%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI610_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 : n016.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 2.68s 1.16s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 19
% Syntax : Number of formulae : 61 ( 24 unt; 0 typ; 18 def)
% Number of atoms : 120 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 96 ( 37 ~; 32 |; 9 &)
% ( 12 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 98 ( 47 atm; 20 fun; 16 num; 15 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 : 16 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?; 15 :)
% 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_6,type,
sF0: $int ).
tff(func_def_7,type,
sF1: $int ).
tff(func_def_8,type,
sF2: $int ).
tff(func_def_9,type,
sF3: $int ).
tff(func_def_10,type,
sF4: $int ).
tff(func_def_11,type,
sF5: $int ).
tff(f1,conjecture,
( ( ! [X0: $int,X1: $int] :
( $lesseq(X0,X1)
=> $lesseq(f(X0),f(X1)) )
& $less(f(b),f(a)) )
=> $lesseq(f(0),f($sum(a,$uminus(b)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_mon_implies_f_a_b_2) ).
tff(f2,negated_conjecture,
~ ( ( ! [X0: $int,X1: $int] :
( $lesseq(X0,X1)
=> $lesseq(f(X0),f(X1)) )
& $less(f(b),f(a)) )
=> $lesseq(f(0),f($sum(a,$uminus(b)))) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( $less(f(b),f(a))
& ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
=> ~ $less(f(X1),f(X0)) ) )
=> ~ $less(f($sum(a,$uminus(b))),f(0)) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
( $less(f($sum(a,$uminus(b))),f(0))
& $less(f(b),f(a))
& ! [X1: $int,X0: $int] :
( $less(X1,X0)
| ~ $less(f(X1),f(X0)) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
( $less(f(b),f(a))
& $less(f($sum(a,$uminus(b))),f(0))
& ! [X1: $int,X0: $int] :
( $less(X1,X0)
| ~ $less(f(X1),f(X0)) ) ),
inference(flattening,[],[f4]) ).
tff(f6,plain,
( $less(f(b),f(a))
& $less(f($sum(a,$uminus(b))),f(0))
& ! [X0: $int,X1: $int] :
( $less(X0,X1)
| ~ $less(f(X0),f(X1)) ) ),
inference(rectify,[],[f5]) ).
tff(f7,plain,
! [X0: $int,X1: $int] :
( ~ $less(f(X0),f(X1))
| $less(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tff(f8,plain,
$less(f($sum(a,$uminus(b))),f(0)),
inference(cnf_transformation,[],[f6]) ).
tff(f9,plain,
$less(f(b),f(a)),
inference(cnf_transformation,[],[f6]) ).
tff(f10,definition,
sF0 = f(b),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f11,plain,
f(b) = sF0,
inference(reorient_equations,[],[f10]) ).
tff(f12,definition,
sF1 = f(a),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f13,plain,
f(a) = sF1,
inference(reorient_equations,[],[f12]) ).
tff(f14,plain,
$less(sF0,sF1),
inference(definition_folding,[],[f9,f13,f11]) ).
tff(f15,definition,
sF2 = $uminus(b),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f16,plain,
$uminus(b) = sF2,
inference(reorient_equations,[],[f15]) ).
tff(f17,definition,
sF3 = $sum(a,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f18,plain,
$sum(a,sF2) = sF3,
inference(reorient_equations,[],[f17]) ).
tff(f19,definition,
sF4 = f(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f20,definition,
sF5 = f(0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f21,plain,
f(0) = sF5,
inference(reorient_equations,[],[f20]) ).
tff(f22,plain,
$less(sF4,sF5),
inference(definition_folding,[],[f8,f21,f19,f18,f16]) ).
tff(f24,definition,
( spl6_1
<=> $less(sF4,sF5) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
tff(f26,plain,
( $less(sF4,sF5)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f24]) ).
tff(f27,plain,
spl6_1,
inference(avatar_split_clause,[],[f22,f24]) ).
tff(f29,definition,
( spl6_2
<=> ( f(a) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
tff(f31,plain,
( ( f(a) = sF1 )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f29]) ).
tff(f32,plain,
spl6_2,
inference(avatar_split_clause,[],[f13,f29]) ).
tff(f34,definition,
( spl6_3
<=> $less(sF0,sF1) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
tff(f36,plain,
( $less(sF0,sF1)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f34]) ).
tff(f37,plain,
spl6_3,
inference(avatar_split_clause,[],[f14,f34]) ).
tff(f39,definition,
( spl6_4
<=> ( f(0) = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
tff(f41,plain,
( ( f(0) = sF5 )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f42,plain,
spl6_4,
inference(avatar_split_clause,[],[f21,f39]) ).
tff(f44,definition,
( spl6_5
<=> ( sF4 = f(sF3) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
tff(f46,plain,
( ( sF4 = f(sF3) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f44]) ).
tff(f47,plain,
spl6_5,
inference(avatar_split_clause,[],[f19,f44]) ).
tff(f49,definition,
( spl6_6
<=> ( $uminus(b) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
tff(f52,plain,
spl6_6,
inference(avatar_split_clause,[],[f16,f49]) ).
tff(f54,definition,
( spl6_7
<=> ( $sum(a,sF2) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
tff(f57,plain,
spl6_7,
inference(avatar_split_clause,[],[f18,f54]) ).
tff(f59,definition,
( spl6_8
<=> ( f(b) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
tff(f61,plain,
( ( f(b) = sF0 )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f59]) ).
tff(f62,plain,
spl6_8,
inference(avatar_split_clause,[],[f11,f59]) ).
tff(f63,plain,
( $less(sF0,f(a))
| ~ spl6_2
| ~ spl6_3 ),
inference(superposition,[],[f36,f31]) ).
