%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI733_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 : 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 09:33:45 AM UTC 2026
% Result : Theorem 5.78s 1.89s
% Output : Refutation 5.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 37 ( 13 ~; 12 |; 12 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 149 ( 32 atm; 48 fun; 55 num; 14 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 : 4 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 2 usr; 10 con; 0-2 aty)
% Number of variables : 14 ( 6 !; 8 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_11,type,
'$inst0': $real ).
tff(func_def_12,type,
'$inst1': $real ).
tff(f1,conjecture,
? [X1: $real,X0: $real] :
( $is_int(X0)
& $lesseq($sum($product(4/1,X0),X1),61/2)
& $lesseq($sum($product(-3/2,X0),X1),1/4)
& $lesseq($sum(X0,$product(-5/2,X1)),-13/1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
tff(f2,negated_conjecture,
~ ? [X1: $real,X0: $real] :
( $is_int(X0)
& $lesseq($sum($product(4/1,X0),X1),61/2)
& $lesseq($sum($product(-3/2,X0),X1),1/4)
& $lesseq($sum(X0,$product(-5/2,X1)),-13/1) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ? [X1: $real,X0: $real] :
( $is_int(X0)
& ~ $less(61/2,$sum($product(4/1,X0),X1))
& ~ $less(1/4,$sum($product(-3/2,X0),X1))
& ~ $less(-13/1,$sum(X0,$product(-5/2,X1))) ),
inference(theory_normalization,[],[f2]) ).
tff(f21,plain,
~ ? [X1: $real,X0: $real] :
( $is_int(X1)
& ~ $less(1/4,$sum($product(-3/2,X1),X0))
& ~ $less(-13/1,$sum(X1,$product(-5/2,X0)))
& ~ $less(61/2,$sum($product(4/1,X1),X0)) ),
inference(rectify,[],[f3]) ).
tff(f22,plain,
! [X1: $real,X0: $real] :
( $less(1/4,$sum($product(-3/2,X1),X0))
| $less(-13/1,$sum(X1,$product(-5/2,X0)))
| ~ $is_int(X1)
| $less(61/2,$sum($product(4/1,X1),X0)) ),
inference(ennf_transformation,[],[f21]) ).
tff(f23,plain,
! [X0: $real,X1: $real] :
( $less(1/4,$sum($product(-3/2,X0),X1))
| $less(-13/1,$sum(X0,$product(-5/2,X1)))
| ~ $is_int(X0)
| $less(61/2,$sum($product(4/1,X0),X1)) ),
inference(rectify,[],[f22]) ).
tff(f24,plain,
! [X0: $real,X1: $real] :
( ~ $is_int(X0)
| $less(61/2,$sum($product(4/1,X0),X1))
| $less(1/4,$sum($product(-3/2,X0),X1))
| $less(-13/1,$sum(X0,$product(-5/2,X1))) ),
inference(cnf_transformation,[],[f23]) ).
tff(f26,plain,
( ~ $is_int(5/1)
| $less(61/2,$sum($product(4/1,5/1),36/5))
| $less(1/4,$sum($product(-3/2,5/1),36/5))
| $less(-13/1,$sum(5/1,$product(-5/2,36/5))) ),
inference(instantiation,[],[f24]) ).
tff(f27,plain,
$false,
inference(interpreted_simplification,[],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI733_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n026.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Mon Sep 28 21:04:27 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running first-order theorem proving
% 0.25/0.31 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
% 5.78/1.89 % (69086)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.78/1.89 % (69103)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2008966526:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.78/1.89 % (69103)Instruction limit reached!
% 5.78/1.89 % (69103)------------------------------
% 5.78/1.89 % (69103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.78/1.89 % (69103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.89 % (69103)CaDiCaL version: 2.1.3
% 5.78/1.89 % (69103)Termination reason: Instruction limit
% 5.78/1.89 % (69103)Termination phase: Saturation
% 5.78/1.89 % (69103)Time elapsed: 0.026 s
% 5.78/1.89 % (69103)Peak memory usage: 112 MB
% 5.78/1.89 % (69103)Instructions burned: 34 (million)
% 5.78/1.89 % (69097)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4110756257:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.78/1.89 % (69098)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3157665024:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.78/1.89 % (69100)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2344793538:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.78/1.89 % (69102)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=701683591:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.78/1.89 % (69101)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=180414768:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.78/1.89 % (69101)Instruction limit reached!
