%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC417-1 : 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 : n009.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 2.76s 0.83s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 73 ( 17 unt; 8 def)
% Number of atoms : 196 ( 34 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 249 ( 126 ~; 115 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 23 !; 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)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f216,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
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f217,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)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f216]) ).
fof(f218,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f219,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f220,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f221,plain,
( sk4 = app(cons(sk5,nil),sk6)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f220]) ).
fof(f222,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f223,plain,
( sk3 = app(sk6,cons(sk5,nil))
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f222]) ).
fof(f226,plain,
( neq(sk4,nil)
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f206,f204,f204]) ).
fof(f233,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| sk4 != app(app(X1,cons(X0,nil)),X2)
| sk3 != app(app(X2,cons(X0,nil)),X1)
| ~ neq(sk4,nil) ),
inference(definition_unfolding,[],[f217,f204,f205]) ).
fof(f241,plain,
neq(sk4,nil),
inference(duplicate_literal_removal,[],[f226]) ).
fof(f250,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f253,definition,
( spl0_4
<=> sk3 = app(sk6,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f254,plain,
( sk3 = app(sk6,cons(sk5,nil))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f255,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f223,f253,f250]) ).
fof(f257,definition,
( spl0_5
<=> sk4 = app(cons(sk5,nil),sk6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f258,plain,
( sk4 = app(cons(sk5,nil),sk6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f259,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f221,f257,f250]) ).
fof(f261,definition,
( spl0_6
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f262,plain,
( ssList(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f263,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f219,f261,f250]) ).
fof(f265,definition,
( spl0_7
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f266,plain,
( ssItem(sk5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f267,plain,
( ~ spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f218,f265,f250]) ).
fof(f269,definition,
( spl0_8
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| sk3 != app(app(X2,cons(X0,nil)),X1)
| sk4 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f270,plain,
( ! [X2,X0,X1] :
( sk4 != app(app(X1,cons(X0,nil)),X2)
| sk3 != app(app(X2,cons(X0,nil)),X1)
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f271,plain,
( ~ spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f233,f269,f250]) ).
fof(f278,plain,
spl0_3,
inference(avatar_split_clause,[],[f241,f250]) ).
fof(f299,plain,
( ! [X0,X1] :
( app(cons(X0,nil),X1) != sk4
| sk3 != app(app(X1,cons(X0,nil)),nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(cons(X0,nil)) )
| ~ spl0_8 ),
inference(superposition,[],[f270,f74]) ).
fof(f302,plain,
( ! [X0,X1] :
( sk3 != app(app(X1,cons(X0,nil)),nil)
| app(cons(X0,nil),X1) != sk4
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(cons(X0,nil)) )
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f299,f8]) ).
fof(f304,definition,
( spl0_11
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f305,plain,
( ~ ssList(cons(sk5,nil))
| spl0_11 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f323,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| spl0_11 ),
inference(resolution,[],[f86,f305]) ).
fof(f324,plain,
( ~ ssItem(sk5)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f323,f8]) ).
fof(f325,plain,
( $false
| ~ spl0_7
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f324,f266]) ).
fof(f326,plain,
( ~ spl0_7
| spl0_11 ),
inference(avatar_contradiction_clause,[],[f325]) ).
fof(f334,plain,
( sk3 != app(sk3,nil)
| sk4 != app(cons(sk5,nil),sk6)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f302,f254]) ).
fof(f338,plain,
( sk3 != app(sk3,nil)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f334,f258]) ).
fof(f340,plain,
( sk3 != app(sk3,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f338,f266]) ).
fof(f342,plain,
( sk3 != app(sk3,nil)
| ~ ssList(cons(sk5,nil))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f340,f262]) ).
fof(f345,definition,
( spl0_14
<=> sk3 = app(sk3,nil) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f346,plain,
( sk3 != app(sk3,nil)
| spl0_14 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f347,plain,
( ~ spl0_11
| ~ spl0_14
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f342,f269,f265,f261,f257,f253,f345,f304]) ).
fof(f352,plain,
( sk3 != sk3
| ~ ssList(sk3)
| spl0_14 ),
inference(superposition,[],[f346,f73]) ).
fof(f353,plain,
( ~ ssList(sk3)
| spl0_14 ),
inference(trivial_inequality_removal,[],[f352]) ).
fof(f354,plain,
( $false
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f353,f202]) ).
