%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA003-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 3.78s 1.30s
% Output : Refutation 4.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 54 ( 9 unt; 5 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 129 ( 57 ~; 67 |; 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 : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X0,minimum(X1,X2))
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum3) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X0,minimum(X1,X2))
| less_or_equal(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum7) ).
fof(f3,axiom,
! [X0,X1] :
( ~ less_or_equal(minimum(X0,X1),n0)
| less_or_equal(X1,n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum9) ).
fof(f4,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/sandbox2/benchmark/theBenchmark.p',less_or_equal_sum_of_halves) ).
fof(f5,axiom,
! [X0] :
( ~ less_or_equal(half(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_and_half) ).
fof(f6,axiom,
! [X0] :
( ~ less_or_equal(delta_1(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f7,axiom,
! [X0] :
( ~ less_or_equal(delta_2(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f8,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/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f10,axiom,
~ less_or_equal(epsilon_0,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
fof(f11,axiom,
! [X0] :
( less_or_equal(absolute(add(xs(X0),negate(a_real_number))),X0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
fof(f12,negated_conjecture,
! [X0] :
( ~ less_or_equal(add(absolute(add(f(xs(X0)),negate(f(a_real_number)))),absolute(add(g(xs(X0)),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_2) ).
fof(f13,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,[],[f11,f2]) ).
fof(f14,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,[],[f11,f1]) ).
fof(f15,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,[],[f4,f12]) ).
fof(f22,plain,
! [X0] :
( ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(half(epsilon_0),n0)
| ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))
| less_or_equal(X0,n0) ),
inference(resolution,[],[f9,f15]) ).
fof(f26,definition,
( spl0_1
<=> less_or_equal(half(epsilon_0),n0) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f27,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f29,definition,
( spl0_2
<=> ! [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(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
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))) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f31,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f22,f29,f26]) ).
fof(f32,plain,
( ! [X0] :
( less_or_equal(X0,n0)
| ~ 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(half(epsilon_0),n0) )
| ~ spl0_2 ),
inference(resolution,[],[f30,f8]) ).
fof(f34,definition,
( spl0_3
<=> ! [X0] :
( less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0))) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f35,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_3 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f36,plain,
( spl0_1
| spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f32,f29,f34,f26]) ).
fof(f37,plain,
( less_or_equal(epsilon_0,n0)
| ~ spl0_1 ),
inference(resolution,[],[f27,f5]) ).
fof(f38,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f37,f10]) ).
fof(f39,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f38]) ).
fof(f44,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_3 ),
inference(resolution,[],[f35,f13]) ).
fof(f45,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_3 ),
inference(duplicate_literal_removal,[],[f44]) ).
fof(f49,definition,
( spl0_4
<=> less_or_equal(delta_2(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f50,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f55,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_3 ),
inference(resolution,[],[f45,f14]) ).
fof(f56,plain,
( less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0)
| ~ spl0_3 ),
inference(duplicate_literal_removal,[],[f55]) ).
fof(f57,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_1(half(epsilon_0)),n0)
| ~ spl0_3 ),
inference(resolution,[],[f56,f3]) ).
fof(f59,definition,
( spl0_6
<=> less_or_equal(delta_1(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f60,plain,
( less_or_equal(delta_1(half(epsilon_0)),n0)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f61,plain,
( spl0_6
| spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f57,f34,f49,f59]) ).
fof(f62,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_4 ),
inference(resolution,[],[f50,f7]) ).
fof(f63,plain,
( spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f62,f49,f26]) ).
fof(f64,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_6 ),
inference(resolution,[],[f60,f6]) ).
fof(f65,plain,
( spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f64,f59,f26]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f36]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f39]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f61]) ).
cnf(s6,plain,
( spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f63]) ).
cnf(s7,plain,
( spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f65]) ).
cnf(s8,plain,
~ spl0_6,
inference(rat,[],[s7,s3]) ).
cnf(s9,plain,
~ spl0_4,
inference(rat,[],[s6,s3]) ).
cnf(s10,plain,
~ spl0_3,
inference(rat,[],[s5,s8,s9]) ).
cnf(s11,plain,
~ spl0_2,
inference(rat,[],[s2,s10,s3]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11,s3]) ).
fof(f66,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA003-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n007.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 20:23:25 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 3.78/1.30 % (2761704)Input is clausal, will run a generic CNF schedule.
