%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI744_1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 09:33:47 AM UTC 2026
% Result : Theorem 5.07s 1.73s
% Output : Refutation 5.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 9 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 102 ( 21 atm; 25 fun; 31 num; 25 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 : 9 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
sqr: $real > $real ).
tff(func_def_2,type,
sqrt: $real > $real ).
tff(func_def_9,type,
'$inst0': $real ).
tff(f4,axiom,
! [X0: $real] :
( $lesseq(0/1,X0)
=> ( sqrt($product(X0,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',square_sqrt) ).
tff(f9,conjecture,
sqrt(4/1) = 2/1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sqrt_four) ).
tff(f10,negated_conjecture,
( ( ~ sqrt(4/1) ) = 2/1 ),
inference(negated_conjecture,[status(cth)],[f9]) ).
tff(f13,plain,
! [X0: $real] :
( ~ $less(X0,0/1)
=> ( sqrt($product(X0,X0)) = X0 ) ),
inference(theory_normalization,[],[f4]) ).
tff(f16,plain,
! [X0: $real,X1: $real] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f21,plain,
! [X0: $real] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f22,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X1,X2)
| $less(X0,X2)
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_transitivity]) ).
tff(f24,plain,
! [X2: $real,X0: $real,X1: $real] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_order_monotonicity]) ).
tff(f25,plain,
! [X0: $real,X1: $real] :
( $less(X0,X1)
| $less(X1,$sum(X0,1/1)) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f33,plain,
sqrt(4/1) != 2/1,
inference(flattening,[],[f10]) ).
tff(f36,plain,
! [X0: $real] :
( ( sqrt($product(X0,X0)) = X0 )
| $less(X0,0/1) ),
inference(ennf_transformation,[],[f13]) ).
tff(f44,plain,
! [X0: $real] :
( $less(X0,0/1)
| ( sqrt($product(X0,X0)) = X0 ) ),
inference(cnf_transformation,[],[f36]) ).
tff(f46,plain,
sqrt(4/1) != 2/1,
inference(cnf_transformation,[],[f33]) ).
tff(f56,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] :
( ~ $less(X2,$sum(X0,X3))
| ~ $less(X0,X1)
| $less(X2,$sum(X1,X3)) ),
inference(resolution,[],[f24,f22]) ).
tff(f130,plain,
! [X0: $real] : $less(X0,$sum(X0,1/1)),
inference(resolution,[],[f25,f21]) ).
tff(f157,plain,
! [X0: $real,X1: $real] :
( $less(X0,$sum(X1,1/1))
| ~ $less(X0,X1) ),
inference(resolution,[],[f130,f56]) ).
tff(f255,plain,
! [X0: $real] : ~ $less($sum(X0,1/1),X0),
inference(resolution,[],[f157,f21]) ).
tff(f286,plain,
! [X0: $real] : ~ $less($sum($sum(X0,1/1),1/1),X0),
inference(resolution,[],[f255,f157]) ).
tff(f300,plain,
! [X0: $real] : ~ $less($sum(1/1,$sum(X0,1/1)),X0),
inference(forward_demodulation,[],[f286,f16]) ).
tff(f415,plain,
sqrt($product($sum(1/1,$sum(0/1,1/1)),$sum(1/1,$sum(0/1,1/1)))) = $sum(1/1,$sum(0/1,1/1)),
inference(resolution,[],[f300,f44]) ).
tff(f426,plain,
sqrt(4/1) = 2/1,
inference(evaluation,[],[f415]) ).
tff(f430,plain,
$false,
inference(forward_subsumption_resolution,[],[f426,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI744_1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n009.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 21:02:00 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.29 Running first-order theorem proving
% 0.23/0.29 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
% 5.07/1.72 % (3472662)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.07/1.72 % (3472671)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=248282563:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.07/1.72 % (3472669)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=4156140794:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.07/1.72 % (3472671)Instruction limit reached!
% 5.07/1.72 % (3472671)------------------------------
% 5.07/1.72 % (3472671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.72 % (3472671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.72 % (3472671)CaDiCaL version: 2.1.3
% 5.07/1.72 % (3472671)Termination reason: Instruction limit
% 5.07/1.72 % (3472671)Termination phase: Saturation
% 5.07/1.72 % (3472671)Time elapsed: 0.004 s
% 5.07/1.72 % (3472671)Peak memory usage: 88 MB
% 5.07/1.72 % (3472671)Instructions burned: 6 (million)
% 5.07/1.72 % (3472669)First to succeed.