tff(f65,definition,
( spl6_9
<=> $less(sF0,f(a)) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
tff(f67,plain,
( $less(sF0,f(a))
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f65]) ).
tff(f68,plain,
( spl6_9
| ~ spl6_2
| ~ spl6_3 ),
inference(avatar_split_clause,[],[f63,f34,f29,f65]) ).
tff(f76,plain,
( $less(f(sF3),sF5)
| ~ spl6_1
| ~ spl6_5 ),
inference(superposition,[],[f26,f46]) ).
tff(f77,plain,
( $less(f(sF3),f(0))
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5 ),
inference(forward_demodulation,[],[f76,f41]) ).
tff(f79,definition,
( spl6_11
<=> $less(f(sF3),f(0)) ),
introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition]) ).
tff(f81,plain,
( $less(f(sF3),f(0))
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f79]) ).
tff(f83,plain,
( spl6_11
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f77,f44,f39,f24,f79]) ).
tff(f84,plain,
( $less(sF3,0)
| ~ spl6_11 ),
inference(resolution,[],[f81,f7]) ).
tff(f86,definition,
( spl6_12
<=> $less(sF3,0) ),
introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition]) ).
tff(f89,plain,
( spl6_12
| ~ spl6_11 ),
inference(avatar_split_clause,[],[f84,f79,f86]) ).
tff(f91,plain,
( ! [X0: $int] :
( ~ $less(sF0,f(X0))
| $less(b,X0) )
| ~ spl6_8 ),
inference(superposition,[],[f7,f61]) ).
tff(f102,plain,
( $less(b,a)
| ~ spl6_8
| ~ spl6_9 ),
inference(resolution,[],[f91,f67]) ).
tff(f105,definition,
( spl6_15
<=> $less(b,a) ),
introduced(definition,[new_symbols(definition,[spl6_15])],[avatar_definition]) ).
tff(f108,plain,
( spl6_15
| ~ spl6_8
| ~ spl6_9 ),
inference(avatar_split_clause,[],[f102,f65,f59,f105]) ).
tff(f109,plain,
$false,
inference(avatar_smt_refutation,[],[f108,f89,f83,f68,f62,f57,f52,f47,f42,f37,f32,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI610_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 : n016.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 20:58:34 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
% 2.68/1.16 % (3997299)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.68/1.16 % (3997328)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3887984111:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.68/1.16 % (3997328)First to succeed.
% 2.68/1.16 % (3997328)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3997299"
% 2.68/1.16 % (3997329)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1875729684:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.68/1.16 % (3997327)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1447716553:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.68/1.16 % (3997333)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2732303693:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.68/1.16 % (3997331)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3704485259:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.68/1.16 % (3997332)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2611151058:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.68/1.16 % (3997331)Instruction limit reached!
% 2.68/1.16 % (3997331)------------------------------
% 2.68/1.16 % (3997331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.16 % (3997331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.16 % (3997331)CaDiCaL version: 2.1.3
% 2.68/1.16 % (3997331)Termination reason: Instruction limit
% 2.68/1.16 % (3997331)Termination phase: Saturation
% 2.68/1.16 % (3997331)Time elapsed: 0.004 s
% 2.68/1.16 % (3997331)Peak memory usage: 88 MB
% 2.68/1.16 % (3997331)Instructions burned: 4 (million)
% 2.68/1.16 % (3997327)Instruction limit reached!
% 2.68/1.16 % (3997327)------------------------------
% 2.68/1.16 % (3997327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.16 % (3997327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.16 % (3997327)CaDiCaL version: 2.1.3
% 2.68/1.16 % (3997327)Termination reason: Instruction limit
% 2.68/1.16 % (3997327)Termination phase: Saturation
% 2.68/1.16 % (3997327)Time elapsed: 0.030 s
% 2.68/1.16 % (3997327)Peak memory usage: 115 MB
% 2.68/1.16 % (3997327)Instructions burned: 12 (million)
% 2.68/1.16 % (3997330)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3485488048:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.68/1.16 % (3997330)Instruction limit reached!
% 2.68/1.16 % (3997330)------------------------------
% 2.68/1.16 % (3997330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.16 % (3997330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.16 % (3997330)CaDiCaL version: 2.1.3
% 2.68/1.16 % (3997330)Termination reason: Instruction limit
% 2.68/1.16 % (3997330)Termination phase: Saturation
% 2.68/1.16 % (3997330)Time elapsed: 0.005 s
% 2.68/1.16 % (3997330)Peak memory usage: 88 MB
% 2.68/1.16 % (3997330)Instructions burned: 7 (million)
% 2.68/1.16 % (3997333)Also succeeded, but the first one will report.
% 2.68/1.16 % (3997332)Also succeeded, but the first one will report.
% 2.68/1.16 % (3997329)Also succeeded, but the first one will report.
% 2.68/1.16 % (3997328)Refutation found. Thanks to Tanya!
% 2.68/1.16 % SZS status Theorem for theBenchmark
% 2.68/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.16 % (3997328)------------------------------
% 2.68/1.16 % (3997328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.16 % (3997328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.16 % (3997328)CaDiCaL version: 2.1.3
% 2.68/1.16 % (3997328)Termination reason: Refutation
% 2.68/1.16 % (3997328)Time elapsed: 0.024 s
% 2.68/1.16 % (3997328)Peak memory usage: 116 MB
% 2.68/1.16 % (3997328)Instructions burned: 20 (million)
% 2.68/1.16 % (3997328)------------------------------
% 2.68/1.16 % (3997328)------------------------------
% 2.68/1.16 % (3997299)Success in time 0.277 s
% 2.68/1.16 % Vampire exiting
%------------------------------------------------------------------------------