%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC012-1 : 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 : n019.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 01:02:02 PM UTC 2026
% Result : Unsatisfiable 2.63s 1.36s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 57 ( 16 unt; 6 def)
% Number of atoms : 153 ( 29 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 201 ( 105 ~; 90 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
fof(f200,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
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)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f213,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk2
| app(X1,X2) != sk1
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f214,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| sk2 != app(app(X1,cons(X0,nil)),X2)
| app(X1,X2) != sk1
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f213]) ).
fof(f215,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f216,negated_conjecture,
( app(sk3,cons(sk5,nil)) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f217,plain,
( sk4 = app(sk3,cons(sk5,nil))
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f216]) ).
fof(f242,plain,
neq(sk2,nil),
inference(duplicate_literal_removal,[],[f206]) ).
fof(f250,definition,
( spl0_1
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f252,plain,
( ~ neq(sk4,nil)
| spl0_1 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f254,definition,
( spl0_2
<=> sk4 = app(sk3,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f256,plain,
( sk4 = app(sk3,cons(sk5,nil))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f257,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f217,f254,f250]) ).
fof(f259,definition,
( spl0_3
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f261,plain,
( ssItem(sk5)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f262,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f215,f259,f250]) ).
fof(f264,definition,
( spl0_4
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| app(X1,X2) != sk1
| sk2 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f265,plain,
( ! [X2,X0,X1] :
( app(X1,X2) != sk1
| ~ ssItem(X0)
| sk2 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f266,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f214,f264,f250]) ).
fof(f268,definition,
( spl0_5
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f275,plain,
spl0_5,
inference(avatar_split_clause,[],[f242,f268]) ).
fof(f281,definition,
( spl0_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f282,plain,
( ssList(nil)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f317,plain,
spl0_7,
inference(avatar_split_clause,[],[f8,f281]) ).
fof(f320,plain,
( ~ neq(sk2,nil)
| spl0_1 ),
inference(forward_demodulation,[],[f252,f204]) ).
fof(f321,plain,
( ~ spl0_5
| spl0_1 ),
inference(avatar_split_clause,[],[f320,f250,f268]) ).
fof(f323,plain,
( sk4 = app(sk1,cons(sk5,nil))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f256,f205]) ).
fof(f325,plain,
( sk2 = app(sk1,cons(sk5,nil))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f323,f204]) ).
fof(f361,plain,
( ! [X0,X1] :
( sk1 != X0
| ~ ssItem(X1)
| sk2 != app(app(X0,cons(X1,nil)),nil)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) )
| ~ spl0_4 ),
inference(superposition,[],[f265,f73]) ).
fof(f362,plain,
( ! [X0,X1] :
( sk1 != X0
| ~ ssItem(X1)
| sk2 != app(app(X0,cons(X1,nil)),nil)
| ~ ssList(nil)
| ~ ssList(X0) )
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f361]) ).
fof(f363,plain,
( ! [X0,X1] :
( ~ ssItem(X1)
| sk1 != X0
| sk2 != app(app(X0,cons(X1,nil)),nil)
| ~ ssList(X0) )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f362,f282]) ).
fof(f377,plain,
( ! [X0] :
( sk1 != X0
| sk2 != app(app(X0,cons(sk5,nil)),nil)
| ~ ssList(X0) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(resolution,[],[f363,f261]) ).
fof(f378,plain,
( sk2 != app(app(sk1,cons(sk5,nil)),nil)
| ~ ssList(sk1)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(equality_resolution,[],[f377]) ).
fof(f379,plain,
( sk2 != app(app(sk1,cons(sk5,nil)),nil)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f378,f200]) ).
fof(f380,plain,
( sk2 != app(sk2,nil)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f379,f325]) ).
fof(f381,plain,
( sk2 != sk2
| ~ ssList(sk2)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f380,f73]) ).
fof(f382,plain,
( ~ ssList(sk2)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f381]) ).
fof(f383,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f382,f201]) ).
fof(f384,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f383]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f257]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f262]) ).
cnf(s3,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f266]) ).
cnf(s8,plain,
spl0_5,
inference(sat_conversion,[],[f275]) ).
cnf(s18,plain,
spl0_7,
inference(sat_conversion,[],[f317]) ).
cnf(s19,plain,
( spl0_1
| ~ spl0_5 ),
inference(sat_conversion,[],[f321]) ).
cnf(s24,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(sat_conversion,[],[f384]) ).
cnf(s29,plain,
spl0_1,
inference(rat,[],[s19,s8]) ).
cnf(s30,plain,
spl0_4,
inference(rat,[],[s3,s29]) ).
cnf(s31,plain,
spl0_3,
inference(rat,[],[s2,s29]) ).
cnf(s32,plain,
~ spl0_2,
inference(rat,[],[s24,s18,s30,s31]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s1,s32,s29]) ).
fof(f385,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC012-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n019.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 07:25:49 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 2.63/1.36 % (3827066)Input is clausal, will run a generic CNF schedule.
% 2.63/1.36 % (3827076)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=714925168:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.63/1.36 % (3827076)First to succeed.
% 2.63/1.36 % (3827076)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3827066"
% 2.63/1.36 % (3827072)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1178476470:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.63/1.36 % (3827071)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=3309950947:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.63/1.36 % (3827073)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=817339097:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.63/1.36 % (3827074)lrs+10_1_sil=8000:sp=occurrence:random_seed=4052802643:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.63/1.36 % (3827075)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3142506178:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.63/1.36 % (3827074)Also succeeded, but the first one will report.
% 2.63/1.36 % (3827075)Also succeeded, but the first one will report.
% 2.63/1.36 % (3827077)dis-21_1_sil=8000:lcm=predicate:random_seed=1246486218: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)
% 2.63/1.36 % (3827077)Instruction limit reached!
% 2.63/1.36 % (3827077)------------------------------
% 2.63/1.36 % (3827077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.36 % (3827077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.36 % (3827077)CaDiCaL version: 2.1.3
% 2.63/1.36 % (3827077)Termination reason: Instruction limit
% 2.63/1.36 % (3827077)Termination phase: Saturation
% 2.63/1.36 % (3827077)Time elapsed: 0.066 s
% 2.63/1.36 % (3827077)Peak memory usage: 90 MB
% 2.63/1.36 % (3827077)Instructions burned: 118 (million)
% 2.63/1.36 % (3827076)Refutation found. Thanks to Tanya!
% 2.63/1.36 % SZS status Unsatisfiable for theBenchmark
% 2.63/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.36 % (3827076)------------------------------
% 2.63/1.36 % (3827076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.36 % (3827076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.36 % (3827076)CaDiCaL version: 2.1.3
% 2.63/1.36 % (3827076)Termination reason: Refutation
% 2.63/1.36 % (3827076)Time elapsed: 0.004 s
% 2.63/1.36 % (3827076)Peak memory usage: 90 MB
% 2.63/1.36 % (3827076)Instructions burned: 11 (million)
% 2.63/1.36 % (3827076)------------------------------
% 2.63/1.36 % (3827076)------------------------------
% 2.63/1.36 % (3827066)Success in time 0.29 s
% 2.63/1.36 % Vampire exiting
%------------------------------------------------------------------------------