%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 09:30:49 AM UTC 2026
% Result : Unsatisfiable 5.06s 1.63s
% Output : Refutation 5.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 56 ( 9 unt; 5 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 135 ( 60 ~; 70 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(add(absolute(X0),absolute(X1)),X2)
| less_or_equal(absolute(add(X0,X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absolute_sum_less_or_equal_sum_of_absolutes2) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X0,minimum(X1,X2))
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum3) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X0,minimum(X1,X2))
| less_or_equal(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum7) ).
fof(f4,axiom,
! [X0,X1] :
( ~ less_or_equal(minimum(X0,X1),n0)
| less_or_equal(X1,n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum9) ).
fof(f5,axiom,
! [X2,X0,X1] :
( less_or_equal(add(X0,X2),X1)
| ~ less_or_equal(X2,half(X1))
| ~ less_or_equal(X0,half(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_sum_of_halves) ).
fof(f6,axiom,
! [X0] :
( ~ less_or_equal(half(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_and_half) ).
fof(f7,axiom,
! [X0] :
( ~ less_or_equal(delta_1(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f8,axiom,
! [X0] :
( ~ less_or_equal(delta_2(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f9,axiom,
! [X0,X1] :
( less_or_equal(absolute(add(f(X1),negate(f(a_real_number)))),X0)
| ~ less_or_equal(absolute(add(X1,negate(a_real_number))),delta_1(X0))
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f10,axiom,
! [X0,X1] :
( less_or_equal(absolute(add(g(X1),negate(g(a_real_number)))),X0)
| ~ less_or_equal(absolute(add(X1,negate(a_real_number))),delta_2(X0))
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f11,axiom,
~ less_or_equal(epsilon_0,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f12,axiom,
! [X0] :
( less_or_equal(absolute(add(xs(X0),negate(a_real_number))),X0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f13,negated_conjecture,
! [X0] :
( ~ less_or_equal(absolute(add(add(f(xs(X0)),negate(f(a_real_number))),add(g(xs(X0)),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7_1) ).
fof(f14,plain,
! [X0,X1] :
( less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X1)
| less_or_equal(minimum(X0,X1),n0) ),
inference(resolution,[],[f12,f3]) ).
fof(f15,plain,
! [X0,X1] :
( less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X0)
| less_or_equal(minimum(X0,X1),n0) ),
inference(resolution,[],[f12,f2]) ).
fof(f16,plain,
! [X2,X0,X1] :
( less_or_equal(absolute(add(X2,X0)),X1)
| ~ less_or_equal(absolute(X2),half(X1))
| ~ less_or_equal(absolute(X0),half(X1)) ),
inference(resolution,[],[f5,f1]) ).
fof(f27,plain,
! [X0] :
( ~ less_or_equal(absolute(add(g(xs(X0)),negate(g(a_real_number)))),half(epsilon_0))
| ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))
| less_or_equal(X0,n0) ),
inference(resolution,[],[f16,f13]) ).
fof(f30,plain,
! [X0] :
( ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))
| less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(half(epsilon_0),n0) ),
inference(resolution,[],[f27,f10]) ).
fof(f40,definition,
( spl0_3
<=> less_or_equal(half(epsilon_0),n0) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f41,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f43,definition,
( spl0_4
<=> ! [X0] :
( ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(X0,n0) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f44,plain,
( ! [X0] :
( ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(X0,n0) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f30,f43,f40]) ).
fof(f49,plain,
( less_or_equal(epsilon_0,n0)
| ~ spl0_3 ),
inference(resolution,[],[f41,f6]) ).
fof(f50,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f49,f11]) ).
fof(f51,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f50]) ).
fof(f52,plain,
( ! [X0] :
( ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(half(epsilon_0),n0) )
| ~ spl0_4 ),
inference(resolution,[],[f44,f9]) ).
fof(f62,definition,
( spl0_7
<=> ! [X0] :
( ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(X0,n0) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f63,plain,
( ! [X0] :
( ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(X0,n0) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f64,plain,
( spl0_3
| spl0_7
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f52,f43,f62,f40]) ).
fof(f67,plain,
( ! [X0] :
( ~ less_or_equal(absolute(add(xs(minimum(X0,delta_2(half(epsilon_0)))),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(minimum(X0,delta_2(half(epsilon_0))),n0)
| less_or_equal(minimum(X0,delta_2(half(epsilon_0))),n0) )
| ~ spl0_7 ),
inference(resolution,[],[f63,f14]) ).
fof(f69,plain,
( ! [X0] :
( ~ less_or_equal(absolute(add(xs(minimum(X0,delta_2(half(epsilon_0)))),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(minimum(X0,delta_2(half(epsilon_0))),n0) )
| ~ spl0_7 ),
inference(duplicate_literal_removal,[],[f67]) ).
fof(f80,definition,
( spl0_10
<=> less_or_equal(delta_2(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f81,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f94,plain,
( less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0)
| less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0)
| ~ spl0_7 ),
inference(resolution,[],[f69,f15]) ).
fof(f96,plain,
( less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0)
| ~ spl0_7 ),
inference(duplicate_literal_removal,[],[f94]) ).
fof(f97,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_1(half(epsilon_0)),n0)
| ~ spl0_7 ),
inference(resolution,[],[f96,f4]) ).
