%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI609_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:33:28 AM UTC 2026
% Result : Theorem 3.74s 1.25s
% Output : Refutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 48 ( 26 unt; 0 typ; 16 def)
% Number of atoms : 87 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 68 ( 29 ~; 13 |; 8 &)
% ( 10 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 115 ( 38 atm; 42 fun; 18 num; 17 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 : 14 ( 10 usr; 11 prp; 0-2 aty)
% Number of functors : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_1,type,
a: $int ).
tff(func_def_2,type,
b: $int ).
tff(func_def_7,type,
sF0: $int ).
tff(func_def_8,type,
sF1: $int ).
tff(func_def_9,type,
sF2: $int ).
tff(func_def_10,type,
sF3: $int ).
tff(func_def_11,type,
sF4: $int ).
tff(func_def_12,type,
sF5: $int ).
tff(f1,conjecture,
( ( $lesseq(0,$sum(a,$uminus(b)))
& ! [X1: $int,X0: $int] :
( $lesseq(X0,X1)
=> $lesseq(f(X0),f(X1)) ) )
=> $lesseq(0,$sum(f(a),$uminus(f(b)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_mon_implies_f_a_b_1) ).
tff(f2,negated_conjecture,
~ ( ( $lesseq(0,$sum(a,$uminus(b)))
& ! [X1: $int,X0: $int] :
( $lesseq(X0,X1)
=> $lesseq(f(X0),f(X1)) ) )
=> $lesseq(0,$sum(f(a),$uminus(f(b)))) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( ~ $less($sum(a,$uminus(b)),0)
& ! [X1: $int,X0: $int] :
( ~ $less(X1,X0)
=> ~ $less(f(X1),f(X0)) ) )
=> ~ $less($sum(f(a),$uminus(f(b))),0) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f16,plain,
~ ( ( ~ $less($sum(a,$uminus(b)),0)
& ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
=> ~ $less(f(X0),f(X1)) ) )
=> ~ $less($sum(f(a),$uminus(f(b))),0) ),
inference(rectify,[],[f3]) ).
tff(f17,plain,
( $less($sum(f(a),$uminus(f(b))),0)
& ~ $less($sum(a,$uminus(b)),0)
& ! [X0: $int,X1: $int] :
( $less(X0,X1)
| ~ $less(f(X0),f(X1)) ) ),
inference(ennf_transformation,[],[f16]) ).
tff(f18,plain,
( $less($sum(f(a),$uminus(f(b))),0)
& ! [X0: $int,X1: $int] :
( $less(X0,X1)
| ~ $less(f(X0),f(X1)) )
& ~ $less($sum(a,$uminus(b)),0) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
~ $less($sum(a,$uminus(b)),0),
inference(cnf_transformation,[],[f18]) ).
tff(f20,plain,
! [X0: $int,X1: $int] :
( ~ $less(f(X0),f(X1))
| $less(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tff(f21,plain,
$less($sum(f(a),$uminus(f(b))),0),
inference(cnf_transformation,[],[f18]) ).
tff(f22,definition,
sF0 = f(a),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f23,plain,
f(a) = sF0,
inference(reorient_equations,[],[f22]) ).
tff(f24,definition,
sF1 = f(b),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f25,plain,
f(b) = sF1,
inference(reorient_equations,[],[f24]) ).
tff(f26,definition,
sF2 = $uminus(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f27,plain,
$uminus(sF1) = sF2,
inference(reorient_equations,[],[f26]) ).
tff(f28,definition,
sF3 = $sum(sF0,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f29,plain,
$less(sF3,0),
inference(definition_folding,[],[f21,f28,f27,f25,f23]) ).
tff(f30,definition,
sF4 = $uminus(b),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f31,plain,
$uminus(b) = sF4,
inference(reorient_equations,[],[f30]) ).
tff(f32,definition,
sF5 = $sum(a,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f33,plain,
$sum(a,sF4) = sF5,
inference(reorient_equations,[],[f32]) ).
tff(f34,plain,
~ $less(sF5,0),
inference(definition_folding,[],[f19,f33,f31]) ).
tff(f36,definition,
( spl6_1
<=> ( $uminus(b) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
tff(f39,plain,
spl6_1,
inference(avatar_split_clause,[],[f31,f36]) ).
