%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN000_5 : TPTP v9.3.1. Bugfixed v5.5.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 01:48:47 PM UTC 2026
% Result : Theorem 0.30s 1.81s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 9 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 27 ( 14 ~; 7 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 103 ( 16 atm; 38 fun; 27 num; 22 var)
% Number of types : 4 ( 0 usr; 3 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 9 usr; 10 con; 0-2 aty)
% Number of variables : 22 ( 11 !; 11 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a_int: $int ).
tff(func_def_1,type,
a_rat: $rat ).
tff(func_def_2,type,
a_real: $real ).
tff(func_def_77,type,
sK0: $real > $real ).
tff(func_def_78,type,
sK1: $real ).
tff(func_def_79,type,
sK2: $rat ).
tff(func_def_80,type,
sK3: $int > $int ).
tff(func_def_81,type,
sK4: $real ).
tff(func_def_82,type,
sK5: $rat > $rat ).
tff(pred_def_1,type,
p_int: $int > $o ).
tff(pred_def_2,type,
p_rat: $rat > $o ).
tff(pred_def_3,type,
p_real: $real > $o ).
tff(f77,conjecture,
? [X2: $real,X0: $int,X1: $rat] :
( ( X1 = $to_rat($sum(X0,2)) )
& ( $greater($to_real(X1),33/10)
| $less($to_int(X1),3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mixed) ).
tff(f78,negated_conjecture,
~ ? [X2: $real,X0: $int,X1: $rat] :
( ( X1 = $to_rat($sum(X0,2)) )
& ( $greater($to_real(X1),33/10)
| $less($to_int(X1),3) ) ),
inference(negated_conjecture,[status(cth)],[f77]) ).
tff(f92,plain,
~ ? [X2: $real,X0: $int,X1: $rat] :
( ( X1 = $to_rat($sum(X0,2)) )
& ( $less(33/10,$to_real(X1))
| $less($to_int(X1),3) ) ),
inference(theory_normalization,[],[f78]) ).
tff(f104,plain,
! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f106,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f181,plain,
~ ? [X1: $int,X2: $rat] :
( ( $to_rat($sum(X1,2)) = X2 )
& ( $less(33/10,$to_real(X2))
| $less($to_int(X2),3) ) ),
inference(rectify,[],[f92]) ).
tff(f187,plain,
! [X2: $rat,X1: $int] :
( ( ~ $less($to_int(X2),3)
& ~ $less(33/10,$to_real(X2)) )
| ( $to_rat($sum(X1,2)) != X2 ) ),
inference(ennf_transformation,[],[f181]) ).
tff(f189,plain,
! [X0: $rat,X1: $int] :
( ( ~ $less($to_int(X0),3)
& ~ $less(33/10,$to_real(X0)) )
| ( $to_rat($sum(X1,2)) != X0 ) ),
inference(rectify,[],[f187]) ).
tff(f218,plain,
! [X0: $rat,X1: $int] :
( ~ $less($to_int(X0),3)
| ( $to_rat($sum(X1,2)) != X0 ) ),
inference(cnf_transformation,[],[f189]) ).
tff(f283,plain,
! [X1: $int] : ~ $less($to_int($to_rat($sum(X1,2))),3),
inference(equality_resolution,[],[f218]) ).
tff(f552,plain,
! [X0: $int] : ~ $less($to_int($to_rat($sum(2,X0))),3),
inference(superposition,[],[f283,f104]) ).
tff(f565,plain,
~ $less($to_int($to_rat(2)),3),
inference(superposition,[],[f552,f106]) ).
tff(f569,plain,
$false,
inference(evaluation,[],[f565]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN000_5 : TPTP v9.3.1. Bugfixed v5.5.1.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n014.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Mon Sep 28 15:18:47 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.31 Running first-order theorem proving
% 0.26/0.31 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.30/1.81 % (1847310)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.30/1.81 % (1847326)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2340932092:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.30/1.81 % (1847326)Instruction limit reached!
% 0.30/1.81 % (1847326)------------------------------
% 0.30/1.81 % (1847326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.81 % (1847326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.81 % (1847326)CaDiCaL version: 2.1.3
% 0.30/1.81 % (1847326)Termination reason: Instruction limit
% 0.30/1.81 % (1847326)Termination phase: Saturation
% 0.30/1.81 % (1847326)Time elapsed: 0.004 s
% 0.30/1.81 % (1847326)Peak memory usage: 88 MB
% 0.30/1.81 % (1847326)Instructions burned: 7 (million)
% 0.30/1.81 % (1847329)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1812101776:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.30/1.81 % (1847329)First to succeed.
% 0.30/1.81 % (1847329)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1847310"
% 0.30/1.81 % (1847323)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3021113223:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.30/1.81 % (1847325)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1392986388:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.30/1.81 % (1847324)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1386941535:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.30/1.81 % (1847328)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3178354612:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.30/1.81 % (1847327)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2443948389:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.30/1.81 % (1847327)Instruction limit reached!
% 0.30/1.81 % (1847327)------------------------------
% 0.30/1.81 % (1847327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.81 % (1847327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.81 % (1847327)CaDiCaL version: 2.1.3
% 0.30/1.81 % (1847327)Termination reason: Instruction limit
% 0.30/1.81 % (1847327)Termination phase: Saturation
% 0.30/1.81 % (1847327)Time elapsed: 0.004 s
% 0.30/1.81 % (1847327)Peak memory usage: 87 MB
% 0.30/1.81 % (1847327)Instructions burned: 4 (million)
% 0.30/1.81 % (1847323)Instruction limit reached!
