%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC013-1 : 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 : n014.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 2.62s 1.31s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 69 ( 17 unt; 7 def)
% Number of atoms : 179 ( 29 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 211 ( 101 ~; 103 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f76,axiom,
! [X0] :
( ssItem(hd(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
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(f118,axiom,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
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(f210,negated_conjecture,
! [X0,X1] :
( ~ ssList(X0)
| sk3 = X0
| ~ ssItem(X1)
| cons(X1,nil) != X0
| hd(sk4) != X1
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,negated_conjecture,
! [X0,X1] :
( ~ ssList(X0)
| sk1 != X0
| ~ ssItem(X1)
| cons(X1,nil) != X0
| hd(sk2) != X1
| ~ neq(nil,sk2)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f214,plain,
( neq(sk4,nil)
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f206,f204,f204]) ).
fof(f218,plain,
! [X0,X1] :
( ~ ssList(X0)
| sk3 != X0
| ~ ssItem(X1)
| cons(X1,nil) != X0
| hd(sk4) != X1
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(definition_unfolding,[],[f211,f205,f204,f204]) ).
fof(f223,plain,
! [X1] :
( ~ ssList(cons(X1,nil))
| sk3 = cons(X1,nil)
| ~ ssItem(X1)
| hd(sk4) != X1
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(equality_resolution,[],[f210]) ).
fof(f224,plain,
( ~ ssList(cons(hd(sk4),nil))
| sk3 = cons(hd(sk4),nil)
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(equality_resolution,[],[f223]) ).
fof(f225,plain,
! [X1] :
( ~ ssList(sk3)
| ~ ssItem(X1)
| sk3 != cons(X1,nil)
| hd(sk4) != X1
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(equality_resolution,[],[f218]) ).
fof(f226,plain,
( ~ ssList(sk3)
| ~ ssItem(hd(sk4))
| sk3 != cons(hd(sk4),nil)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(equality_resolution,[],[f225]) ).
fof(f230,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f231,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f230]) ).
fof(f234,plain,
neq(sk4,nil),
inference(duplicate_literal_removal,[],[f214]) ).
fof(f243,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f246,definition,
( spl0_4
<=> neq(nil,sk4) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f247,plain,
( ~ neq(nil,sk4)
| spl0_4 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f249,definition,
( spl0_5
<=> sk3 = cons(hd(sk4),nil) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f252,definition,
( spl0_6
<=> ssItem(hd(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f253,plain,
( ~ ssItem(hd(sk4))
| spl0_6 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f255,definition,
( spl0_7
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f256,plain,
( ~ ssList(sk3)
| spl0_7 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f226,f255,f252,f249,f246,f243]) ).
fof(f260,definition,
( spl0_8
<=> ssList(cons(hd(sk4),nil)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f261,plain,
( ~ ssList(cons(hd(sk4),nil))
| spl0_8 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f262,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f224,f260,f249,f252,f246,f243]) ).
fof(f263,plain,
( neq(sk4,nil)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f266,plain,
spl0_3,
inference(avatar_split_clause,[],[f234,f243]) ).
fof(f276,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| nil = sk4
| spl0_4 ),
inference(resolution,[],[f102,f247]) ).
fof(f281,plain,
( ~ ssList(sk4)
| nil = sk4
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f276,f8]) ).
fof(f282,plain,
( nil = sk4
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f281,f203]) ).
fof(f289,definition,
( spl0_9
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f290,plain,
( nil = sk4
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f300,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f282,f246,f289]) ).
fof(f304,plain,
( neq(nil,nil)
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f263,f290]) ).
fof(f326,plain,
( ~ ssList(nil)
| ~ spl0_3
| ~ spl0_9 ),
inference(resolution,[],[f304,f231]) ).
fof(f327,plain,
( $false
| ~ spl0_3
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f326,f8]) ).
fof(f328,plain,
( ~ spl0_3
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f327]) ).
fof(f329,plain,
( ~ ssList(sk4)
| nil = sk4
| spl0_6 ),
inference(resolution,[],[f253,f76]) ).