fof(f99,definition,
( spl0_14
<=> less_or_equal(delta_1(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f100,plain,
( less_or_equal(delta_1(half(epsilon_0)),n0)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f101,plain,
( spl0_14
| spl0_10
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f97,f62,f80,f99]) ).
fof(f102,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_10 ),
inference(resolution,[],[f81,f8]) ).
fof(f103,plain,
( spl0_3
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f102,f80,f40]) ).
fof(f104,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_14 ),
inference(resolution,[],[f100,f7]) ).
fof(f105,plain,
( spl0_3
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f104,f99,f40]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f45]) ).
cnf(s3,plain,
~ spl0_3,
inference(sat_conversion,[],[f51]) ).
cnf(s5,plain,
( spl0_3
| ~ spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f64]) ).
cnf(s9,plain,
( ~ spl0_7
| spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f101]) ).
cnf(s10,plain,
( spl0_3
| ~ spl0_10 ),
inference(sat_conversion,[],[f103]) ).
cnf(s11,plain,
( spl0_3
| ~ spl0_14 ),
inference(sat_conversion,[],[f105]) ).
cnf(s12,plain,
~ spl0_14,
inference(rat,[],[s11,s3]) ).
cnf(s13,plain,
~ spl0_10,
inference(rat,[],[s10,s3]) ).
cnf(s14,plain,
~ spl0_7,
inference(rat,[],[s9,s12,s13]) ).
cnf(s15,plain,
~ spl0_4,
inference(rat,[],[s5,s3,s14]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s2,s15,s3]) ).
fof(f106,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n019.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Mon Sep 28 20:26:18 UTC 2026
% 0.23/0.27 % CPUTime :
% 0.23/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.32 Running first-order theorem proving
% 0.23/0.32 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
% 5.06/1.63 % (193060)Input is clausal, will run a generic CNF schedule.
% 5.06/1.63 % (193068)lrs+10_1_sil=8000:sp=occurrence:random_seed=3213541058:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.06/1.63 % (193068)Refutation not found, incomplete strategy
% 5.06/1.63 % (193068)------------------------------
% 5.06/1.63 % (193068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.06/1.63 % (193068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.06/1.63 % (193068)CaDiCaL version: 2.1.3
% 5.06/1.63 % (193068)Termination reason: Refutation not found, incomplete strategy
% 5.06/1.63 % (193068)Time elapsed: 0.002 s
% 5.06/1.63 % (193068)Peak memory usage: 88 MB
% 5.06/1.63 % (193068)Instructions burned: 1 (million)
% 5.06/1.63 % (193066)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=743291535:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.06/1.63 % (193067)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=999553594:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.06/1.63 % (193070)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2107954300:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.06/1.63 % (193071)dis-21_1_sil=8000:lcm=predicate:random_seed=1275056694: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)
% 5.06/1.63 % (193065)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=2243959629:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.06/1.63 % (193069)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1467162493:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.06/1.63 % (193069)Refutation not found, incomplete strategy
% 5.06/1.63 % (193069)------------------------------
% 5.06/1.63 % (193069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.06/1.63 % (193069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.06/1.63 % (193069)CaDiCaL version: 2.1.3
% 5.06/1.63 % (193069)Termination reason: Refutation not found, incomplete strategy
% 5.06/1.63 % (193069)Time elapsed: 0.002 s
% 5.06/1.63 % (193069)Peak memory usage: 87 MB
% 5.06/1.63 % (193071)First to succeed.
% 5.06/1.63 % (193071)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-193060"
% 5.06/1.63 % (193068)------------------------------
% 5.06/1.63 % (193068)------------------------------
% 5.06/1.63 % (193070)Instruction limit reached!
% 5.06/1.63 % (193070)------------------------------
% 5.06/1.63 % (193070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.06/1.63 % (193070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.06/1.63 % (193070)CaDiCaL version: 2.1.3
% 5.06/1.63 % (193070)Termination reason: Instruction limit
% 5.06/1.63 % (193070)Termination phase: Saturation
% 5.06/1.63 % (193070)Time elapsed: 0.187 s
% 5.06/1.63 % (193070)Peak memory usage: 90 MB
% 5.06/1.63 % (193070)Instructions burned: 180 (million)
% 5.06/1.63 % (193069)------------------------------
% 5.06/1.63 % (193069)------------------------------
% 5.06/1.63 % (193071)Refutation found. Thanks to Tanya!
% 5.06/1.63 % SZS status Unsatisfiable for theBenchmark
% 5.06/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 5.85/1.88 % (193071)------------------------------
% 5.85/1.88 % (193071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.88 % (193071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.88 % (193071)CaDiCaL version: 2.1.3
% 5.85/1.88 % (193071)Termination reason: Refutation
% 5.85/1.88 % (193071)Time elapsed: 0.006 s
% 5.85/1.88 % (193071)Peak memory usage: 89 MB
% 5.85/1.88 % (193071)Instructions burned: 3 (million)
% 5.85/1.88 % (193071)------------------------------
% 5.85/1.88 % (193071)------------------------------
% 5.85/1.88 % (193060)Success in time 0.689 s
% 5.85/1.88 % Vampire exiting
%------------------------------------------------------------------------------