tff(f40,plain,
$sum(sF4,a) = sF5,
inference(forward_demodulation,[],[f33,f4]) ).
tff(f42,definition,
( spl6_2
<=> $less(sF5,0) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
tff(f45,plain,
~ spl6_2,
inference(avatar_split_clause,[],[f34,f42]) ).
tff(f47,definition,
( spl6_3
<=> ( $uminus(sF1) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
tff(f50,plain,
spl6_3,
inference(avatar_split_clause,[],[f27,f47]) ).
tff(f52,definition,
( spl6_4
<=> ( f(a) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
tff(f54,plain,
( ( f(a) = sF0 )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f52]) ).
tff(f55,plain,
spl6_4,
inference(avatar_split_clause,[],[f23,f52]) ).
tff(f57,definition,
( spl6_5
<=> $less(sF3,0) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
tff(f60,plain,
spl6_5,
inference(avatar_split_clause,[],[f29,f57]) ).
tff(f62,definition,
( spl6_6
<=> ( sF3 = $sum(sF0,sF2) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
tff(f65,plain,
spl6_6,
inference(avatar_split_clause,[],[f28,f62]) ).
tff(f67,definition,
( spl6_7
<=> ( f(b) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
tff(f69,plain,
( ( f(b) = sF1 )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f67]) ).
tff(f70,plain,
spl6_7,
inference(avatar_split_clause,[],[f25,f67]) ).
tff(f72,definition,
( spl6_8
<=> ( $sum(sF4,a) = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
tff(f75,plain,
spl6_8,
inference(avatar_split_clause,[],[f40,f72]) ).
tff(f77,plain,
( ! [X0: $int] :
( ~ $less(sF0,f(X0))
| $less(a,X0) )
| ~ spl6_4 ),
inference(superposition,[],[f20,f54]) ).
tff(f104,plain,
( ~ $less(sF0,sF1)
| $less(a,b)
| ~ spl6_4
| ~ spl6_7 ),
inference(superposition,[],[f77,f69]) ).
tff(f106,definition,
( spl6_13
<=> $less(a,b) ),
introduced(definition,[new_symbols(definition,[spl6_13])],[avatar_definition]) ).
tff(f110,definition,
( spl6_14
<=> $less(sF0,sF1) ),
introduced(definition,[new_symbols(definition,[spl6_14])],[avatar_definition]) ).
tff(f113,plain,
( spl6_13
| ~ spl6_14
| ~ spl6_4
| ~ spl6_7 ),
inference(avatar_split_clause,[],[f104,f67,f52,f110,f106]) ).
tff(f114,plain,
$false,
inference(avatar_smt_refutation,[],[f113,f75,f70,f65,f60,f55,f50,f45,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI609_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n026.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 20:56:27 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 3.02/1.11 % (60801)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.02/1.11 % (60889)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2912873887:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.02/1.11 % (60889)Instruction limit reached!
% 3.02/1.11 % (60889)------------------------------
% 3.02/1.11 % (60889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.11 % (60889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.11 % (60889)CaDiCaL version: 2.1.3
% 3.02/1.11 % (60889)Termination reason: Instruction limit
% 3.02/1.11 % (60889)Termination phase: Saturation
% 3.02/1.11 % (60889)Time elapsed: 0.003 s
% 3.02/1.11 % (60889)Peak memory usage: 89 MB
% 3.02/1.11 % (60889)Instructions burned: 7 (million)
% 3.02/1.11 % (60886)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2405551837:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.02/1.11 % (60885)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2047467311:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.02/1.11 % (60888)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3228647788:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.02/1.11 % (60887)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2314803276:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.02/1.11 % (60890)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3387156903:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.02/1.11 % (60888)Instruction limit reached!
