%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI655_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 09:33:35 AM UTC 2026
% Result : Theorem 0.27s 1.71s
% Output : Refutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 36 ( 28 unt; 0 typ; 13 def)
% Number of atoms : 44 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 0 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 55 ( 15 atm; 33 fun; 7 num; 0 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 8 usr; 9 prp; 0-2 aty)
% Number of functors : 14 ( 9 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_1,type,
b: $int ).
tff(func_def_2,type,
c: $int ).
tff(func_def_3,type,
d: $int ).
tff(func_def_9,type,
sF0: $int ).
tff(func_def_10,type,
sF1: $int ).
tff(func_def_11,type,
sF2: $int ).
tff(func_def_12,type,
sF3: $int ).
tff(func_def_13,type,
sF4: $int ).
tff(f1,axiom,
$lesseq(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,axiom,
$lesseq(d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_001) ).
tff(f3,conjecture,
$lesseq(0,$product($difference(a,b),$difference(c,d))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_002) ).
tff(f4,negated_conjecture,
~ $lesseq(0,$product($difference(a,b),$difference(c,d))),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
~ ~ $less($product($sum(a,$uminus(b)),$sum(c,$uminus(d))),0),
inference(theory_normalization,[],[f4]) ).
tff(f6,plain,
~ $less(c,d),
inference(theory_normalization,[],[f2]) ).
tff(f7,plain,
~ $less(a,b),
inference(theory_normalization,[],[f1]) ).
tff(f8,plain,
$less($product($sum(a,$uminus(b)),$sum(c,$uminus(d))),0),
inference(flattening,[],[f5]) ).
tff(f9,plain,
~ $less(a,b),
inference(cnf_transformation,[],[f7]) ).
tff(f10,plain,
$less($product($sum(a,$uminus(b)),$sum(c,$uminus(d))),0),
inference(cnf_transformation,[],[f8]) ).
tff(f11,plain,
~ $less(c,d),
inference(cnf_transformation,[],[f6]) ).
tff(f12,definition,
sF0 = $uminus(b),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f13,definition,
sF1 = $sum(a,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f14,definition,
sF2 = $uminus(d),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f15,plain,
$uminus(d) = sF2,
inference(reorient_equations,[],[f14]) ).
tff(f16,definition,
sF3 = $sum(c,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f17,plain,
$sum(c,sF2) = sF3,
inference(reorient_equations,[],[f16]) ).
tff(f18,definition,
sF4 = $product(sF1,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f19,plain,
$less(sF4,0),
inference(definition_folding,[],[f10,f18,f17,f15,f13,f12]) ).
tff(f21,definition,
( spl5_1
<=> ( $sum(c,sF2) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f24,plain,
spl5_1,
inference(avatar_split_clause,[],[f17,f21]) ).
tff(f26,definition,
( spl5_2
<=> $less(a,b) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f29,plain,
~ spl5_2,
inference(avatar_split_clause,[],[f9,f26]) ).
tff(f31,definition,
( spl5_3
<=> ( sF1 = $sum(a,sF0) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
tff(f34,plain,
spl5_3,
inference(avatar_split_clause,[],[f13,f31]) ).
tff(f36,definition,
( spl5_4
<=> ( $uminus(d) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
tff(f39,plain,
spl5_4,
inference(avatar_split_clause,[],[f15,f36]) ).
tff(f41,definition,
( spl5_5
<=> ( sF4 = $product(sF1,sF3) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
tff(f44,plain,
spl5_5,
inference(avatar_split_clause,[],[f18,f41]) ).
tff(f46,definition,
( spl5_6
<=> ( sF0 = $uminus(b) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
tff(f49,plain,
spl5_6,
inference(avatar_split_clause,[],[f12,f46]) ).
tff(f51,definition,
( spl5_7
<=> $less(c,d) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
tff(f54,plain,
~ spl5_7,
inference(avatar_split_clause,[],[f11,f51]) ).
tff(f56,definition,
( spl5_8
<=> $less(sF4,0) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
tff(f59,plain,
spl5_8,
inference(avatar_split_clause,[],[f19,f56]) ).
tff(f60,plain,
$false,
inference(avatar_smt_refutation,[],[f59,f54,f49,f44,f39,f34,f29,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI655_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n008.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Mon Sep 28 20:55:54 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running first-order theorem proving
% 0.25/0.29 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
% 0.27/1.71 % (2638273)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.27/1.71 % (2638278)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1145522210:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.27/1.71 % (2638281)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4202154851:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.27/1.71 % (2638281)Instruction limit reached!
% 0.27/1.71 % (2638281)------------------------------
% 0.27/1.71 % (2638281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/1.71 % (2638281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/1.71 % (2638281)CaDiCaL version: 2.1.3
% 0.27/1.71 % (2638281)Termination reason: Instruction limit
% 0.27/1.71 % (2638281)Termination phase: Saturation
% 0.27/1.71 % (2638281)Time elapsed: 0.006 s
% 0.27/1.71 % (2638281)Peak memory usage: 88 MB
% 0.27/1.71 % (2638281)Instructions burned: 8 (million)
% 0.27/1.71 % (2638278)Instruction limit reached!
