%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC419-1 : 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 : n016.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 01:03:54 PM UTC 2026
% Result : Unsatisfiable 3.62s 1.19s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 69 ( 17 unt; 7 def)
% Number of atoms : 168 ( 32 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 201 ( 102 ~; 92 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
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),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk2
| app(app(X2,cons(X0,nil)),X1) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| sk2 != app(app(X1,cons(X0,nil)),X2)
| sk1 != app(app(X2,cons(X0,nil)),X1) ),
inference(reorient_equations,[],[f207]) ).
fof(f210,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f211,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f212,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f213,plain,
( sk4 = app(cons(sk5,nil),sk6)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f212]) ).
fof(f214,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f215,plain,
( sk3 = app(sk6,cons(sk5,nil))
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f214]) ).
fof(f218,plain,
neq(sk4,nil),
inference(definition_unfolding,[],[f206,f204]) ).
fof(f219,plain,
! [X2,X0,X1] :
( sk4 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| sk3 != app(app(X2,cons(X0,nil)),X1) ),
inference(definition_unfolding,[],[f208,f204,f205]) ).
fof(f235,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f236,plain,
( ~ neq(sk4,nil)
| spl0_3 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f238,definition,
( spl0_4
<=> sk3 = app(sk6,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f239,plain,
( sk3 = app(sk6,cons(sk5,nil))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f240,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f215,f238,f235]) ).
fof(f242,definition,
( spl0_5
<=> sk4 = app(cons(sk5,nil),sk6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f243,plain,
( sk4 = app(cons(sk5,nil),sk6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f244,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f213,f242,f235]) ).
fof(f246,definition,
( spl0_6
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f247,plain,
( ssList(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f248,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f211,f246,f235]) ).
fof(f250,definition,
( spl0_7
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f251,plain,
( ssItem(sk5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f252,plain,
( ~ spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f210,f250,f235]) ).
fof(f260,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f236,f218]) ).
fof(f261,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f260]) ).
fof(f282,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) != sk4
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssItem(X0)
| sk3 != app(app(X1,cons(X0,nil)),nil)
| ~ ssList(cons(X0,nil)) ),
inference(superposition,[],[f219,f74]) ).
fof(f285,plain,
! [X0,X1] :
( sk3 != app(app(X1,cons(X0,nil)),nil)
| ~ ssList(X1)
| ~ ssItem(X0)
| app(cons(X0,nil),X1) != sk4
| ~ ssList(cons(X0,nil)) ),
inference(forward_subsumption_resolution,[],[f282,f8]) ).
fof(f287,definition,
( spl0_12
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f288,plain,
( ~ ssList(cons(sk5,nil))
| spl0_12 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f306,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| spl0_12 ),
inference(resolution,[],[f86,f288]) ).
fof(f307,plain,
( ~ ssItem(sk5)
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f306,f8]) ).
fof(f308,plain,
( $false
| ~ spl0_7
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f307,f251]) ).
fof(f309,plain,
( ~ spl0_7
| spl0_12 ),
inference(avatar_contradiction_clause,[],[f308]) ).
fof(f317,plain,
( sk3 != app(sk3,nil)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| sk4 != app(cons(sk5,nil),sk6)
| ~ ssList(cons(sk5,nil))
| ~ spl0_4 ),
inference(superposition,[],[f285,f239]) ).
fof(f321,plain,
( sk3 != app(sk3,nil)
| ~ ssItem(sk5)
| sk4 != app(cons(sk5,nil),sk6)
| ~ ssList(cons(sk5,nil))
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f317,f247]) ).
fof(f323,plain,
( sk3 != app(sk3,nil)
| sk4 != app(cons(sk5,nil),sk6)
| ~ ssList(cons(sk5,nil))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f321,f251]) ).
fof(f325,plain,
( sk3 != app(sk3,nil)
| ~ ssList(cons(sk5,nil))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f323,f243]) ).
fof(f328,definition,
( spl0_15
<=> sk3 = app(sk3,nil) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f329,plain,
( sk3 != app(sk3,nil)
| spl0_15 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f330,plain,
( ~ spl0_12
| ~ spl0_15
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f325,f250,f246,f242,f238,f328,f287]) ).
fof(f335,plain,
( sk3 != sk3
| ~ ssList(sk3)
| spl0_15 ),
inference(superposition,[],[f329,f73]) ).