fof(f355,plain,
spl0_14,
inference(avatar_contradiction_clause,[],[f354]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f255]) ).
cnf(s3,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f259]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f263]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f267]) ).
cnf(s6,plain,
( ~ spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f271]) ).
cnf(s12,plain,
spl0_3,
inference(sat_conversion,[],[f278]) ).
cnf(s16,plain,
( ~ spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f326]) ).
cnf(s17,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11
| ~ spl0_14 ),
inference(sat_conversion,[],[f347]) ).
cnf(s18,plain,
spl0_14,
inference(sat_conversion,[],[f355]) ).
cnf(s19,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_11 ),
inference(rat,[],[s17,s18]) ).
cnf(s20,plain,
spl0_8,
inference(rat,[],[s6,s12]) ).
cnf(s21,plain,
spl0_7,
inference(rat,[],[s5,s12]) ).
cnf(s22,plain,
spl0_11,
inference(rat,[],[s16,s21]) ).
cnf(s23,plain,
spl0_6,
inference(rat,[],[s4,s12]) ).
cnf(s24,plain,
spl0_5,
inference(rat,[],[s3,s12]) ).
cnf(s25,plain,
~ spl0_4,
inference(rat,[],[s19,s22,s20,s21,s23,s24]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s2,s25,s12]) ).
fof(f356,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC417-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 09:33:45 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.76/0.83 % (2912685)Input is clausal, will run a generic CNF schedule.
% 2.76/0.83 % (2912696)dis-21_1_sil=8000:lcm=predicate:random_seed=1563704432: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)
% 2.76/0.83 % (2912696)Instruction limit reached!
% 2.76/0.83 % (2912696)------------------------------
% 2.76/0.83 % (2912696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/0.83 % (2912696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/0.83 % (2912696)CaDiCaL version: 2.1.3
% 2.76/0.83 % (2912696)Termination reason: Instruction limit
% 2.76/0.83 % (2912696)Termination phase: Saturation
% 2.76/0.83 % (2912696)Time elapsed: 0.029 s
% 2.76/0.83 % (2912696)Peak memory usage: 89 MB
% 2.76/0.83 % (2912696)Instructions burned: 119 (million)
% 2.76/0.83 % (2912695)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1144159678:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.76/0.83 % (2912691)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1465689752:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.76/0.83 % (2912692)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2571269425:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.76/0.83 % (2912694)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1719161558:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.76/0.83 % (2912690)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=4207157163:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.76/0.83 % (2912693)lrs+10_1_sil=8000:sp=occurrence:random_seed=2833946419:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.76/0.83 % (2912694)First to succeed.
% 2.76/0.83 % (2912694)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2912685"
% 2.76/0.83 % (2912695)Also succeeded, but the first one will report.
% 2.76/0.83 % (2912693)Instruction limit reached!
% 2.76/0.83 % (2912693)------------------------------
% 2.76/0.83 % (2912693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/0.83 % (2912693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/0.83 % (2912693)CaDiCaL version: 2.1.3
% 2.76/0.83 % (2912693)Termination reason: Instruction limit
% 2.76/0.83 % (2912693)Termination phase: Saturation
% 2.76/0.83 % (2912693)Time elapsed: 0.064 s
% 2.76/0.83 % (2912693)Peak memory usage: 90 MB
% 2.76/0.83 % (2912693)Instructions burned: 109 (million)
% 2.76/0.83 % (2912698)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=158995976:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.76/0.83 % (2912698)Also succeeded, but the first one will report.
% 2.76/0.83 % (2912706)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1250896717: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)
% 2.76/0.83 % (2912694)Refutation found. Thanks to Tanya!
% 2.76/0.83 % SZS status Unsatisfiable for theBenchmark
% 2.76/0.83 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.03 % (2912694)------------------------------
% 0.19/1.03 % (2912694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.03 % (2912694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.03 % (2912694)CaDiCaL version: 2.1.3
% 0.19/1.03 % (2912694)Termination reason: Refutation
% 0.19/1.03 % (2912694)Time elapsed: 0.006 s
% 0.19/1.03 % (2912694)Peak memory usage: 90 MB
% 0.19/1.03 % (2912694)Instructions burned: 6 (million)
% 0.19/1.03 % (2912694)------------------------------
% 0.19/1.03 % (2912694)------------------------------
% 0.19/1.03 % (2912685)Success in time 0.413 s
% 0.19/1.03 % Vampire exiting
%------------------------------------------------------------------------------