%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC380-1 : 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 : 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 01:03:43 PM UTC 2026
% Result : Unsatisfiable 2.77s 1.16s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 62 ( 12 unt; 6 def)
% Number of atoms : 165 ( 21 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 209 ( 106 ~; 97 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f125,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause120) ).
fof(f126,plain,
! [X0,X1] :
( cons(X0,X1) = app(cons(X0,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f125]) ).
fof(f149,axiom,
! [X2,X0,X1] :
( X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| memberP(cons(X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause138) ).
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,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f215,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk1
| ~ memberP(sk2,X0)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f216,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f217,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f218,negated_conjecture,
( cons(sk5,nil) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f219,plain,
( sk3 = cons(sk5,nil)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f218]) ).
fof(f220,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f221,plain,
( sk4 = app(cons(sk5,nil),sk6)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f220]) ).
fof(f224,plain,
( neq(sk4,nil)
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f206,f204,f204]) ).
fof(f231,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk3
| ~ memberP(sk4,X0)
| ~ neq(sk4,nil) ),
inference(definition_unfolding,[],[f215,f205,f204]) ).
fof(f237,plain,
! [X2,X1] :
( ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(equality_resolution,[],[f149]) ).
fof(f238,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(duplicate_literal_removal,[],[f237]) ).
fof(f242,plain,
neq(sk4,nil),
inference(duplicate_literal_removal,[],[f224]) ).
fof(f251,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f254,definition,
( spl0_4
<=> sk4 = app(cons(sk5,nil),sk6) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f255,plain,
( sk4 = app(cons(sk5,nil),sk6)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f256,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f221,f254,f251]) ).
fof(f258,definition,
( spl0_5
<=> sk3 = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f259,plain,
( sk3 = cons(sk5,nil)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f260,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f219,f258,f251]) ).
fof(f262,definition,
( spl0_6
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f263,plain,
( ssList(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f264,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f217,f262,f251]) ).
fof(f266,definition,
( spl0_7
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f267,plain,
( ssItem(sk5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f268,plain,
( ~ spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f216,f266,f251]) ).
fof(f270,definition,
( spl0_8
<=> ! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk4,X0)
| cons(X0,nil) != sk3 ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f271,plain,
( ! [X0] :
( cons(X0,nil) != sk3
| ~ memberP(sk4,X0)
| ~ ssItem(X0) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f272,plain,
( ~ spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f231,f270,f251]) ).
fof(f279,plain,
spl0_3,
inference(avatar_split_clause,[],[f242,f251]) ).
fof(f280,plain,
( sk4 = app(sk3,sk6)
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f255,f259]) ).
fof(f281,plain,
( sk3 != sk3
| ~ memberP(sk4,sk5)
| ~ ssItem(sk5)
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f271,f259]) ).
fof(f282,plain,
( ~ memberP(sk4,sk5)
| ~ ssItem(sk5)
| ~ spl0_5
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f281]) ).
fof(f283,plain,
( ~ memberP(sk4,sk5)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f282,f267]) ).
fof(f344,plain,
( ! [X0] :
( cons(sk5,X0) = app(sk3,X0)
| ~ ssList(X0)
| ~ ssItem(sk5) )
| ~ spl0_5 ),
inference(superposition,[],[f126,f259]) ).
fof(f359,plain,
( ! [X0] :
( cons(sk5,X0) = app(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f344,f267]) ).
fof(f375,plain,
( ! [X0] :
( memberP(app(sk3,X0),sk5)
| ~ ssItem(sk5)
| ~ ssList(X0)
| ~ ssList(X0) )
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f238,f359]) ).
fof(f382,plain,
( ! [X0] :
( memberP(app(sk3,X0),sk5)
| ~ ssItem(sk5)
| ~ ssList(X0) )
| ~ spl0_5
| ~ spl0_7 ),
inference(duplicate_literal_removal,[],[f375]) ).
fof(f389,plain,
( ! [X0] :
( memberP(app(sk3,X0),sk5)
| ~ ssList(X0) )
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f382,f267]) ).
fof(f663,plain,
( memberP(sk4,sk5)
| ~ ssList(sk6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f389,f280]) ).
fof(f664,plain,
( ~ ssList(sk6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f663,f283]) ).
fof(f665,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f664,f263]) ).
fof(f666,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f665]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f256]) ).
cnf(s3,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f260]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f264]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f268]) ).
cnf(s6,plain,
( ~ spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f272]) ).
cnf(s12,plain,
spl0_3,
inference(sat_conversion,[],[f279]) ).
cnf(s29,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f666]) ).
cnf(s30,plain,
spl0_8,
inference(rat,[],[s6,s12]) ).
cnf(s31,plain,
spl0_7,
inference(rat,[],[s5,s12]) ).
cnf(s33,plain,
spl0_6,
inference(rat,[],[s4,s12]) ).
cnf(s34,plain,
spl0_5,
inference(rat,[],[s3,s12]) ).
cnf(s35,plain,
~ spl0_4,
inference(rat,[],[s29,s30,s31,s33,s34]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s2,s35,s12]) ).
fof(f667,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC380-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 09:22:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.77/1.16 % (226626)Input is clausal, will run a generic CNF schedule.
% 2.77/1.16 % (226635)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1795249638:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.77/1.16 % (226635)First to succeed.
% 2.77/1.16 % (226635)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-226626"
% 2.77/1.16 % (226632)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2425702208:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.77/1.16 % (226637)dis-21_1_sil=8000:lcm=predicate:random_seed=3916457922: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)
% 2.77/1.16 % (226631)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=2573184253:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.77/1.16 % (226633)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3906673367:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.77/1.16 % (226634)lrs+10_1_sil=8000:sp=occurrence:random_seed=1747134149:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.77/1.16 % (226636)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=653354322:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.77/1.16 % (226634)Also succeeded, but the first one will report.
% 2.77/1.16 % (226636)Also succeeded, but the first one will report.
% 2.77/1.16 % (226637)Instruction limit reached!
% 2.77/1.16 % (226637)------------------------------
% 2.77/1.16 % (226637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.16 % (226637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.16 % (226637)CaDiCaL version: 2.1.3
% 2.77/1.16 % (226637)Termination reason: Instruction limit
% 2.77/1.16 % (226637)Termination phase: Saturation
% 2.77/1.16 % (226637)Time elapsed: 0.065 s
% 2.77/1.16 % (226637)Peak memory usage: 90 MB
% 2.77/1.16 % (226637)Instructions burned: 118 (million)
% 2.77/1.16 % (226635)Refutation found. Thanks to Tanya!
% 2.77/1.16 % SZS status Unsatisfiable for theBenchmark
% 2.77/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.17 % (226635)------------------------------
% 2.77/1.17 % (226635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.17 % (226635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.17 % (226635)CaDiCaL version: 2.1.3
% 2.77/1.17 % (226635)Termination reason: Refutation
% 2.77/1.17 % (226635)Time elapsed: 0.007 s
% 2.77/1.17 % (226635)Peak memory usage: 90 MB
% 2.77/1.17 % (226635)Instructions burned: 17 (million)
% 2.77/1.17 % (226635)------------------------------
% 2.77/1.17 % (226635)------------------------------
% 2.77/1.17 % (226626)Success in time 0.302 s
% 2.77/1.17 % Vampire exiting
%------------------------------------------------------------------------------