%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC379-1 : 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 : n002.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 01:03:43 PM UTC 2026
% Result : Unsatisfiable 1.88s 0.68s
% Output : Refutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 89 ( 13 unt; 12 def)
% Number of atoms : 268 ( 10 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 330 ( 151 ~; 167 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 21 ( 0 sgn 21 !; 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,
! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ssItem(sk5(X0))
| ~ memberP(sk4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X0] :
( memberP(sk4,sk5(X0))
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
! [X0] :
( leq(sk5(X0),X0)
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| memberP(sk3,X0)
| X0 != sk5(X0)
| ~ memberP(sk4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
! [X0] :
( ~ ssItem(X0)
| memberP(sk3,X0)
| sk5(X0) != X0
| ~ memberP(sk4,X0) ),
inference(reorient_equations,[],[f209]) ).
fof(f211,negated_conjecture,
! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0)
| memberP(sk4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f212,negated_conjecture,
! [X0,X1] :
( ~ ssItem(X0)
| ~ memberP(sk3,X0)
| ~ ssItem(X1)
| X0 = X1
| ~ memberP(sk4,X1)
| ~ leq(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f213,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f214,negated_conjecture,
( memberP(sk1,sk6)
| memberP(sk2,sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f215,negated_conjecture,
! [X0] :
( memberP(sk1,sk6)
| ~ ssItem(X0)
| sk6 = X0
| ~ memberP(sk2,X0)
| ~ leq(X0,sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f216,negated_conjecture,
( ssItem(sk7)
| ~ memberP(sk2,sk6)
| ~ memberP(sk1,sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
fof(f217,negated_conjecture,
( memberP(sk2,sk7)
| ~ memberP(sk2,sk6)
| ~ memberP(sk1,sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
fof(f218,negated_conjecture,
( leq(sk7,sk6)
| ~ memberP(sk2,sk6)
| ~ memberP(sk1,sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f219,negated_conjecture,
( sk6 != sk7
| ~ memberP(sk2,sk6)
| ~ memberP(sk1,sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
fof(f222,plain,
( memberP(sk3,sk6)
| memberP(sk4,sk6) ),
inference(definition_unfolding,[],[f214,f205,f204]) ).
fof(f223,plain,
! [X0] :
( memberP(sk3,sk6)
| ~ ssItem(X0)
| sk6 = X0
| ~ memberP(sk4,X0)
| ~ leq(X0,sk6) ),
inference(definition_unfolding,[],[f215,f205,f204]) ).
fof(f224,plain,
( ssItem(sk7)
| ~ memberP(sk4,sk6)
| ~ memberP(sk3,sk6) ),
inference(definition_unfolding,[],[f216,f204,f205]) ).
fof(f225,plain,
( memberP(sk4,sk7)
| ~ memberP(sk4,sk6)
| ~ memberP(sk3,sk6) ),
inference(definition_unfolding,[],[f217,f204,f204,f205]) ).
fof(f226,plain,
( leq(sk7,sk6)
| ~ memberP(sk4,sk6)
| ~ memberP(sk3,sk6) ),
inference(definition_unfolding,[],[f218,f204,f205]) ).
fof(f227,plain,
( sk6 != sk7
| ~ memberP(sk4,sk6)
| ~ memberP(sk3,sk6) ),
inference(definition_unfolding,[],[f219,f204,f205]) ).
fof(f247,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f248,plain,
! [X0] :
( ~ sQ0_eqProxy(sk5(X0),X0)
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk4,X0) ),
inference(equality_proxy_replacement,[],[f210,f247]) ).
fof(f249,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ memberP(sk3,X0)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ memberP(sk4,X1)
| ~ leq(X1,X0) ),
inference(equality_proxy_replacement,[],[f212,f247]) ).
fof(f250,plain,
! [X0] :
( memberP(sk3,sk6)
| ~ ssItem(X0)
| sQ0_eqProxy(sk6,X0)
| ~ memberP(sk4,X0)
| ~ leq(X0,sk6) ),
inference(equality_proxy_replacement,[],[f223,f247]) ).
fof(f251,plain,
( ~ sQ0_eqProxy(sk6,sk7)
| ~ memberP(sk4,sk6)
| ~ memberP(sk3,sk6) ),
inference(equality_proxy_replacement,[],[f227,f247]) ).
fof(f302,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f247]) ).
fof(f335,definition,
( spl1_8
<=> memberP(sk3,sk6) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f336,plain,
( ~ memberP(sk3,sk6)
| spl1_8 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f338,definition,
( spl1_9
<=> memberP(sk4,sk6) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f341,definition,
( spl1_10
<=> sQ0_eqProxy(sk6,sk7) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f342,plain,
( ~ sQ0_eqProxy(sk6,sk7)
| spl1_10 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f343,plain,
( ~ spl1_8
| ~ spl1_9
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f251,f341,f338,f335]) ).
fof(f345,definition,
( spl1_11
<=> leq(sk7,sk6) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f347,plain,
( ~ spl1_8
| ~ spl1_9
| spl1_11 ),
inference(avatar_split_clause,[],[f226,f345,f338,f335]) ).
