%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI613_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 : n013.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 09:33:29 AM UTC 2026
% Result : Theorem 5.99s 1.74s
% Output : Refutation 5.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 10 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 82 ( 32 ~; 26 |; 15 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 119 ( 22 atm; 20 fun; 38 num; 39 var)
% Number of types : 2 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 2 usr; 7 con; 0-2 aty)
% Number of variables : 39 ( 33 !; 6 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_5,type,
'$inst0': $int ).
tff(func_def_7,type,
'$inst1': $int ).
tff(pred_def_1,type,
p: $int > $o ).
tff(pred_def_2,type,
q: $int > $o ).
tff(f1,conjecture,
( ( ! [X0: $int] :
( $less(3,X0)
=> p(X0) )
& ! [X0: $int] :
( $less(X0,1)
=> q(X0) ) )
=> ? [X1: $int,X0: $int] :
( q(X1)
& p(X0)
& ( $sum(X0,X1) = 0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interv_3_infty_and_neginfty_1_contain_compl) ).
tff(f2,negated_conjecture,
~ ( ( ! [X0: $int] :
( $less(3,X0)
=> p(X0) )
& ! [X0: $int] :
( $less(X0,1)
=> q(X0) ) )
=> ? [X1: $int,X0: $int] :
( q(X1)
& p(X0)
& ( $sum(X0,X1) = 0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f7,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f12,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f13,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(definition,[],[tha_minus_minus_x]) ).
tff(f15,plain,
~ ( ( ! [X1: $int] :
( $less(X1,1)
=> q(X1) )
& ! [X0: $int] :
( $less(3,X0)
=> p(X0) ) )
=> ? [X3: $int,X2: $int] :
( ( 0 = $sum(X3,X2) )
& q(X2)
& p(X3) ) ),
inference(rectify,[],[f2]) ).
tff(f16,plain,
( ! [X3: $int,X2: $int] :
( ( 0 != $sum(X3,X2) )
| ~ p(X3)
| ~ q(X2) )
& ! [X1: $int] :
( ~ $less(X1,1)
| q(X1) )
& ! [X0: $int] :
( p(X0)
| ~ $less(3,X0) ) ),
inference(ennf_transformation,[],[f15]) ).
tff(f17,plain,
( ! [X1: $int] :
( ~ $less(X1,1)
| q(X1) )
& ! [X0: $int] :
( p(X0)
| ~ $less(3,X0) )
& ! [X3: $int,X2: $int] :
( ( 0 != $sum(X3,X2) )
| ~ p(X3)
| ~ q(X2) ) ),
inference(flattening,[],[f16]) ).
tff(f18,plain,
( ! [X0: $int] :
( ~ $less(X0,1)
| q(X0) )
& ! [X1: $int] :
( p(X1)
| ~ $less(3,X1) )
& ! [X2: $int,X3: $int] :
( ( 0 != $sum(X2,X3) )
| ~ p(X2)
| ~ q(X3) ) ),
inference(rectify,[],[f17]) ).
tff(f19,plain,
! [X2: $int,X3: $int] :
( ( 0 != $sum(X2,X3) )
| ~ q(X3)
| ~ p(X2) ),
inference(cnf_transformation,[],[f18]) ).
tff(f20,plain,
! [X1: $int] :
( ~ $less(3,X1)
| p(X1) ),
inference(cnf_transformation,[],[f18]) ).
tff(f21,plain,
! [X0: $int] :
( ~ $less(X0,1)
| q(X0) ),
inference(cnf_transformation,[],[f18]) ).
tff(f33,plain,
! [X0: $int] :
( ~ p(X0)
| ( 0 != 0 )
| ~ q($uminus(X0)) ),
inference(superposition,[],[f19,f7]) ).
tff(f34,plain,
! [X0: $int] :
( ~ q($uminus(X0))
| ~ p(X0) ),
inference(trivial_inequality_removal,[],[f33]) ).
tff(f35,plain,
! [X0: $int] :
( ~ p($uminus(X0))
| ~ q(X0) ),
inference(superposition,[],[f34,f13]) ).