% 0.30/1.81 % (1847323)------------------------------
% 0.30/1.81 % (1847323)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.81 % (1847323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.81 % (1847323)CaDiCaL version: 2.1.3
% 0.30/1.81 % (1847323)Termination reason: Instruction limit
% 0.30/1.81 % (1847323)Termination phase: Saturation
% 0.30/1.81 % (1847323)Time elapsed: 0.043 s
% 0.30/1.81 % (1847323)Peak memory usage: 116 MB
% 0.30/1.81 % (1847323)Instructions burned: 12 (million)
% 0.30/1.81 % (1847324)Refutation not found, incomplete strategy
% 0.30/1.81 % (1847324)------------------------------
% 0.30/1.81 % (1847324)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.81 % (1847324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.81 % (1847324)CaDiCaL version: 2.1.3
% 0.30/1.81 % (1847324)Termination reason: Refutation not found, incomplete strategy
% 0.30/1.81 % (1847324)Time elapsed: 0.050 s
% 0.30/1.81 % (1847324)Peak memory usage: 116 MB
% 0.30/1.81 % (1847324)Instructions burned: 16 (million)
% 0.30/1.81 % (1847328)Refutation not found, incomplete strategy
% 0.30/1.81 % (1847328)------------------------------
% 0.30/1.81 % (1847328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.81 % (1847328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.81 % (1847328)CaDiCaL version: 2.1.3
% 0.30/1.81 % (1847328)Termination reason: Refutation not found, incomplete strategy
% 0.30/1.81 % (1847328)Time elapsed: 0.050 s
% 0.30/1.81 % (1847328)Peak memory usage: 116 MB
% 0.30/1.81 % (1847328)Instructions burned: 16 (million)
% 0.30/1.81 % (1847331)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=4088064491:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.30/1.81 % (1847331)Refutation not found, incomplete strategy
% 0.30/1.81 % (1847331)------------------------------
% 0.30/1.81 % (1847331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.81 % (1847331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.81 % (1847331)CaDiCaL version: 2.1.3
% 0.30/1.81 % (1847331)Termination reason: Refutation not found, incomplete strategy
% 0.30/1.81 % (1847331)Time elapsed: 0.002 s
% 0.30/1.81 % (1847331)Peak memory usage: 89 MB
% 0.30/1.81 % (1847331)Instructions burned: 1 (million)
% 0.30/1.81 % (1847325)Instruction limit reached!
% 0.30/1.81 % (1847325)------------------------------
% 0.30/1.81 % (1847325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.81 % (1847325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.81 % (1847325)CaDiCaL version: 2.1.3
% 0.30/1.81 % (1847325)Termination reason: Instruction limit
% 0.30/1.81 % (1847325)Termination phase: Saturation
% 0.30/1.81 % (1847325)Time elapsed: 0.175 s
% 0.30/1.81 % (1847325)Peak memory usage: 113 MB
% 0.30/1.81 % (1847325)Instructions burned: 202 (million)
% 0.30/1.81 % (1847339)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=4173245556:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 0.30/1.81 % (1847338)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=2603243696:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 0.30/1.81 % (1847339)Instruction limit reached!
% 0.30/1.81 % (1847339)------------------------------
% 0.30/1.81 % (1847339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.81 % (1847339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.81 % (1847339)CaDiCaL version: 2.1.3
% 0.30/1.81 % (1847339)Termination reason: Instruction limit
% 0.30/1.81 % (1847339)Termination phase: Saturation
% 0.30/1.81 % (1847339)Time elapsed: 0.018 s
% 0.30/1.81 % (1847339)Peak memory usage: 90 MB
% 0.30/1.81 % (1847339)Instructions burned: 17 (million)
% 0.30/1.81 % (1847338)Instruction limit reached!
% 0.30/1.81 % (1847338)------------------------------
% 0.30/1.81 % (1847338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.81 % (1847338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.81 % (1847338)CaDiCaL version: 2.1.3
% 0.30/1.81 % (1847338)Termination reason: Instruction limit
% 0.30/1.81 % (1847338)Termination phase: Saturation
% 0.30/1.81 % (1847338)Time elapsed: 0.034 s
% 0.30/1.81 % (1847338)Peak memory usage: 89 MB
% 0.30/1.81 % (1847338)Instructions burned: 29 (million)
% 0.30/1.81 % (1847331)------------------------------
% 0.30/1.81 % (1847331)------------------------------
% 0.30/1.81 % (1847329)Refutation found. Thanks to Tanya!
% 0.30/1.81 % SZS status Theorem for theBenchmark
% 0.30/1.81 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/1.81 % (1847329)------------------------------
% 0.30/1.81 % (1847329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.81 % (1847329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.81 % (1847329)CaDiCaL version: 2.1.3
% 0.30/1.81 % (1847329)Termination reason: Refutation
% 0.30/1.81 % (1847329)Time elapsed: 0.043 s
% 0.30/1.81 % (1847329)Peak memory usage: 116 MB
% 0.30/1.81 % (1847329)Instructions burned: 23 (million)
% 0.30/1.81 % (1847329)------------------------------
% 0.30/1.81 % (1847329)------------------------------
% 0.30/1.81 % (1847310)Success in time 0.604 s
% 0.30/1.81 % Vampire exiting
%------------------------------------------------------------------------------