%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC407-1 : 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 01:03:51 PM UTC 2026
% Result : Unsatisfiable 3.19s 0.98s
% Output : Refutation 3.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 66 ( 14 unt; 5 def)
% Number of atoms : 161 ( 32 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 179 ( 84 ~; 90 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 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 : 15 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f71,axiom,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
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(f173,axiom,
! [X2,X0,X1] :
( ~ memberP(cons(X0,X1),X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X2)
| memberP(X1,X2)
| X2 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause161) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X0,X1),X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X2)
| memberP(X1,X2)
| X0 = X2 ),
inference(reorient_equations,[],[f173]) ).
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,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
memberP(sk1,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
~ memberP(sk2,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
( ssItem(sk6)
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
( ssItem(sk6)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,negated_conjecture,
( cons(sk6,nil) = sk3
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f212,plain,
( sk3 = cons(sk6,nil)
| nil = sk4 ),
inference(reorient_equations,[],[f211]) ).
fof(f214,negated_conjecture,
( cons(sk6,nil) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f215,plain,
( sk3 = cons(sk6,nil)
| nil = sk3 ),
inference(reorient_equations,[],[f214]) ).
fof(f216,negated_conjecture,
( memberP(sk4,sk6)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f219,plain,
memberP(sk3,sk5),
inference(definition_unfolding,[],[f207,f205]) ).
fof(f220,plain,
~ memberP(sk4,sk5),
inference(definition_unfolding,[],[f208,f204]) ).
fof(f228,definition,
( spl0_1
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f230,plain,
( nil = sk3
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f232,definition,
( spl0_2
<=> memberP(sk4,sk6) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f234,plain,
( memberP(sk4,sk6)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f235,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f216,f232,f228]) ).
fof(f237,definition,
( spl0_3
<=> sk3 = cons(sk6,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f239,plain,
( sk3 = cons(sk6,nil)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f240,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f215,f237,f228]) ).
fof(f242,definition,
( spl0_4
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f244,plain,
( nil = sk4
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f246,plain,
( spl0_4
| spl0_3 ),
inference(avatar_split_clause,[],[f212,f237,f242]) ).
fof(f248,definition,
( spl0_5
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f250,plain,
( ssItem(sk6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,plain,
( spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f210,f248,f228]) ).
fof(f252,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f209,f248,f242]) ).
fof(f267,plain,
( nil != sk3
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ spl0_3 ),
inference(superposition,[],[f99,f239]) ).
fof(f268,plain,
( nil != sk3
| ~ ssList(nil)
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f267,f250]) ).
fof(f269,plain,
( nil != sk3
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f268,f8]) ).
fof(f270,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f269,f248,f237,f228]) ).
fof(f476,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssItem(X0)
| memberP(nil,X0)
| sk6 = X0 )
| ~ spl0_3 ),
inference(superposition,[],[f174,f239]) ).
fof(f479,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(sk6)
| ~ ssItem(X0)
| memberP(nil,X0)
| sk6 = X0 )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f476,f8]) ).
fof(f480,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0)
| memberP(nil,X0)
| sk6 = X0 )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f479,f250]) ).
fof(f481,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0)
| sk6 = X0 )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f480,f71]) ).
fof(f482,plain,
( ~ ssItem(sk5)
| sk5 = sk6
| ~ spl0_3
| ~ spl0_5 ),
inference(resolution,[],[f481,f219]) ).
fof(f484,plain,
( sk5 = sk6
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f482,f206]) ).
fof(f495,plain,
( memberP(sk4,sk5)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f234,f484]) ).
fof(f504,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f495,f220]) ).
fof(f505,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f504]) ).
fof(f508,plain,
( memberP(nil,sk5)
| ~ spl0_1 ),
inference(superposition,[],[f219,f230]) ).
fof(f512,plain,
( ~ memberP(nil,sk5)
| ~ spl0_4 ),
inference(superposition,[],[f220,f244]) ).
fof(f517,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f512,f508]) ).
fof(f518,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f517]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f235]) ).
cnf(s2,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f240]) ).
cnf(s4,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f246]) ).
cnf(s5,plain,
( spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f251]) ).
cnf(s6,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f252]) ).
cnf(s7,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f270]) ).
cnf(s10,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f505]) ).
cnf(s11,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f518]) ).
cnf(s12,plain,
spl0_1,
inference(rat,[],[s10,s1,s2,s5]) ).
cnf(s13,plain,
~ spl0_4,
inference(rat,[],[s11,s12]) ).
cnf(s14,plain,
spl0_5,
inference(rat,[],[s6,s13]) ).
cnf(s15,plain,
spl0_3,
inference(rat,[],[s4,s13]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s7,s12,s14,s15]) ).
fof(f519,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC407-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 09:31:07 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 3.19/0.98 % (231372)Input is clausal, will run a generic CNF schedule.
% 3.19/0.98 % (231378)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3655885912:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.19/0.98 % (231379)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=197803751:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.19/0.98 % (231377)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=635382005:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.19/0.98 % (231380)lrs+10_1_sil=8000:sp=occurrence:random_seed=4293425183:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.19/0.98 % (231383)dis-21_1_sil=8000:lcm=predicate:random_seed=697248975: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)
% 3.19/0.98 % (231380)First to succeed.
% 3.19/0.98 % (231380)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-231372"
% 3.19/0.98 % (231383)Instruction limit reached!
% 3.19/0.98 % (231383)------------------------------
% 3.19/0.98 % (231383)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/0.98 % (231383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/0.98 % (231383)CaDiCaL version: 2.1.3
% 3.19/0.98 % (231383)Termination reason: Instruction limit
% 3.19/0.98 % (231383)Termination phase: Saturation
% 3.19/0.98 % (231383)Time elapsed: 0.027 s
% 3.19/0.98 % (231383)Peak memory usage: 89 MB
% 3.19/0.98 % (231383)Instructions burned: 120 (million)
% 3.19/0.98 % (231382)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=957754:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.19/0.98 % (231381)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1500816384:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.19/0.98 % (231381)Also succeeded, but the first one will report.
% 3.19/0.98 % (231382)Also succeeded, but the first one will report.
% 3.19/0.98 % (231421)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3187015435:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.19/0.98 % (231421)Also succeeded, but the first one will report.
% 3.19/0.98 % (231380)Refutation found. Thanks to Tanya!
% 3.19/0.98 % SZS status Unsatisfiable for theBenchmark
% 3.19/0.98 % SZS output start Proof for theBenchmark
% See solution above
% 3.19/0.98 % (231380)------------------------------
% 3.19/0.98 % (231380)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/0.98 % (231380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/0.98 % (231380)CaDiCaL version: 2.1.3
% 3.19/0.98 % (231380)Termination reason: Refutation
% 3.19/0.98 % (231380)Time elapsed: 0.010 s
% 3.19/0.98 % (231380)Peak memory usage: 89 MB
% 3.19/0.98 % (231380)Instructions burned: 12 (million)
% 3.19/0.98 % (231380)------------------------------
% 3.19/0.98 % (231380)------------------------------
% 3.19/0.98 % (231372)Success in time 0.429 s
% 3.19/0.98 % Vampire exiting
%------------------------------------------------------------------------------