tff(f52,plain,
! [X0: $int] :
( p(X0)
| $less(X0,$sum(3,1)) ),
inference(resolution,[],[f12,f20]) ).
tff(f53,plain,
! [X0: $int] :
( q(X0)
| $less(1,$sum(X0,1)) ),
inference(resolution,[],[f12,f21]) ).
tff(f58,plain,
! [X0: $int] :
( p(X0)
| $less(X0,4) ),
inference(evaluation,[],[f52]) ).
tff(f62,plain,
! [X0: $int] :
( ~ q(X0)
| $less($uminus(X0),4) ),
inference(resolution,[],[f58,f35]) ).
tff(f63,plain,
( ~ q(-4)
| $less($uminus(-4),4) ),
inference(instantiation,[],[f62]) ).
tff(f64,plain,
~ q(-4),
inference(interpreted_simplification,[],[f63]) ).
tff(f74,plain,
$less(1,$sum(-4,1)),
inference(resolution,[],[f53,f64]) ).
tff(f75,plain,
$false,
inference(evaluation,[],[f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI613_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 % Computer : n013.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Mon Sep 28 20:53:06 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.29 Running first-order theorem proving
% 0.26/0.29 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
% 5.99/1.74 % (1565137)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.99/1.74 % (1565142)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1595887514:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.99/1.74 % (1565145)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3946552065:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.99/1.74 % (1565145)Instruction limit reached!
% 5.99/1.74 % (1565145)------------------------------
% 5.99/1.74 % (1565145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.99/1.74 % (1565145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.99/1.74 % (1565145)CaDiCaL version: 2.1.3
% 5.99/1.74 % (1565145)Termination reason: Instruction limit
% 5.99/1.74 % (1565145)Termination phase: Saturation
% 5.99/1.74 % (1565145)Time elapsed: 0.007 s
% 5.99/1.74 % (1565145)Peak memory usage: 88 MB
% 5.99/1.74 % (1565145)Instructions burned: 8 (million)
% 5.99/1.74 % (1565142)Instruction limit reached!
% 5.99/1.74 % (1565142)------------------------------
% 5.99/1.74 % (1565142)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.99/1.74 % (1565142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.99/1.74 % (1565142)CaDiCaL version: 2.1.3
% 5.99/1.74 % (1565142)Termination reason: Instruction limit
% 5.99/1.74 % (1565142)Termination phase: Saturation
% 5.99/1.74 % (1565142)Time elapsed: 0.026 s
% 5.99/1.74 % (1565142)Peak memory usage: 115 MB
% 5.99/1.74 % (1565142)Instructions burned: 13 (million)
% 5.99/1.74 % (1565143)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3487971621:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.99/1.74 % (1565146)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=951517215:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.99/1.74 % (1565144)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1255630853:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.99/1.74 % (1565146)Instruction limit reached!
% 5.99/1.74 % (1565146)------------------------------
% 5.99/1.74 % (1565146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.99/1.74 % (1565146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.99/1.74 % (1565146)CaDiCaL version: 2.1.3
% 5.99/1.74 % (1565146)Termination reason: Instruction limit
% 5.99/1.74 % (1565146)Termination phase: Saturation
% 5.99/1.74 % (1565146)Time elapsed: 0.005 s
% 5.99/1.74 % (1565146)Peak memory usage: 88 MB
% 5.99/1.74 % (1565146)Instructions burned: 4 (million)
% 5.99/1.74 % (1565147)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2440979872:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.99/1.74 % (1565148)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2456627181:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.99/1.74 % (1565143)Refutation not found, incomplete strategy
% 5.99/1.74 % (1565143)------------------------------
% 5.99/1.74 % (1565143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.99/1.74 % (1565143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.99/1.74 % (1565143)CaDiCaL version: 2.1.3
% 5.99/1.74 % (1565143)Termination reason: Refutation not found, incomplete strategy
% 5.99/1.74 % (1565143)Time elapsed: 0.036 s
% 5.99/1.74 % (1565143)Peak memory usage: 112 MB
% 5.99/1.74 % (1565143)Instructions burned: 5 (million)
% 5.99/1.74 % (1565144)First to succeed.