% 5.78/1.89 % (69101)------------------------------
% 5.78/1.89 % (69101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.78/1.89 % (69101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.89 % (69101)CaDiCaL version: 2.1.3
% 5.78/1.89 % (69101)Termination reason: Instruction limit
% 5.78/1.89 % (69101)Termination phase: Saturation
% 5.78/1.89 % (69101)Time elapsed: 0.005 s
% 5.78/1.89 % (69101)Peak memory usage: 88 MB
% 5.78/1.89 % (69101)Instructions burned: 4 (million)
% 5.78/1.89 % (69100)Instruction limit reached!
% 5.78/1.89 % (69100)------------------------------
% 5.78/1.89 % (69100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.78/1.89 % (69100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.89 % (69100)CaDiCaL version: 2.1.3
% 5.78/1.89 % (69100)Termination reason: Instruction limit
% 5.78/1.89 % (69100)Termination phase: Saturation
% 5.78/1.89 % (69100)Time elapsed: 0.006 s
% 5.78/1.89 % (69100)Peak memory usage: 88 MB
% 5.78/1.89 % (69100)Instructions burned: 7 (million)
% 5.78/1.89 % (69105)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3311082580:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 5.78/1.89 % (69105)Refutation not found, incomplete strategy
% 5.78/1.89 % (69105)------------------------------
% 5.78/1.89 % (69105)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.78/1.89 % (69105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.89 % (69105)CaDiCaL version: 2.1.3
% 5.78/1.89 % (69105)Termination reason: Refutation not found, incomplete strategy
% 5.78/1.89 % (69105)Time elapsed: 0.0000 s
% 5.78/1.89 % (69105)Peak memory usage: 88 MB
% 5.78/1.89 % (69098)Refutation not found, incomplete strategy
% 5.78/1.89 % (69098)------------------------------
% 5.78/1.89 % (69098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.78/1.89 % (69098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.89 % (69098)CaDiCaL version: 2.1.3
% 5.78/1.89 % (69098)Termination reason: Refutation not found, incomplete strategy
% 5.78/1.89 % (69098)Time elapsed: 0.037 s
% 5.78/1.89 % (69098)Peak memory usage: 111 MB
% 5.78/1.89 % (69098)Instructions burned: 5 (million)
% 5.78/1.89 % (69097)Instruction limit reached!
% 5.78/1.89 % (69097)------------------------------
% 5.78/1.89 % (69097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.78/1.89 % (69097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.89 % (69097)CaDiCaL version: 2.1.3
% 5.78/1.89 % (69097)Termination reason: Instruction limit
% 5.78/1.89 % (69097)Termination phase: Saturation
% 5.78/1.89 % (69097)Time elapsed: 0.040 s
% 5.78/1.89 % (69097)Peak memory usage: 112 MB
% 5.78/1.89 % (69097)Instructions burned: 12 (million)
% 5.78/1.89 % (69099)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3268773773:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.78/1.89 % (69102)Refutation not found, incomplete strategy
% 5.78/1.89 % (69102)------------------------------
% 5.78/1.89 % (69102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.78/1.89 % (69102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.89 % (69102)CaDiCaL version: 2.1.3
% 5.78/1.89 % (69102)Termination reason: Refutation not found, incomplete strategy
% 5.78/1.89 % (69102)Time elapsed: 0.037 s
% 5.78/1.89 % (69102)Peak memory usage: 111 MB
% 5.78/1.89 % (69102)Instructions burned: 5 (million)
% 5.78/1.89 % (69099)First to succeed.