fof(f349,definition,
( spl1_12
<=> memberP(sk4,sk7) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f351,plain,
( ~ spl1_8
| ~ spl1_9
| spl1_12 ),
inference(avatar_split_clause,[],[f225,f349,f338,f335]) ).
fof(f353,definition,
( spl1_13
<=> ssItem(sk7) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f355,plain,
( ~ spl1_8
| ~ spl1_9
| spl1_13 ),
inference(avatar_split_clause,[],[f224,f353,f338,f335]) ).
fof(f357,definition,
( spl1_14
<=> ! [X0] :
( ~ ssItem(X0)
| ~ leq(X0,sk6)
| ~ memberP(sk4,X0)
| sQ0_eqProxy(sk6,X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f358,plain,
( ! [X0] :
( sQ0_eqProxy(sk6,X0)
| ~ leq(X0,sk6)
| ~ memberP(sk4,X0)
| ~ ssItem(X0) )
| ~ spl1_14 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f359,plain,
( memberP(sk3,sk6)
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f360,plain,
( spl1_14
| spl1_8 ),
inference(avatar_split_clause,[],[f250,f335,f357]) ).
fof(f362,plain,
( spl1_9
| spl1_8 ),
inference(avatar_split_clause,[],[f222,f335,f338]) ).
fof(f363,plain,
( ~ ssItem(sk6)
| memberP(sk4,sk6)
| ~ spl1_8 ),
inference(resolution,[],[f211,f359]) ).
fof(f365,definition,
( spl1_15
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition]) ).
fof(f366,plain,
( ~ ssItem(sk6)
| spl1_15 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f367,plain,
( spl1_9
| ~ spl1_15
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f363,f335,f365,f338]) ).
fof(f368,plain,
( $false
| spl1_15 ),
inference(resolution,[],[f366,f213]) ).
fof(f369,plain,
spl1_15,
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f372,plain,
( ~ memberP(sk3,sk6)
| ~ ssItem(sk7)
| ~ ssItem(sk6)
| ~ memberP(sk4,sk7)
| ~ leq(sk7,sk6)
| spl1_10 ),
inference(resolution,[],[f249,f342]) ).
fof(f378,plain,
( ~ spl1_11
| ~ spl1_12
| ~ spl1_15
| ~ spl1_13
| ~ spl1_8
| spl1_10 ),
inference(avatar_split_clause,[],[f372,f341,f335,f353,f365,f349,f345]) ).
fof(f379,plain,
( ~ ssItem(sk6)
| ssItem(sk5(sk6))
| ~ memberP(sk4,sk6)
| spl1_8 ),
inference(resolution,[],[f336,f206]) ).
fof(f381,definition,
( spl1_16
<=> ssItem(sk5(sk6)) ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f383,plain,
( ~ spl1_9
| spl1_16
| ~ spl1_15
| spl1_8 ),
inference(avatar_split_clause,[],[f379,f335,f365,f381,f338]) ).
fof(f389,plain,
! [X0] :
( ~ sQ0_eqProxy(X0,sk5(X0))
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk4,X0) ),
inference(resolution,[],[f302,f248]) ).
fof(f394,plain,
( memberP(sk3,sk6)
| ~ ssItem(sk6)
| ~ memberP(sk4,sk6)
| ~ leq(sk5(sk6),sk6)
| ~ memberP(sk4,sk5(sk6))
| ~ ssItem(sk5(sk6))
| ~ spl1_14 ),
inference(resolution,[],[f389,f358]) ).
fof(f398,definition,
( spl1_17
<=> memberP(sk4,sk5(sk6)) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f399,plain,
( ~ memberP(sk4,sk5(sk6))
| spl1_17 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f401,definition,
( spl1_18
<=> leq(sk5(sk6),sk6) ),
introduced(definition,[new_symbols(definition,[spl1_18])],[avatar_definition]) ).
fof(f402,plain,
( ~ leq(sk5(sk6),sk6)
| spl1_18 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f403,plain,
( ~ spl1_16
| ~ spl1_17
| ~ spl1_18
| ~ spl1_9
| ~ spl1_15
| spl1_8
| ~ spl1_14 ),
inference(avatar_split_clause,[],[f394,f357,f335,f365,f338,f401,f398,f381]) ).
fof(f404,plain,
( memberP(sk3,sk6)
| ~ ssItem(sk6)
| ~ memberP(sk4,sk6)
| spl1_17 ),
inference(resolution,[],[f399,f207]) ).
fof(f405,plain,
( ~ spl1_9
| ~ spl1_15
| spl1_8
| spl1_17 ),
inference(avatar_split_clause,[],[f404,f398,f335,f365,f338]) ).
fof(f406,plain,
( memberP(sk3,sk6)
| ~ ssItem(sk6)
| ~ memberP(sk4,sk6)
| spl1_18 ),
inference(resolution,[],[f402,f208]) ).