% 5.99/1.74 % (1565144)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1565137"
% 5.99/1.74 % (1565147)Refutation not found, incomplete strategy
% 5.99/1.74 % (1565147)------------------------------
% 5.99/1.74 % (1565147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.99/1.74 % (1565147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.99/1.74 % (1565147)CaDiCaL version: 2.1.3
% 5.99/1.74 % (1565147)Termination reason: Refutation not found, incomplete strategy
% 5.99/1.74 % (1565147)Time elapsed: 0.037 s
% 5.99/1.74 % (1565147)Peak memory usage: 112 MB
% 5.99/1.74 % (1565147)Instructions burned: 5 (million)
% 5.99/1.74 % (1565148)Also succeeded, but the first one will report.
% 5.99/1.74 % (1565151)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2170943131:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 5.99/1.74 % (1565151)Refutation not found, incomplete strategy
% 5.99/1.74 % (1565151)------------------------------
% 5.99/1.74 % (1565151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.99/1.74 % (1565151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.99/1.74 % (1565151)CaDiCaL version: 2.1.3
% 5.99/1.74 % (1565151)Termination reason: Refutation not found, incomplete strategy
% 5.99/1.74 % (1565151)Time elapsed: 0.001 s
% 5.99/1.74 % (1565151)Peak memory usage: 88 MB
% 5.99/1.74 % (1565152)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=1424871384:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 5.99/1.74 % (1565152)Instruction limit reached!
% 5.99/1.74 % (1565152)------------------------------
% 5.99/1.74 % (1565152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.99/1.74 % (1565152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.99/1.74 % (1565152)CaDiCaL version: 2.1.3
% 5.99/1.74 % (1565152)Termination reason: Instruction limit
% 5.99/1.74 % (1565152)Termination phase: Saturation
% 5.99/1.74 % (1565152)Time elapsed: 0.026 s
% 5.99/1.74 % (1565152)Peak memory usage: 88 MB
% 5.99/1.74 % (1565152)Instructions burned: 29 (million)
% 5.99/1.74 % (1565156)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=4019710412:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 5.99/1.74 % (1565156)Refutation not found, incomplete strategy
% 5.99/1.74 % (1565156)------------------------------
% 5.99/1.74 % (1565156)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.99/1.74 % (1565156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.99/1.74 % (1565156)CaDiCaL version: 2.1.3
% 5.99/1.74 % (1565156)Termination reason: Refutation not found, incomplete strategy
% 5.99/1.74 % (1565156)Time elapsed: 0.012 s
% 5.99/1.74 % (1565156)Peak memory usage: 90 MB
% 5.99/1.74 % (1565156)Instructions burned: 10 (million)
% 5.99/1.74 % (1565151)------------------------------
% 5.99/1.74 % (1565151)------------------------------
% 5.99/1.74 % (1565143)------------------------------
% 5.99/1.74 % (1565143)------------------------------
% 5.99/1.74 % (1565147)------------------------------
% 5.99/1.74 % (1565147)------------------------------
% 5.99/1.74 % (1565144)Refutation found. Thanks to Tanya!
% 5.99/1.74 % SZS status Theorem for theBenchmark
% 5.99/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 5.99/1.74 % (1565144)------------------------------
% 5.99/1.74 % (1565144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.99/1.74 % (1565144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.99/1.74 % (1565144)CaDiCaL version: 2.1.3
% 5.99/1.74 % (1565144)Termination reason: Refutation
% 5.99/1.74 % (1565144)Time elapsed: 0.051 s
% 5.99/1.74 % (1565144)Peak memory usage: 116 MB
% 5.99/1.74 % (1565144)Instructions burned: 14 (million)
% 5.99/1.74 % (1565144)------------------------------
% 5.99/1.74 % (1565144)------------------------------
% 5.99/1.74 % (1565137)Success in time 0.736 s
% 5.99/1.74 % Vampire exiting
%------------------------------------------------------------------------------