% 0.27/1.71 % (2638278)------------------------------
% 0.27/1.71 % (2638278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/1.71 % (2638278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/1.71 % (2638278)CaDiCaL version: 2.1.3
% 0.27/1.71 % (2638278)Termination reason: Instruction limit
% 0.27/1.71 % (2638278)Termination phase: Saturation
% 0.27/1.71 % (2638278)Time elapsed: 0.027 s
% 0.27/1.71 % (2638278)Peak memory usage: 117 MB
% 0.27/1.71 % (2638278)Instructions burned: 12 (million)
% 0.27/1.71 % (2638282)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2090932855:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.27/1.71 % (2638279)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3268965165:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.27/1.71 % (2638280)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=888828575:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.27/1.71 % (2638282)Instruction limit reached!
% 0.27/1.71 % (2638282)------------------------------
% 0.27/1.71 % (2638282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/1.71 % (2638282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/1.71 % (2638282)CaDiCaL version: 2.1.3
% 0.27/1.71 % (2638282)Termination reason: Instruction limit
% 0.27/1.71 % (2638282)Termination phase: Saturation
% 0.27/1.71 % (2638282)Time elapsed: 0.006 s
% 0.27/1.71 % (2638282)Peak memory usage: 88 MB
% 0.27/1.71 % (2638282)Instructions burned: 4 (million)
% 0.27/1.71 % (2638284)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=892387332:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.27/1.71 % (2638283)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2116961400:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.27/1.71 % (2638279)First to succeed.
% 0.27/1.71 % (2638279)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2638273"
% 0.27/1.71 % (2638284)Also succeeded, but the first one will report.
% 0.27/1.71 % (2638283)Also succeeded, but the first one will report.
% 0.27/1.71 % (2638288)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=618658555:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 0.27/1.71 % (2638287)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1557729075:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.27/1.71 % (2638287)Refutation not found, incomplete strategy
% 0.27/1.71 % (2638287)------------------------------
% 0.27/1.71 % (2638287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/1.71 % (2638287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/1.71 % (2638287)CaDiCaL version: 2.1.3
% 0.27/1.71 % (2638287)Termination reason: Refutation not found, incomplete strategy
% 0.27/1.71 % (2638287)Time elapsed: 0.002 s
% 0.27/1.71 % (2638287)Peak memory usage: 88 MB
% 0.27/1.71 % (2638288)Instruction limit reached!
% 0.27/1.71 % (2638288)------------------------------
% 0.27/1.71 % (2638288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/1.71 % (2638288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/1.71 % (2638288)CaDiCaL version: 2.1.3
% 0.27/1.71 % (2638288)Termination reason: Instruction limit
% 0.27/1.71 % (2638288)Termination phase: Saturation
% 0.27/1.71 % (2638288)Time elapsed: 0.018 s
% 0.27/1.71 % (2638288)Peak memory usage: 88 MB
% 0.27/1.71 % (2638288)Instructions burned: 31 (million)
% 0.27/1.71 % (2638280)Instruction limit reached!
% 0.27/1.71 % (2638280)------------------------------
% 0.27/1.71 % (2638280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/1.71 % (2638280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/1.71 % (2638280)CaDiCaL version: 2.1.3
% 0.27/1.71 % (2638280)Termination reason: Instruction limit
% 0.27/1.71 % (2638280)Termination phase: Saturation
% 0.27/1.71 % (2638280)Time elapsed: 0.262 s
% 0.27/1.71 % (2638280)Peak memory usage: 117 MB
% 0.27/1.71 % (2638280)Instructions burned: 201 (million)
% 0.27/1.71 % (2638294)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2208165337:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 0.27/1.71 % (2638294)Instruction limit reached!
% 0.27/1.71 % (2638294)------------------------------
% 0.27/1.71 % (2638294)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/1.71 % (2638294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/1.71 % (2638294)CaDiCaL version: 2.1.3
% 0.27/1.71 % (2638294)Termination reason: Instruction limit
% 0.27/1.71 % (2638294)Termination phase: Saturation
% 0.27/1.71 % (2638294)Time elapsed: 0.016 s
% 0.27/1.71 % (2638294)Peak memory usage: 90 MB
% 0.27/1.71 % (2638294)Instructions burned: 17 (million)
% 0.27/1.71 % (2638297)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=3916816307:i=24:canc=force:rtra=on_2995 on theBenchmark for (2995ds/24Mi)
% 0.27/1.71 % (2638297)Instruction limit reached!
% 0.27/1.71 % (2638297)------------------------------
% 0.27/1.71 % (2638297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/1.71 % (2638297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/1.71 % (2638297)CaDiCaL version: 2.1.3
% 0.27/1.71 % (2638297)Termination reason: Instruction limit
% 0.27/1.71 % (2638297)Termination phase: Saturation
% 0.27/1.71 % (2638297)Time elapsed: 0.016 s
% 0.27/1.71 % (2638297)Peak memory usage: 89 MB
% 0.27/1.71 % (2638297)Instructions burned: 24 (million)
% 0.27/1.71 % (2638279)Refutation found. Thanks to Tanya!
% 0.27/1.71 % SZS status Theorem for theBenchmark
% 0.27/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 0.27/1.71 % (2638279)------------------------------
% 0.27/1.71 % (2638279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/1.71 % (2638279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/1.71 % (2638279)CaDiCaL version: 2.1.3
% 0.27/1.71 % (2638279)Termination reason: Refutation
% 0.27/1.71 % (2638279)Time elapsed: 0.049 s
% 0.27/1.71 % (2638279)Peak memory usage: 117 MB
% 0.27/1.71 % (2638279)Instructions burned: 12 (million)
% 0.27/1.71 % (2638279)------------------------------
% 0.27/1.71 % (2638279)------------------------------
% 0.27/1.71 % (2638273)Success in time 0.732 s
% 0.27/1.71 % Vampire exiting
%------------------------------------------------------------------------------