%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO617-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 02:28:27 PM UTC 2026
% Result : Unsatisfiable 4.41s 1.42s
% Output : Refutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 12 unt; 3 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 198 ( 103 ~; 92 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : le(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ le(max(X0,X1),X2)
| le(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ le(max(X0,X1),X2)
| le(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(f4,axiom,
! [X0] :
( eq(f(X0),a2)
| eq(f(X0),a1)
| eq(f(X0),a0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(f5,axiom,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
fof(f6,axiom,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a1)
| ~ eq(f(X0),a1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(f7,axiom,
! [X0,X1] :
( ~ le(s(X0),X1)
| ~ eq(f(X1),a2)
| ~ eq(f(X0),a2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(f8,plain,
! [X0,X1] : le(X0,max(X0,X1)),
inference(resolution,[],[f2,f1]) ).
fof(f10,plain,
! [X0,X1] : le(X0,max(X1,X0)),
inference(resolution,[],[f3,f1]) ).
fof(f11,plain,
! [X2,X0,X1] : le(X0,max(max(X1,X0),X2)),
inference(resolution,[],[f3,f8]) ).
fof(f12,plain,
! [X2,X0,X1] : le(X0,max(X1,max(X2,X0))),
inference(resolution,[],[f10,f3]) ).
fof(f13,plain,
! [X2,X0,X1] : le(X0,max(X1,max(X0,X2))),
inference(resolution,[],[f10,f2]) ).
fof(f18,plain,
! [X0,X1] :
( ~ eq(f(max(X0,s(X1))),a0)
| ~ eq(f(X1),a0) ),
inference(resolution,[],[f5,f10]) ).
fof(f21,plain,
! [X2,X3,X0,X1] : le(X0,max(max(X1,max(X0,X2)),X3)),
inference(resolution,[],[f11,f2]) ).
fof(f23,plain,
! [X0] :
( ~ eq(f(s(X0)),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[],[f6,f1]) ).
fof(f24,plain,
! [X0,X1] :
( ~ eq(f(max(s(X0),X1)),a1)
| ~ eq(f(X0),a1) ),
inference(resolution,[],[f6,f8]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ eq(f(max(X0,max(X1,s(X2)))),a1)
| ~ eq(f(X2),a1) ),
inference(resolution,[],[f12,f6]) ).
fof(f33,plain,
! [X0,X1] :
( ~ eq(f(max(s(X0),X1)),a2)
| ~ eq(f(X0),a2) ),
inference(resolution,[],[f7,f8]) ).
fof(f34,plain,
! [X0,X1] :
( ~ eq(f(max(X0,s(X1))),a2)
| ~ eq(f(X1),a2) ),
inference(resolution,[],[f7,f10]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ eq(f(max(X0,max(s(X1),X2))),a0)
| ~ eq(f(X1),a0) ),
inference(resolution,[],[f13,f5]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( ~ eq(f(max(max(X0,max(s(X1),X2)),X3)),a0)
| ~ eq(f(X1),a0) ),
inference(resolution,[],[f21,f5]) ).
fof(f69,plain,
! [X0,X1] :
( eq(f(max(s(X0),X1)),a1)
| ~ eq(f(X0),a2)
| eq(f(max(s(X0),X1)),a0) ),
inference(resolution,[],[f33,f4]) ).
fof(f75,plain,
! [X0,X1] :
( eq(f(max(X1,s(X0))),a1)
| ~ eq(f(X0),a2)
| eq(f(max(X1,s(X0))),a0) ),
inference(resolution,[],[f34,f4]) ).
fof(f159,plain,
! [X2,X0,X1] :
( eq(f(max(s(X0),max(X1,s(X2)))),a0)
| ~ eq(f(X0),a2)
| ~ eq(f(X2),a1) ),
inference(resolution,[],[f69,f30]) ).
fof(f166,plain,
! [X0,X1] :
( eq(f(max(s(X1),s(X0))),a0)
| ~ eq(f(X0),a2)
| ~ eq(f(X1),a1) ),
inference(resolution,[],[f75,f24]) ).