fof(f407,plain,
( ~ spl1_9
| ~ spl1_15
| spl1_8
| spl1_18 ),
inference(avatar_split_clause,[],[f406,f401,f335,f365,f338]) ).
cnf(s7,plain,
( ~ spl1_8
| ~ spl1_9
| ~ spl1_10 ),
inference(sat_conversion,[],[f343]) ).
cnf(s8,plain,
( ~ spl1_8
| ~ spl1_9
| spl1_11 ),
inference(sat_conversion,[],[f347]) ).
cnf(s9,plain,
( ~ spl1_8
| ~ spl1_9
| spl1_12 ),
inference(sat_conversion,[],[f351]) ).
cnf(s10,plain,
( ~ spl1_8
| ~ spl1_9
| spl1_13 ),
inference(sat_conversion,[],[f355]) ).
cnf(s11,plain,
( spl1_8
| spl1_14 ),
inference(sat_conversion,[],[f360]) ).
cnf(s12,plain,
( spl1_8
| spl1_9 ),
inference(sat_conversion,[],[f362]) ).
cnf(s13,plain,
( ~ spl1_8
| spl1_9
| ~ spl1_15 ),
inference(sat_conversion,[],[f367]) ).
cnf(s14,plain,
spl1_15,
inference(sat_conversion,[],[f369]) ).
cnf(s15,plain,
( ~ spl1_8
| spl1_10
| ~ spl1_11
| ~ spl1_12
| ~ spl1_13
| ~ spl1_15 ),
inference(sat_conversion,[],[f378]) ).
cnf(s16,plain,
( spl1_8
| ~ spl1_9
| ~ spl1_15
| spl1_16 ),
inference(sat_conversion,[],[f383]) ).
cnf(s19,plain,
( spl1_8
| ~ spl1_9
| ~ spl1_14
| ~ spl1_15
| ~ spl1_16
| ~ spl1_17
| ~ spl1_18 ),
inference(sat_conversion,[],[f403]) ).
cnf(s20,plain,
( spl1_8
| ~ spl1_9
| ~ spl1_15
| spl1_17 ),
inference(sat_conversion,[],[f405]) ).
cnf(s21,plain,
( spl1_8
| ~ spl1_9
| ~ spl1_15
| spl1_18 ),
inference(sat_conversion,[],[f407]) ).
cnf(s22,plain,
( ~ spl1_8
| spl1_9 ),
inference(rat,[],[s13,s14]) ).
cnf(s29,plain,
spl1_8,
inference(rat,[],[s19,s16,s20,s21,s11,s12,s14]) ).
cnf(s30,plain,
spl1_9,
inference(rat,[],[s22,s29]) ).
cnf(s31,plain,
spl1_13,
inference(rat,[],[s10,s29,s30]) ).
cnf(s32,plain,
spl1_12,
inference(rat,[],[s9,s29,s30]) ).
cnf(s33,plain,
spl1_11,
inference(rat,[],[s8,s29,s30]) ).
cnf(s34,plain,
~ spl1_10,
inference(rat,[],[s7,s29,s30]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s15,s14,s31,s32,s29,s33,s34]) ).
fof(f408,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC379-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n002.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
% 0.08/0.19 % DateTime : Mon Sep 28 09:24:37 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 1.88/0.68 % (231356)Input is clausal, will run a generic CNF schedule.
% 1.88/0.68 % (231367)dis-21_1_sil=8000:lcm=predicate:random_seed=1215545513: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)
% 1.88/0.68 % (231367)First to succeed.
% 1.88/0.68 % (231367)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-231356"
% 1.88/0.68 % (231362)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2734155823:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.88/0.68 % (231366)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2894517364:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.88/0.68 % (231361)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=3383495189:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.88/0.68 % (231364)lrs+10_1_sil=8000:sp=occurrence:random_seed=3525008449:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.88/0.68 % (231365)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=190078853:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.88/0.68 % (231363)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=324381393:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.88/0.68 % (231365)Also succeeded, but the first one will report.
% 1.88/0.68 % (231364)Also succeeded, but the first one will report.
% 1.88/0.68 % (231366)Also succeeded, but the first one will report.
% 1.88/0.68 % (231367)Refutation found. Thanks to Tanya!
% 1.88/0.68 % SZS status Unsatisfiable for theBenchmark
% 1.88/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 2.13/0.78 % (231367)------------------------------
% 2.13/0.78 % (231367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.13/0.78 % (231367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.13/0.78 % (231367)CaDiCaL version: 2.1.3
% 2.13/0.78 % (231367)Termination reason: Refutation
% 2.13/0.78 % (231367)Time elapsed: 0.003 s
% 2.13/0.78 % (231367)Peak memory usage: 89 MB
% 2.13/0.78 % (231367)Instructions burned: 8 (million)
% 2.13/0.78 % (231367)------------------------------
% 2.13/0.78 % (231367)------------------------------
% 2.13/0.78 % (231356)Success in time 0.263 s
% 2.13/0.78 % Vampire exiting
%------------------------------------------------------------------------------