% 3.78/1.30 % (2761840)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1516419083:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.78/1.30 % (2761839)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=959652355:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.78/1.30 % (2761842)lrs+10_1_sil=8000:sp=occurrence:random_seed=391044458:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.78/1.30 % (2761841)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4053098958:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.78/1.30 % (2761842)Refutation not found, incomplete strategy
% 3.78/1.30 % (2761842)------------------------------
% 3.78/1.30 % (2761842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.30 % (2761842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.30 % (2761842)CaDiCaL version: 2.1.3
% 3.78/1.30 % (2761842)Termination reason: Refutation not found, incomplete strategy
% 3.78/1.30 % (2761842)Time elapsed: 0.002 s
% 3.78/1.30 % (2761842)Peak memory usage: 88 MB
% 3.78/1.30 % (2761842)Instructions burned: 1 (million)
% 3.78/1.30 % (2761843)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1553166875:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.78/1.30 % (2761843)Refutation not found, incomplete strategy
% 3.78/1.30 % (2761843)------------------------------
% 3.78/1.30 % (2761843)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.30 % (2761843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.30 % (2761843)CaDiCaL version: 2.1.3
% 3.78/1.30 % (2761843)Termination reason: Refutation not found, incomplete strategy
% 3.78/1.30 % (2761843)Time elapsed: 0.001 s
% 3.78/1.30 % (2761843)Peak memory usage: 87 MB
% 3.78/1.30 % (2761844)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=951929451:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.78/1.30 % (2761845)dis-21_1_sil=8000:lcm=predicate:random_seed=2176532723: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)
% 3.78/1.30 % (2761845)First to succeed.
% 3.78/1.30 % (2761845)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2761704"
% 3.78/1.30 % (2761844)Instruction limit reached!
% 3.78/1.30 % (2761844)------------------------------
% 3.78/1.30 % (2761844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.30 % (2761844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.30 % (2761844)CaDiCaL version: 2.1.3
% 3.78/1.30 % (2761844)Termination reason: Instruction limit
% 3.78/1.30 % (2761844)Termination phase: Saturation
% 3.78/1.30 % (2761844)Time elapsed: 0.107 s
% 3.78/1.30 % (2761844)Peak memory usage: 90 MB
% 3.78/1.30 % (2761844)Instructions burned: 181 (million)
% 3.78/1.30 % (2761842)------------------------------
% 3.78/1.30 % (2761842)------------------------------
% 3.78/1.30 % (2761843)------------------------------
% 3.78/1.30 % (2761843)------------------------------
% 3.78/1.30 % (2761853)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=3576527697:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.78/1.30 % (2761853)Also succeeded, but the first one will report.
% 3.78/1.30 % (2761854)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=304293961:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2995 on theBenchmark for (2995ds/189Mi)
% 3.78/1.30 % (2761855)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4169210017:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 3.78/1.30 % (2761855)Also succeeded, but the first one will report.
% 3.78/1.30 % (2761845)Refutation found. Thanks to Tanya!
% 3.78/1.30 % SZS status Unsatisfiable for theBenchmark
% 3.78/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 4.84/1.52 % (2761845)------------------------------
% 4.84/1.52 % (2761845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.84/1.52 % (2761845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.52 % (2761845)CaDiCaL version: 2.1.3
% 4.84/1.52 % (2761845)Termination reason: Refutation
% 4.84/1.52 % (2761845)Time elapsed: 0.003 s
% 4.84/1.52 % (2761845)Peak memory usage: 89 MB
% 4.84/1.52 % (2761845)Instructions burned: 2 (million)
% 4.84/1.52 % (2761845)------------------------------
% 4.84/1.52 % (2761845)------------------------------
% 4.84/1.52 % (2761704)Success in time 0.603 s
% 4.84/1.52 % Vampire exiting
%------------------------------------------------------------------------------