fof(f326,definition,
( spl0_1
<=> ! [X1] : ~ eq(f(X1),a0) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f327,plain,
( ! [X1] : ~ eq(f(X1),a0)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f355,definition,
( spl0_4
<=> ! [X0] : ~ eq(f(X0),a2) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f356,plain,
( ! [X0] : ~ eq(f(X0),a2)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f359,definition,
( spl0_5
<=> ! [X1] : ~ eq(f(X1),a1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f360,plain,
( ! [X1] : ~ eq(f(X1),a1)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f366,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),X1)),a0)
| ~ eq(f(X0),a2) )
| ~ spl0_5 ),
inference(resolution,[],[f360,f69]) ).
fof(f377,plain,
( ! [X0,X1] :
( ~ eq(f(X0),a2)
| ~ eq(f(X1),a0) )
| ~ spl0_5 ),
inference(resolution,[],[f366,f18]) ).
fof(f390,plain,
( spl0_1
| spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f377,f359,f355,f326]) ).
fof(f393,plain,
( ! [X0] : ~ eq(f(X0),a2)
| ~ spl0_1
| ~ spl0_5 ),
inference(resolution,[],[f327,f366]) ).
fof(f396,plain,
( spl0_4
| ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f393,f359,f326,f355]) ).
fof(f397,plain,
( ! [X0] :
( eq(f(X0),a1)
| eq(f(X0),a0) )
| ~ spl0_4 ),
inference(resolution,[],[f356,f4]) ).
fof(f399,plain,
( ! [X0,X1] :
( eq(f(max(s(X0),X1)),a0)
| ~ eq(f(X0),a1) )
| ~ spl0_4 ),
inference(resolution,[],[f397,f24]) ).
fof(f413,plain,
( ! [X0] : eq(f(X0),a0)
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[],[f397,f360]) ).
fof(f428,plain,
( ! [X0] : ~ eq(f(X0),a0)
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[],[f413,f63]) ).
fof(f429,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[],[f413,f327]) ).
fof(f430,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f429]) ).
fof(f431,plain,
( spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f428,f359,f355,f326]) ).
fof(f438,plain,
( ! [X0,X1] :
( ~ eq(f(X0),a1)
| ~ eq(f(X1),a0) )
| ~ spl0_4 ),
inference(resolution,[],[f399,f18]) ).
fof(f451,plain,
( spl0_1
| spl0_5
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f438,f355,f359,f326]) ).
fof(f461,plain,
! [X2,X0,X1] :
( ~ eq(f(X0),a2)
| ~ eq(f(X1),a1)
| ~ eq(f(X2),a0) ),
inference(resolution,[],[f159,f42]) ).
fof(f466,plain,
( spl0_1
| spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f461,f355,f359,f326]) ).
fof(f469,plain,
( ! [X0,X1] :
( ~ eq(f(X0),a2)
| ~ eq(f(X1),a1) )
| ~ spl0_1 ),
inference(resolution,[],[f327,f166]) ).
fof(f474,plain,
( spl0_5
| spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f469,f326,f355,f359]) ).
fof(f475,plain,
( ! [X0] :
( eq(f(X0),a1)
| eq(f(X0),a0) )
| ~ spl0_4 ),
inference(resolution,[],[f356,f4]) ).
fof(f481,plain,
( ! [X0] :
( eq(f(s(X0)),a0)
| ~ eq(f(X0),a1) )
| ~ spl0_4 ),
inference(resolution,[],[f475,f23]) ).
fof(f498,plain,
( ! [X0] : ~ eq(f(X0),a1)
| ~ spl0_1
| ~ spl0_4 ),
inference(resolution,[],[f481,f327]) ).
fof(f499,plain,
( spl0_5
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f498,f355,f326,f359]) ).
cnf(s17,plain,
( spl0_1
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f390]) ).
cnf(s18,plain,
( ~ spl0_1
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f396]) ).
cnf(s20,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f430]) ).
cnf(s21,plain,
( spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f431]) ).
cnf(s42,plain,
( spl0_1
| ~ spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f451]) ).
cnf(s45,plain,
( spl0_1
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f466]) ).