% 3.02/1.11 % (60888)------------------------------
% 3.02/1.11 % (60888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.11 % (60888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.11 % (60888)CaDiCaL version: 2.1.3
% 3.02/1.11 % (60888)Termination reason: Instruction limit
% 3.02/1.11 % (60888)Termination phase: Saturation
% 3.02/1.11 % (60888)Time elapsed: 0.005 s
% 3.02/1.11 % (60888)Peak memory usage: 88 MB
% 3.02/1.11 % (60888)Instructions burned: 7 (million)
% 3.02/1.11 % (60891)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=768212969:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.02/1.11 % (60890)Refutation not found, incomplete strategy
% 3.02/1.11 % (60890)------------------------------
% 3.02/1.11 % (60890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.11 % (60890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.11 % (60890)CaDiCaL version: 2.1.3
% 3.02/1.11 % (60890)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.11 % (60890)Time elapsed: 0.029 s
% 3.02/1.11 % (60890)Peak memory usage: 115 MB
% 3.02/1.11 % (60890)Instructions burned: 6 (million)
% 3.02/1.11 % (60885)Instruction limit reached!
% 3.02/1.11 % (60885)------------------------------
% 3.02/1.11 % (60885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.11 % (60885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.11 % (60885)CaDiCaL version: 2.1.3
% 3.02/1.11 % (60885)Termination reason: Instruction limit
% 3.02/1.11 % (60885)Termination phase: Saturation
% 3.02/1.11 % (60885)Time elapsed: 0.032 s
% 3.02/1.11 % (60885)Peak memory usage: 115 MB
% 3.02/1.11 % (60885)Instructions burned: 13 (million)
% 3.02/1.11 % (60886)Refutation not found, incomplete strategy
% 3.02/1.11 % (60886)------------------------------
% 3.02/1.11 % (60886)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.11 % (60886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.11 % (60886)CaDiCaL version: 2.1.3
% 3.02/1.11 % (60886)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.11 % (60886)Time elapsed: 0.032 s
% 3.02/1.11 % (60886)Peak memory usage: 115 MB
% 3.02/1.11 % (60886)Instructions burned: 10 (million)
% 3.02/1.11 % (60891)First to succeed.
% 3.02/1.11 % (60891)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-60801"
% 3.02/1.11 % (60893)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1602000600:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.02/1.11 % (60893)Refutation not found, incomplete strategy
% 3.02/1.11 % (60893)------------------------------
% 3.02/1.11 % (60893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.25 % (60893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.25 % (60893)CaDiCaL version: 2.1.3
% 3.74/1.25 % (60893)Termination reason: Refutation not found, incomplete strategy
% 3.74/1.25 % (60893)Time elapsed: 0.001 s
% 3.74/1.25 % (60893)Peak memory usage: 88 MB
% 3.74/1.25 % (60887)Also succeeded, but the first one will report.
% 3.74/1.25 % (60900)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=3963275127:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.74/1.25 % (60900)Instruction limit reached!
% 3.74/1.25 % (60900)------------------------------
% 3.74/1.25 % (60900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.25 % (60900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.25 % (60900)CaDiCaL version: 2.1.3
% 3.74/1.25 % (60900)Termination reason: Instruction limit
% 3.74/1.25 % (60900)Termination phase: Saturation
% 3.74/1.25 % (60900)Time elapsed: 0.032 s
% 3.74/1.25 % (60900)Peak memory usage: 88 MB
% 3.74/1.25 % (60900)Instructions burned: 42 (million)
% 3.74/1.25 % (60901)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2524260436:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.74/1.25 % (60901)Also succeeded, but the first one will report.
% 3.74/1.25 % (60893)------------------------------
% 3.74/1.25 % (60893)------------------------------
% 3.74/1.25 % (60886)------------------------------
% 3.74/1.25 % (60886)------------------------------
% 3.74/1.25 % (60890)------------------------------
% 3.74/1.25 % (60890)------------------------------
% 3.74/1.25 % (60891)Refutation found. Thanks to Tanya!
% 3.74/1.25 % SZS status Theorem for theBenchmark
% 3.74/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.74/1.26 % (60891)------------------------------
% 3.74/1.26 % (60891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.26 % (60891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.26 % (60891)CaDiCaL version: 2.1.3
% 3.74/1.26 % (60891)Termination reason: Refutation
% 3.74/1.26 % (60891)Time elapsed: 0.038 s
% 3.74/1.26 % (60891)Peak memory usage: 116 MB
% 3.74/1.26 % (60891)Instructions burned: 16 (million)
% 3.74/1.26 % (60891)------------------------------
% 3.74/1.26 % (60891)------------------------------
% 3.74/1.26 % (60801)Success in time 0.453 s
% 3.74/1.26 % Vampire exiting
%------------------------------------------------------------------------------