%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI742_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 : 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 09:33:46 AM UTC 2026
% Result : Theorem 3.48s 1.26s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 4 ~; 3 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 33 ( 5 atm; 5 fun; 19 num; 4 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 : 4 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 4 ( 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
sqr: $real > $real ).
tff(func_def_2,type,
sqrt: $real > $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(f7,conjecture,
sqrt(0/1) = 0/1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sqrt_zero) ).
tff(f8,negated_conjecture,
( ( ~ sqrt(0/1) ) = 0/1 ),
inference(negated_conjecture,[status(cth)],[f7]) ).
tff(f13,plain,
! [X0: $real] :
( ~ $less(X0,0/1)
=> ( sqrt($product(X0,X0)) = X0 ) ),
inference(theory_normalization,[],[f4]) ).
tff(f31,plain,
0/1 != sqrt(0/1),
inference(flattening,[],[f8]) ).
tff(f38,plain,
! [X0: $real] :
( ( sqrt($product(X0,X0)) = X0 )
| $less(X0,0/1) ),
inference(ennf_transformation,[],[f13]) ).
tff(f42,plain,
0/1 != sqrt(0/1),
inference(cnf_transformation,[],[f31]) ).
tff(f43,plain,
! [X0: $real] :
( ( sqrt($product(X0,X0)) = X0 )
| $less(X0,0/1) ),
inference(cnf_transformation,[],[f38]) ).
tff(f63,plain,
( ( 0/1 = sqrt($product(0/1,0/1)) )
| $less(0/1,0/1) ),
inference(instantiation,[],[f43]) ).
tff(f67,plain,
0/1 = sqrt(0/1),
inference(evaluation,[],[f63]) ).
tff(f71,plain,
$false,
inference(forward_subsumption_resolution,[],[f67,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI742_1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n014.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 21:01:46 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 3.48/1.25 % (2182348)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.48/1.25 % (2182355)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3605335834:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.48/1.25 % (2182359)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=46892230:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.48/1.25 % (2182358)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2328791596:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.48/1.25 % (2182356)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=321667874:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.48/1.25 % (2182354)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1932277024:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.48/1.25 % (2182353)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3696275335:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.48/1.25 % (2182356)First to succeed.
% 3.48/1.25 % (2182356)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2182348"
% 3.48/1.25 % (2182357)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1595292492:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.48/1.25 % (2182355)Also succeeded, but the first one will report.
% 3.48/1.25 % (2182357)Instruction limit reached!
% 3.48/1.25 % (2182357)------------------------------
% 3.48/1.25 % (2182357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.25 % (2182357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.25 % (2182357)CaDiCaL version: 2.1.3
% 3.48/1.25 % (2182357)Termination reason: Instruction limit
% 3.48/1.25 % (2182357)Termination phase: Saturation
% 3.48/1.25 % (2182357)Time elapsed: 0.003 s
% 3.48/1.25 % (2182357)Peak memory usage: 88 MB
% 3.48/1.25 % (2182357)Instructions burned: 4 (million)
% 3.48/1.25 % (2182353)Instruction limit reached!
% 3.48/1.25 % (2182353)------------------------------
% 3.48/1.25 % (2182353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.25 % (2182353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.25 % (2182353)CaDiCaL version: 2.1.3
% 3.48/1.25 % (2182353)Termination reason: Instruction limit
% 3.48/1.25 % (2182353)Termination phase: Saturation
% 3.48/1.25 % (2182353)Time elapsed: 0.030 s
% 3.48/1.25 % (2182353)Peak memory usage: 115 MB
% 3.48/1.25 % (2182353)Instructions burned: 12 (million)
% 3.48/1.25 % (2182359)Also succeeded, but the first one will report.
% 3.48/1.25 % (2182358)Instruction limit reached!