% 5.07/1.72 % (3472669)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3472662"
% 5.07/1.72 % (3472670)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2205836001:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.07/1.72 % (3472668)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3519226992:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.07/1.72 % (3472672)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4174637873:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.07/1.72 % (3472673)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1245828353:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.07/1.72 % (3472667)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3054429046:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.07/1.72 % (3472670)Also succeeded, but the first one will report.
% 5.07/1.72 % (3472667)Instruction limit reached!
% 5.07/1.72 % (3472667)------------------------------
% 5.07/1.72 % (3472667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.73 % (3472667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.73 % (3472667)CaDiCaL version: 2.1.3
% 5.07/1.73 % (3472667)Termination reason: Instruction limit
% 5.07/1.73 % (3472667)Termination phase: Saturation
% 5.07/1.73 % (3472667)Time elapsed: 0.043 s
% 5.07/1.73 % (3472667)Peak memory usage: 115 MB
% 5.07/1.73 % (3472667)Instructions burned: 12 (million)
% 5.07/1.73 % (3472673)Instruction limit reached!
% 5.07/1.73 % (3472673)------------------------------
% 5.07/1.73 % (3472673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.73 % (3472673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.73 % (3472673)CaDiCaL version: 2.1.3
% 5.07/1.73 % (3472673)Termination reason: Instruction limit
% 5.07/1.73 % (3472673)Termination phase: Saturation
% 5.07/1.73 % (3472673)Time elapsed: 0.072 s
% 5.07/1.73 % (3472673)Peak memory usage: 118 MB
% 5.07/1.73 % (3472673)Instructions burned: 33 (million)
% 5.07/1.73 % (3472672)Instruction limit reached!
% 5.07/1.73 % (3472672)------------------------------
% 5.07/1.73 % (3472672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.73 % (3472672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.73 % (3472672)CaDiCaL version: 2.1.3
% 5.07/1.73 % (3472672)Termination reason: Instruction limit
% 5.07/1.73 % (3472672)Termination phase: Saturation
% 5.07/1.73 % (3472672)Time elapsed: 0.074 s
% 5.07/1.73 % (3472672)Peak memory usage: 115 MB
% 5.07/1.73 % (3472672)Instructions burned: 46 (million)
% 5.07/1.73 % (3472676)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=968167456:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 5.07/1.73 % (3472676)Instruction limit reached!
% 5.07/1.73 % (3472676)------------------------------
% 5.07/1.73 % (3472676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.73 % (3472676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.73 % (3472676)CaDiCaL version: 2.1.3
% 5.07/1.73 % (3472676)Termination reason: Instruction limit
% 5.07/1.73 % (3472676)Termination phase: Saturation
% 5.07/1.73 % (3472676)Time elapsed: 0.008 s
% 5.07/1.73 % (3472676)Peak memory usage: 88 MB
% 5.07/1.73 % (3472676)Instructions burned: 15 (million)
% 5.07/1.73 % (3472685)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=4054232480:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 5.07/1.73 % (3472685)Instruction limit reached!
% 5.07/1.73 % (3472685)------------------------------
% 5.07/1.73 % (3472685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.73 % (3472685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.73 % (3472685)CaDiCaL version: 2.1.3
% 5.07/1.73 % (3472685)Termination reason: Instruction limit
% 5.07/1.73 % (3472685)Termination phase: Saturation
% 5.07/1.73 % (3472685)Time elapsed: 0.019 s
% 5.07/1.73 % (3472685)Peak memory usage: 89 MB
% 5.07/1.73 % (3472685)Instructions burned: 24 (million)
% 5.07/1.73 % (3472683)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=2986899623:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2996 on theBenchmark for (2996ds/29Mi)
% 5.07/1.73 % (3472669)Refutation found. Thanks to Tanya!
% 5.07/1.73 % SZS status Theorem for theBenchmark
% 5.07/1.73 % SZS output start Proof for theBenchmark
% See solution above
% 5.07/1.73 % (3472669)------------------------------
% 5.07/1.73 % (3472669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.73 % (3472669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.73 % (3472669)CaDiCaL version: 2.1.3
% 5.07/1.73 % (3472669)Termination reason: Refutation
% 5.07/1.73 % (3472669)Time elapsed: 0.052 s
% 5.07/1.73 % (3472669)Peak memory usage: 116 MB
% 5.07/1.73 % (3472669)Instructions burned: 31 (million)
% 5.07/1.73 % (3472669)------------------------------
% 5.07/1.73 % (3472669)------------------------------
% 5.07/1.73 % (3472662)Success in time 0.592 s
% 5.07/1.73 % Vampire exiting
%------------------------------------------------------------------------------