% 5.78/1.89 % (69099)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-69086"
% 5.78/1.89 % (69113)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2350671799:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 5.78/1.89 % (69113)Refutation not found, incomplete strategy
% 5.78/1.89 % (69113)------------------------------
% 5.78/1.89 % (69113)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.78/1.89 % (69113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.89 % (69113)CaDiCaL version: 2.1.3
% 5.78/1.89 % (69113)Termination reason: Refutation not found, incomplete strategy
% 5.78/1.89 % (69113)Time elapsed: 0.007 s
% 5.78/1.89 % (69113)Peak memory usage: 90 MB
% 5.78/1.89 % (69113)Instructions burned: 14 (million)
% 5.78/1.89 % (69112)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=3441596184:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 5.78/1.89 % (69115)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=2195132277:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 5.78/1.89 % (69112)Instruction limit reached!
% 5.78/1.89 % (69112)------------------------------
% 5.78/1.89 % (69112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.78/1.89 % (69112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.89 % (69112)CaDiCaL version: 2.1.3
% 5.78/1.89 % (69112)Termination reason: Instruction limit
% 5.78/1.89 % (69112)Termination phase: Saturation
% 5.78/1.89 % (69112)Time elapsed: 0.025 s
% 5.78/1.89 % (69112)Peak memory usage: 88 MB
% 5.78/1.89 % (69112)Instructions burned: 30 (million)
% 5.78/1.89 % (69115)Instruction limit reached!
% 5.78/1.89 % (69115)------------------------------
% 5.78/1.89 % (69115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.78/1.89 % (69115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.89 % (69115)CaDiCaL version: 2.1.3
% 5.78/1.89 % (69115)Termination reason: Instruction limit
% 5.78/1.89 % (69115)Termination phase: Saturation
% 5.78/1.89 % (69115)Time elapsed: 0.025 s
% 5.78/1.89 % (69115)Peak memory usage: 89 MB
% 5.78/1.89 % (69115)Instructions burned: 24 (million)
% 5.78/1.89 % (69119)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=3756589107:i=27:canc=cautious:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/27Mi)
% 5.78/1.89 % (69113)------------------------------
% 5.78/1.89 % (69113)------------------------------
% 5.78/1.89 % (69105)------------------------------
% 5.78/1.89 % (69105)------------------------------
% 5.78/1.89 % (69119)Instruction limit reached!
% 5.78/1.89 % (69119)------------------------------
% 5.78/1.89 % (69119)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.78/1.89 % (69119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.89 % (69119)CaDiCaL version: 2.1.3
% 5.78/1.89 % (69119)Termination reason: Instruction limit
% 5.78/1.89 % (69119)Termination phase: Saturation
% 5.78/1.89 % (69119)Time elapsed: 0.018 s
% 5.78/1.89 % (69119)Peak memory usage: 89 MB
% 5.78/1.89 % (69119)Instructions burned: 30 (million)
% 5.78/1.89 % (69098)------------------------------
% 5.78/1.89 % (69098)------------------------------
% 5.78/1.89 % (69102)------------------------------
% 5.78/1.89 % (69102)------------------------------
% 5.78/1.89 % (69099)Refutation found. Thanks to Tanya!
% 5.78/1.89 % SZS status Theorem for theBenchmark
% 5.78/1.89 % SZS output start Proof for theBenchmark
% See solution above
% 5.78/1.89 % (69099)------------------------------
% 5.78/1.89 % (69099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.78/1.89 % (69099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.78/1.89 % (69099)CaDiCaL version: 2.1.3
% 5.78/1.89 % (69099)Termination reason: Refutation
% 5.78/1.89 % (69099)Time elapsed: 0.043 s
% 5.78/1.89 % (69099)Peak memory usage: 116 MB
% 5.78/1.89 % (69099)Instructions burned: 9 (million)
% 5.78/1.89 % (69099)------------------------------
% 5.78/1.89 % (69099)------------------------------
% 5.78/1.89 % (69086)Success in time 0.687 s
% 5.78/1.89 % Vampire exiting
%------------------------------------------------------------------------------