain,
( ! [X0] :
( nil = X0
| ~ ssList(X0)
| sk2 != app(app(sk6,X0),sk7)
| ~ ssList(sk7) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f431,f283]) ).
fof(f448,plain,
( ! [X0] :
( sk2 != app(app(sk6,X0),sk7)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f435,f278]) ).
fof(f461,plain,
( sk2 != sk2
| ~ ssList(cons(sk5,nil))
| nil = cons(sk5,nil)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f448,f356]) ).
fof(f462,plain,
( ~ ssList(cons(sk5,nil))
| nil = cons(sk5,nil)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f461]) ).
fof(f464,definition,
( spl0_22
<=> nil = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f466,plain,
( nil = cons(sk5,nil)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f468,definition,
( spl0_23
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f470,plain,
( ~ ssList(cons(sk5,nil))
| spl0_23 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f471,plain,
( spl0_22
| ~ spl0_23
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f462,f312,f291,f281,f276,f271,f266,f468,f464]) ).
fof(f505,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| spl0_23 ),
inference(resolution,[],[f86,f470]) ).
fof(f506,plain,
( ~ ssItem(sk5)
| ~ spl0_11
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f505,f313]) ).
fof(f507,plain,
( $false
| ~ spl0_7
| ~ spl0_11
| spl0_23 ),
inference(forward_subsumption_resolution,[],[f506,f288]) ).
fof(f508,plain,
( ~ spl0_7
| ~ spl0_11
| spl0_23 ),
inference(avatar_contradiction_clause,[],[f507]) ).
fof(f519,plain,
( nil != nil
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ spl0_22 ),
inference(superposition,[],[f99,f466]) ).
fof(f521,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f519]) ).
fof(f522,plain,
( ~ ssList(nil)
| ~ spl0_7
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f521,f288]) ).
fof(f523,plain,
( $false
| ~ spl0_7
| ~ spl0_11
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f522,f313]) ).
fof(f524,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f523]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f269]) ).
cnf(s3,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f274]) ).
cnf(s4,plain,
( ~ spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f279]) ).
cnf(s5,plain,
( ~ spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f284]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_7 ),
inference(sat_conversion,[],[f289]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_8 ),
inference(sat_conversion,[],[f293]) ).
cnf(s16,plain,
spl0_9,
inference(sat_conversion,[],[f306]) ).
cnf(s26,plain,
spl0_11,
inference(sat_conversion,[],[f348]) ).
cnf(s27,plain,
( spl0_1
| ~ spl0_9 ),
inference(sat_conversion,[],[f352]) ).
cnf(s31,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11
| spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f471]) ).
cnf(s34,plain,
( ~ spl0_7
| ~ spl0_11
| spl0_23 ),
inference(sat_conversion,[],[f508]) ).
cnf(s35,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_22 ),
inference(sat_conversion,[],[f524]) ).
cnf(s40,plain,
spl0_1,
inference(rat,[],[s27,s16]) ).
cnf(s41,plain,
spl0_8,
inference(rat,[],[s7,s40]) ).
cnf(s42,plain,
spl0_7,
inference(rat,[],[s6,s40]) ).
cnf(s43,plain,
~ spl0_22,
inference(rat,[],[s35,s26,s42]) ).
cnf(s44,plain,
spl0_23,
inference(rat,[],[s34,s26,s42]) ).
cnf(s45,plain,
spl0_6,
inference(rat,[],[s5,s40]) ).
cnf(s46,plain,
spl0_5,
inference(rat,[],[s4,s40]) ).
cnf(s47,plain,
spl0_4,
inference(rat,[],[s3,s40]) ).
cnf(s48,plain,
~ spl0_3,
inference(rat,[],[s31,s44,s43,s26,s41,s45,s46,s47]) ).
cnf(s49,plain,
$false,
inference(rat,[],[s2,s48,s40]) ).
fof(f525,plain,
$false,
inference(avatar_sat_refutation,[],[s49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC003-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n003.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 07:26:12 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 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
% 2.36/1.18 % (1406172)Input is clausal, will run a generic CNF schedule.
% 2.36/1.18 % (1406182)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3900773444:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.36/1.18 % (1406182)First to succeed.
% 2.36/1.18 % (1406182)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1406172"
% 2.36/1.18 % (1406177)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=3019465620:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.36/1.18 % (1406180)lrs+10_1_sil=8000:sp=occurrence:random_seed=2073689376:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.36/1.18 % (1406178)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1476939671:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.36/1.18 % (1406179)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=629631817:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.36/1.18 % (1406181)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=47607804:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.36/1.18 % (1406180)Also succeeded, but the first one will report.
% 2.36/1.18 % (1406181)Also succeeded, but the first one will report.
% 2.36/1.18 % (1406183)dis-21_1_sil=8000:lcm=predicate:random_seed=3146489134: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)
% 2.36/1.18 % (1406183)Also succeeded, but the first one will report.
% 2.36/1.18 % (1406182)Refutation found. Thanks to Tanya!
% 2.36/1.18 % SZS status Unsatisfiable for theBenchmark
% 2.36/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.27 % (1406182)------------------------------
% 2.72/1.27 % (1406182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.27 % (1406182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.27 % (1406182)CaDiCaL version: 2.1.3
% 2.72/1.27 % (1406182)Termination reason: Refutation
% 2.72/1.27 % (1406182)Time elapsed: 0.007 s
% 2.72/1.27 % (1406182)Peak memory usage: 90 MB
% 2.72/1.27 % (1406182)Instructions burned: 17 (million)
% 2.72/1.27 % (1406182)------------------------------
% 2.72/1.27 % (1406182)------------------------------
% 2.72/1.27 % (1406172)Success in time 0.321 s
% 2.72/1.27 % Vampire exiting
%------------------------------------------------------------------------------