% 3.48/1.25 % (2182358)------------------------------
% 3.48/1.25 % (2182358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.25 % (2182358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.25 % (2182358)CaDiCaL version: 2.1.3
% 3.48/1.25 % (2182358)Termination reason: Instruction limit
% 3.48/1.25 % (2182358)Termination phase: Saturation
% 3.48/1.25 % (2182358)Time elapsed: 0.050 s
% 3.48/1.25 % (2182358)Peak memory usage: 115 MB
% 3.48/1.25 % (2182358)Instructions burned: 48 (million)
% 3.48/1.25 % (2182367)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3579517668:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.48/1.26 % (2182367)Instruction limit reached!
% 3.48/1.26 % (2182367)------------------------------
% 3.48/1.26 % (2182367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.26 % (2182367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.26 % (2182367)CaDiCaL version: 2.1.3
% 3.48/1.26 % (2182367)Termination reason: Instruction limit
% 3.48/1.26 % (2182367)Termination phase: Saturation
% 3.48/1.26 % (2182367)Time elapsed: 0.009 s
% 3.48/1.26 % (2182367)Peak memory usage: 88 MB
% 3.48/1.26 % (2182367)Instructions burned: 14 (million)
% 3.48/1.26 % (2182368)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=152413456:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.48/1.26 % (2182369)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1344803494:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.48/1.26 % (2182369)Instruction limit reached!
% 3.48/1.26 % (2182369)------------------------------
% 3.48/1.26 % (2182369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.26 % (2182369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.26 % (2182369)CaDiCaL version: 2.1.3
% 3.48/1.26 % (2182369)Termination reason: Instruction limit
% 3.48/1.26 % (2182369)Termination phase: Saturation
% 3.48/1.26 % (2182369)Time elapsed: 0.010 s
% 3.48/1.26 % (2182369)Peak memory usage: 90 MB
% 3.48/1.26 % (2182369)Instructions burned: 18 (million)
% 3.48/1.26 % (2182368)Instruction limit reached!
% 3.48/1.26 % (2182368)------------------------------
% 3.48/1.26 % (2182368)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.26 % (2182368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.26 % (2182368)CaDiCaL version: 2.1.3
% 3.48/1.26 % (2182368)Termination reason: Instruction limit
% 3.48/1.26 % (2182368)Termination phase: Saturation
% 3.48/1.26 % (2182368)Time elapsed: 0.023 s
% 3.48/1.26 % (2182368)Peak memory usage: 89 MB
% 3.48/1.26 % (2182368)Instructions burned: 30 (million)
% 3.48/1.26 % (2182354)Instruction limit reached!
% 3.48/1.26 % (2182354)------------------------------
% 3.48/1.26 % (2182354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.26 % (2182354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.26 % (2182354)CaDiCaL version: 2.1.3
% 3.48/1.26 % (2182354)Termination reason: Instruction limit
% 3.48/1.26 % (2182354)Termination phase: Saturation
% 3.48/1.26 % (2182354)Time elapsed: 0.202 s
% 3.48/1.26 % (2182354)Peak memory usage: 116 MB
% 3.48/1.26 % (2182354)Instructions burned: 308 (million)
% 3.48/1.26 % (2182371)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1446518603:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 3.48/1.26 % (2182371)Also succeeded, but the first one will report.
% 3.48/1.26 % (2182356)Refutation found. Thanks to Tanya!
% 3.48/1.26 % SZS status Theorem for theBenchmark
% 3.48/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.26 % (2182356)------------------------------
% 3.48/1.26 % (2182356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.26 % (2182356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.26 % (2182356)CaDiCaL version: 2.1.3
% 3.48/1.26 % (2182356)Termination reason: Refutation
% 3.48/1.26 % (2182356)Time elapsed: 0.003 s
% 3.48/1.26 % (2182356)Peak memory usage: 89 MB
% 3.48/1.26 % (2182356)Instructions burned: 2 (million)
% 3.48/1.26 % (2182356)------------------------------
% 3.48/1.26 % (2182356)------------------------------
% 3.48/1.26 % (2182348)Success in time 0.407 s
% 3.48/1.26 % Vampire exiting
%------------------------------------------------------------------------------