fof(f330,plain,
( nil = sk4
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f329,f203]) ).
fof(f331,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f330,f252,f289]) ).
fof(f332,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk4))
| spl0_8 ),
inference(resolution,[],[f261,f86]) ).
fof(f333,plain,
( ~ ssItem(hd(sk4))
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f332,f8]) ).
fof(f334,plain,
( ~ spl0_6
| spl0_8 ),
inference(avatar_split_clause,[],[f333,f260,f252]) ).
fof(f335,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f256,f202]) ).
fof(f336,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f335]) ).
cnf(s2,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f257]) ).
cnf(s3,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f262]) ).
cnf(s6,plain,
spl0_3,
inference(sat_conversion,[],[f266]) ).
cnf(s9,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f300]) ).
cnf(s12,plain,
( ~ spl0_3
| ~ spl0_9 ),
inference(sat_conversion,[],[f328]) ).
cnf(s13,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f331]) ).
cnf(s14,plain,
( ~ spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f334]) ).
cnf(s15,plain,
spl0_7,
inference(sat_conversion,[],[f336]) ).
cnf(s16,plain,
~ spl0_9,
inference(rat,[],[s12,s6]) ).
cnf(s17,plain,
spl0_6,
inference(rat,[],[s13,s16]) ).
cnf(s18,plain,
spl0_4,
inference(rat,[],[s9,s16]) ).
cnf(s19,plain,
spl0_8,
inference(rat,[],[s14,s17]) ).
cnf(s20,plain,
spl0_5,
inference(rat,[],[s3,s19,s17,s18,s6]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s2,s15,s17,s20,s18,s6]) ).
fof(f337,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC013-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n014.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 07:25:46 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 2.62/1.31 % (1608274)Input is clausal, will run a generic CNF schedule.
% 2.62/1.31 % (1608283)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3928310376:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.62/1.31 % (1608283)First to succeed.
% 2.62/1.31 % (1608283)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1608274"
% 2.62/1.31 % (1608282)lrs+10_1_sil=8000:sp=occurrence:random_seed=2967178713:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.62/1.31 % (1608279)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=1511276475:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.62/1.31 % (1608280)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1237449711:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.62/1.31 % (1608284)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=749584169:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.62/1.31 % (1608281)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4187618816:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.62/1.31 % (1608285)dis-21_1_sil=8000:lcm=predicate:random_seed=3036997221: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)
% 2.62/1.31 % (1608282)Also succeeded, but the first one will report.
% 2.62/1.31 % (1608284)Also succeeded, but the first one will report.
% 2.62/1.31 % (1608285)Instruction limit reached!
% 2.62/1.31 % (1608285)------------------------------
% 2.62/1.31 % (1608285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.31 % (1608285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.31 % (1608285)CaDiCaL version: 2.1.3
% 2.62/1.31 % (1608285)Termination reason: Instruction limit
% 2.62/1.31 % (1608285)Termination phase: Saturation
% 2.62/1.31 % (1608285)Time elapsed: 0.053 s
% 2.62/1.31 % (1608285)Peak memory usage: 89 MB
% 2.62/1.31 % (1608285)Instructions burned: 117 (million)
% 2.62/1.31 % (1608283)Refutation found. Thanks to Tanya!
% 2.62/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.62/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.32 % (1608283)------------------------------
% 2.62/1.32 % (1608283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (1608283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (1608283)CaDiCaL version: 2.1.3
% 2.62/1.32 % (1608283)Termination reason: Refutation
% 2.62/1.32 % (1608283)Time elapsed: 0.003 s
% 2.62/1.32 % (1608283)Peak memory usage: 90 MB
% 2.62/1.32 % (1608283)Instructions burned: 5 (million)
% 2.62/1.32 % (1608283)------------------------------
% 2.62/1.32 % (1608283)------------------------------
% 2.62/1.32 % (1608274)Success in time 0.286 s
% 2.62/1.32 % Vampire exiting
%------------------------------------------------------------------------------