cnf(s48,plain,
( ~ spl0_1
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f474]) ).
cnf(s49,plain,
( ~ spl0_1
| ~ spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f499]) ).
cnf(s50,plain,
( ~ spl0_4
| spl0_1 ),
inference(rat,[],[s21,s42]) ).
cnf(s51,plain,
( spl0_4
| spl0_1 ),
inference(rat,[],[s45,s17]) ).
cnf(s52,plain,
spl0_1,
inference(rat,[],[s51,s50]) ).
cnf(s53,plain,
~ spl0_4,
inference(rat,[],[s20,s49,s52]) ).
cnf(s55,plain,
~ spl0_5,
inference(rat,[],[s18,s52,s53]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s48,s52,s53,s55]) ).
fof(f500,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO617-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n005.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Mon Sep 28 17:56:17 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.31 Running first-order theorem proving
% 0.24/0.31 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
% 4.41/1.42 % (1000718)Input is clausal, will run a generic CNF schedule.
% 4.41/1.42 % (1000732)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3602055563:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 4.41/1.42 % (1000737)dis-21_1_sil=8000:lcm=predicate:random_seed=3947079445:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 4.41/1.42 % (1000737)First to succeed.
% 4.41/1.42 % (1000737)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1000718"
% 4.41/1.42 % (1000734)lrs+10_1_sil=8000:sp=occurrence:random_seed=2088641712:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 4.41/1.42 % (1000731)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=886758319:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 4.41/1.42 % (1000736)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=247610620:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 4.41/1.42 % (1000733)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2314200542:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 4.41/1.42 % (1000735)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=850606871:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 4.41/1.42 % (1000734)Refutation not found, incomplete strategy
% 4.41/1.42 % (1000734)------------------------------
% 4.41/1.42 % (1000734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.42 % (1000735)Refutation not found, incomplete strategy
% 4.41/1.42 % (1000735)------------------------------
% 4.41/1.42 % (1000735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.42 % (1000734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.42 % (1000735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.42 % (1000734)CaDiCaL version: 2.1.3
% 4.41/1.42 % (1000735)CaDiCaL version: 2.1.3
% 4.41/1.42 % (1000735)Termination reason: Refutation not found, incomplete strategy
% 4.41/1.42 % (1000735)Time elapsed: 0.001 s
% 4.41/1.42 % (1000734)Termination reason: Refutation not found, incomplete strategy
% 4.41/1.42 % (1000734)Time elapsed: 0.001 s
% 4.41/1.42 % (1000735)Peak memory usage: 86 MB
% 4.41/1.42 % (1000734)Peak memory usage: 86 MB
% 4.41/1.42 % (1000736)Instruction limit reached!
% 4.41/1.42 % (1000736)------------------------------
% 4.41/1.42 % (1000736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.42 % (1000736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.42 % (1000736)CaDiCaL version: 2.1.3
% 4.41/1.42 % (1000736)Termination reason: Instruction limit
% 4.41/1.42 % (1000736)Termination phase: Saturation
% 4.41/1.42 % (1000736)Time elapsed: 0.124 s
% 4.41/1.42 % (1000736)Peak memory usage: 88 MB
% 4.41/1.42 % (1000736)Instructions burned: 180 (million)
% 4.41/1.42 % (1000737)Refutation found. Thanks to Tanya!
% 4.41/1.42 % SZS status Unsatisfiable for theBenchmark
% 4.41/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 4.41/1.42 % (1000737)------------------------------
% 4.41/1.42 % (1000737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.42 % (1000737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.42 % (1000737)CaDiCaL version: 2.1.3
% 4.41/1.42 % (1000737)Termination reason: Refutation
% 4.41/1.42 % (1000737)Time elapsed: 0.012 s
% 4.41/1.42 % (1000737)Peak memory usage: 89 MB
% 4.41/1.42 % (1000737)Instructions burned: 15 (million)
% 4.41/1.42 % (1000737)------------------------------
% 4.41/1.42 % (1000737)------------------------------
% 4.41/1.42 % (1000718)Success in time 0.522 s
% 4.41/1.42 % Vampire exiting
%------------------------------------------------------------------------------