%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC317-1 : 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 : n003.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 01:03:26 PM UTC 2026
% Result : Unsatisfiable 2.54s 1.13s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 50 ( 12 unt; 7 def)
% Number of atoms : 118 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 138 ( 70 ~; 61 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f216,negated_conjecture,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) != sk1
| app(X1,cons(X0,nil)) != sk2
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f217,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) != sk1
| sk2 != app(X1,cons(X0,nil))
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f216]) ).
fof(f218,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f219,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
fof(f220,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
fof(f221,plain,
( sk3 = app(cons(sk5,nil),sk6)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f220]) ).
fof(f222,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f223,plain,
( sk4 = 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,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) != sk3
| sk4 != app(X1,cons(X0,nil))
| ~ neq(sk4,nil) ),
inference(definition_unfolding,[],[f217,f205,f204]) ).
fof(f249,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f253,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ sQ0_eqProxy(app(cons(X0,nil),X1),sk3)
| ~ sQ0_eqProxy(sk4,app(X1,cons(X0,nil)))
| ~ neq(sk4,nil) ),
inference(equality_proxy_replacement,[],[f233,f249,f249]) ).
fof(f254,plain,
( sQ0_eqProxy(sk3,app(cons(sk5,nil),sk6))
| ~ neq(sk4,nil) ),
inference(equality_proxy_replacement,[],[f221,f249]) ).
fof(f255,plain,
( sQ0_eqProxy(sk4,app(sk6,cons(sk5,nil)))
| ~ neq(sk4,nil) ),
inference(equality_proxy_replacement,[],[f223,f249]) ).
fof(f300,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f249]) ).
fof(f306,plain,
neq(sk4,nil),
inference(duplicate_literal_removal,[],[f226]) ).
fof(f327,definition,
( spl1_6
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f330,definition,
( spl1_7
<=> sQ0_eqProxy(sk4,app(sk6,cons(sk5,nil))) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f332,plain,
( ~ spl1_6
| spl1_7 ),
inference(avatar_split_clause,[],[f255,f330,f327]) ).
fof(f334,definition,
( spl1_8
<=> sQ0_eqProxy(sk3,app(cons(sk5,nil),sk6)) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f335,plain,
( sQ0_eqProxy(sk3,app(cons(sk5,nil),sk6))
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f336,plain,
( ~ spl1_6
| spl1_8 ),
inference(avatar_split_clause,[],[f254,f334,f327]) ).
fof(f338,definition,
( spl1_9
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f340,plain,
( ~ spl1_6
| spl1_9 ),
inference(avatar_split_clause,[],[f219,f338,f327]) ).
fof(f342,definition,
( spl1_10
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f344,plain,
( ~ spl1_6
| spl1_10 ),
inference(avatar_split_clause,[],[f218,f342,f327]) ).
fof(f346,definition,
( spl1_11
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ sQ0_eqProxy(sk4,app(X1,cons(X0,nil)))
| ~ sQ0_eqProxy(app(cons(X0,nil),X1),sk3)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f347,plain,
( ! [X0,X1] :
( ~ sQ0_eqProxy(app(cons(X0,nil),X1),sk3)
| ~ sQ0_eqProxy(sk4,app(X1,cons(X0,nil)))
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f348,plain,
( ~ spl1_6
| spl1_11 ),
inference(avatar_split_clause,[],[f253,f346,f327]) ).
fof(f355,plain,
spl1_6,
inference(avatar_split_clause,[],[f306,f327]) ).
fof(f358,plain,
( ! [X0,X1] :
( ~ sQ0_eqProxy(sk3,app(cons(X0,nil),X1))
| ~ sQ0_eqProxy(sk4,app(X1,cons(X0,nil)))
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl1_11 ),
inference(resolution,[],[f300,f347]) ).
fof(f359,plain,
( ~ sQ0_eqProxy(sk4,app(sk6,cons(sk5,nil)))
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ spl1_8
| ~ spl1_11 ),
inference(resolution,[],[f358,f335]) ).
fof(f364,plain,
( ~ spl1_9
| ~ spl1_10
| ~ spl1_7
| ~ spl1_8
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f359,f346,f334,f330,f342,f338]) ).
cnf(s5,plain,
( ~ spl1_6
| spl1_7 ),
inference(sat_conversion,[],[f332]) ).
cnf(s6,plain,
( ~ spl1_6
| spl1_8 ),
inference(sat_conversion,[],[f336]) ).
cnf(s7,plain,
( ~ spl1_6
| spl1_9 ),
inference(sat_conversion,[],[f340]) ).
cnf(s8,plain,
( ~ spl1_6
| spl1_10 ),
inference(sat_conversion,[],[f344]) ).
cnf(s9,plain,
( ~ spl1_6
| spl1_11 ),
inference(sat_conversion,[],[f348]) ).
cnf(s15,plain,
spl1_6,
inference(sat_conversion,[],[f355]) ).
cnf(s17,plain,
( ~ spl1_7
| ~ spl1_8
| ~ spl1_9
| ~ spl1_10
| ~ spl1_11 ),
inference(sat_conversion,[],[f364]) ).
cnf(s18,plain,
spl1_11,
inference(rat,[],[s9,s15]) ).
cnf(s19,plain,
spl1_10,
inference(rat,[],[s8,s15]) ).
cnf(s20,plain,
spl1_9,
inference(rat,[],[s7,s15]) ).
cnf(s21,plain,
spl1_8,
inference(rat,[],[s6,s15]) ).
cnf(s22,plain,
~ spl1_7,
inference(rat,[],[s17,s18,s19,s20,s21]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s5,s22,s15]) ).
fof(f365,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC317-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 09:03:42 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 2.54/1.13 % (1448764)Input is clausal, will run a generic CNF schedule.
% 2.54/1.13 % (1448775)dis-21_1_sil=8000:lcm=predicate:random_seed=1197485341: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)
% 2.54/1.13 % (1448775)First to succeed.
% 2.54/1.13 % (1448775)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1448764"
% 2.54/1.13 % (1448770)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2164291645:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.54/1.13 % (1448772)lrs+10_1_sil=8000:sp=occurrence:random_seed=596895928:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.54/1.13 % (1448773)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1881561716:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.54/1.13 % (1448771)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3176726935:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.54/1.13 % (1448769)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=2795456368:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.54/1.13 % (1448773)Also succeeded, but the first one will report.
% 2.54/1.13 % (1448772)Also succeeded, but the first one will report.
% 2.54/1.13 % (1448774)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3109902564:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.54/1.13 % (1448774)Also succeeded, but the first one will report.
% 2.54/1.13 % (1448775)Refutation found. Thanks to Tanya!
% 2.54/1.13 % SZS status Unsatisfiable for theBenchmark
% 2.54/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/1.13 % (1448775)------------------------------
% 2.54/1.13 % (1448775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.13 % (1448775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.13 % (1448775)CaDiCaL version: 2.1.3
% 2.54/1.13 % (1448775)Termination reason: Refutation
% 2.54/1.13 % (1448775)Time elapsed: 0.003 s
% 2.54/1.13 % (1448775)Peak memory usage: 89 MB
% 2.54/1.13 % (1448775)Instructions burned: 6 (million)
% 2.54/1.13 % (1448775)------------------------------
% 2.54/1.13 % (1448775)------------------------------
% 2.54/1.13 % (1448764)Success in time 0.279 s
% 2.54/1.13 % Vampire exiting
%------------------------------------------------------------------------------