fof(f336,plain,
( ~ ssList(sk3)
| spl0_15 ),
inference(trivial_inequality_removal,[],[f335]) ).
fof(f337,plain,
( $false
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f336,f202]) ).
fof(f338,plain,
spl0_15,
inference(avatar_contradiction_clause,[],[f337]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f240]) ).
cnf(s3,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f244]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f248]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f252]) ).
cnf(s7,plain,
spl0_3,
inference(sat_conversion,[],[f261]) ).
cnf(s11,plain,
( ~ spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f309]) ).
cnf(s12,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_15 ),
inference(sat_conversion,[],[f330]) ).
cnf(s13,plain,
spl0_15,
inference(sat_conversion,[],[f338]) ).
cnf(s14,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12 ),
inference(rat,[],[s12,s13]) ).
cnf(s15,plain,
spl0_7,
inference(rat,[],[s5,s7]) ).
cnf(s16,plain,
spl0_12,
inference(rat,[],[s11,s15]) ).
cnf(s17,plain,
spl0_6,
inference(rat,[],[s4,s7]) ).
cnf(s18,plain,
spl0_5,
inference(rat,[],[s3,s7]) ).
cnf(s19,plain,
~ spl0_4,
inference(rat,[],[s14,s16,s15,s17,s18]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s2,s19,s7]) ).
fof(f339,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC419-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n016.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 09:38:48 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 3.62/1.19 % (3510888)Input is clausal, will run a generic CNF schedule.
% 3.62/1.19 % (3510893)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=3557549949:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.62/1.19 % (3510894)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=27910429:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.62/1.19 % (3510896)lrs+10_1_sil=8000:sp=occurrence:random_seed=3779143757:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.62/1.19 % (3510898)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3835624541:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.62/1.19 % (3510895)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1850886003:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.62/1.19 % (3510897)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3419588858:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.62/1.19 % (3510897)First to succeed.
% 3.62/1.19 % (3510897)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3510888"
% 3.62/1.19 % (3510899)dis-21_1_sil=8000:lcm=predicate:random_seed=4190303003: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)
% 3.62/1.19 % (3510898)Also succeeded, but the first one will report.
% 3.62/1.19 % (3510896)Instruction limit reached!
% 3.62/1.19 % (3510896)------------------------------
% 3.62/1.19 % (3510896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.19 % (3510896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.19 % (3510896)CaDiCaL version: 2.1.3
% 3.62/1.19 % (3510896)Termination reason: Instruction limit
% 3.62/1.19 % (3510896)Termination phase: Saturation
% 3.62/1.19 % (3510896)Time elapsed: 0.063 s
% 3.62/1.19 % (3510896)Peak memory usage: 89 MB
% 3.62/1.19 % (3510896)Instructions burned: 108 (million)
% 3.62/1.19 % (3510899)Instruction limit reached!
% 3.62/1.19 % (3510899)------------------------------
% 3.62/1.19 % (3510899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.19 % (3510899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.19 % (3510899)CaDiCaL version: 2.1.3
% 3.62/1.19 % (3510899)Termination reason: Instruction limit
% 3.62/1.19 % (3510899)Termination phase: Saturation
% 3.62/1.19 % (3510899)Time elapsed: 0.062 s
% 3.62/1.19 % (3510899)Peak memory usage: 89 MB
% 3.62/1.19 % (3510899)Instructions burned: 117 (million)
% 3.62/1.19 % (3510908)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1747373119:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.62/1.19 % (3510907)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=2704523523:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.62/1.19 % (3510897)Refutation found. Thanks to Tanya!
% 3.62/1.19 % SZS status Unsatisfiable for theBenchmark
% 3.62/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.19 % (3510897)------------------------------
% 3.62/1.19 % (3510897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.19 % (3510897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.19 % (3510897)CaDiCaL version: 2.1.3
% 3.62/1.19 % (3510897)Termination reason: Refutation
% 3.62/1.19 % (3510897)Time elapsed: 0.006 s
% 3.62/1.19 % (3510897)Peak memory usage: 90 MB
% 3.62/1.19 % (3510897)Instructions burned: 6 (million)
% 3.62/1.19 % (3510897)------------------------------
% 3.62/1.19 % (3510897)------------------------------
% 3.62/1.19 % (3510888)Success in time 0.44 s
% 3.62/1.19 % Vampire exiting
%------------------------------------------------------------------------------