%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI743_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 : n007.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 5.83s 1.93s
% Output : Refutation 5.83s
% 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 : 5 ( 2 usr; 2 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(f8,conjecture,
sqrt(1/1) = 1/1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sqrt_one) ).
tff(f9,negated_conjecture,
( ( ~ sqrt(1/1) ) = 1/1 ),
inference(negated_conjecture,[status(cth)],[f8]) ).
tff(f12,plain,
! [X0: $real] :
( ~ $less(X0,0/1)
=> ( sqrt($product(X0,X0)) = X0 ) ),
inference(theory_normalization,[],[f4]) ).
tff(f34,plain,
1/1 != sqrt(1/1),
inference(flattening,[],[f9]) ).
tff(f41,plain,
! [X0: $real] :
( ( sqrt($product(X0,X0)) = X0 )
| $less(X0,0/1) ),
inference(ennf_transformation,[],[f12]) ).
tff(f46,plain,
1/1 != sqrt(1/1),
inference(cnf_transformation,[],[f34]) ).
tff(f47,plain,
! [X0: $real] :
( ( sqrt($product(X0,X0)) = X0 )
| $less(X0,0/1) ),
inference(cnf_transformation,[],[f41]) ).
tff(f103,plain,
( $less(1/1,0/1)
| ( 1/1 = sqrt($product(1/1,1/1)) ) ),
inference(instantiation,[],[f47]) ).
tff(f109,plain,
1/1 = sqrt(1/1),
inference(evaluation,[],[f103]) ).
tff(f114,plain,
$false,
inference(forward_subsumption_resolution,[],[f109,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI743_1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 % Computer : n007.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Mon Sep 28 20:59:55 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.28 Running first-order theorem proving
% 0.27/0.28 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
% 5.83/1.92 % (2816354)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.83/1.92 % (2816364)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2340446131:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.83/1.92 % (2816365)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1611829478:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.83/1.92 % (2816364)Instruction limit reached!
% 5.83/1.92 % (2816364)------------------------------
% 5.83/1.92 % (2816364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.92 % (2816364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.92 % (2816364)CaDiCaL version: 2.1.3
% 5.83/1.92 % (2816364)Termination reason: Instruction limit
% 5.83/1.92 % (2816364)Termination phase: Saturation
% 5.83/1.92 % (2816364)Time elapsed: 0.044 s
% 5.83/1.92 % (2816364)Peak memory usage: 115 MB
% 5.83/1.92 % (2816364)Instructions burned: 47 (million)
% 5.83/1.92 % (2816365)Instruction limit reached!
% 5.83/1.92 % (2816365)------------------------------
% 5.83/1.92 % (2816365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.93 % (2816365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.93 % (2816365)CaDiCaL version: 2.1.3
% 5.83/1.93 % (2816365)Termination reason: Instruction limit
% 5.83/1.93 % (2816365)Termination phase: Saturation
% 5.83/1.93 % (2816365)Time elapsed: 0.060 s
% 5.83/1.93 % (2816365)Peak memory usage: 118 MB
% 5.83/1.93 % (2816365)Instructions burned: 33 (million)
% 5.83/1.93 % (2816361)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=903806620:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.83/1.93 % (2816359)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=964526963:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.83/1.93 % (2816360)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1134672598:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.83/1.93 % (2816362)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1842317399:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.83/1.93 % (2816362)First to succeed.
% 5.83/1.93 % (2816362)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2816354"
% 5.83/1.93 % (2816359)Instruction limit reached!
% 5.83/1.93 % (2816359)------------------------------
% 5.83/1.93 % (2816359)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.93 % (2816359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.93 % (2816359)CaDiCaL version: 2.1.3
% 5.83/1.93 % (2816359)Termination reason: Instruction limit
% 5.83/1.93 % (2816359)Termination phase: Saturation
% 5.83/1.93 % (2816359)Time elapsed: 0.044 s
% 5.83/1.93 % (2816359)Peak memory usage: 115 MB
% 5.83/1.93 % (2816359)Instructions burned: 12 (million)
% 5.83/1.93 % (2816361)Also succeeded, but the first one will report.
% 5.83/1.93 % (2816363)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3800625562:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.83/1.93 % (2816363)Instruction limit reached!
% 5.83/1.93 % (2816363)------------------------------
% 5.83/1.93 % (2816363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.93 % (2816363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.93 % (2816363)CaDiCaL version: 2.1.3
% 5.83/1.93 % (2816363)Termination reason: Instruction limit
% 5.83/1.93 % (2816363)Termination phase: Saturation
% 5.83/1.93 % (2816363)Time elapsed: 0.006 s
% 5.83/1.93 % (2816363)Peak memory usage: 88 MB
% 5.83/1.93 % (2816363)Instructions burned: 5 (million)
% 5.83/1.93 % (2816369)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=1670349945:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 5.83/1.93 % (2816368)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=36522177:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 5.83/1.93 % (2816369)Instruction limit reached!
% 5.83/1.93 % (2816369)------------------------------
% 5.83/1.93 % (2816369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.93 % (2816369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.93 % (2816369)CaDiCaL version: 2.1.3
% 5.83/1.93 % (2816369)Termination reason: Instruction limit
% 5.83/1.93 % (2816369)Termination phase: Saturation
% 5.83/1.93 % (2816369)Time elapsed: 0.018 s
% 5.83/1.93 % (2816369)Peak memory usage: 88 MB
% 5.83/1.93 % (2816369)Instructions burned: 31 (million)
% 5.83/1.93 % (2816368)Instruction limit reached!
% 5.83/1.93 % (2816368)------------------------------
% 5.83/1.93 % (2816368)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.93 % (2816368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.93 % (2816368)CaDiCaL version: 2.1.3
% 5.83/1.93 % (2816368)Termination reason: Instruction limit
% 5.83/1.93 % (2816368)Termination phase: Saturation
% 5.83/1.93 % (2816368)Time elapsed: 0.015 s
% 5.83/1.93 % (2816368)Peak memory usage: 88 MB
% 5.83/1.93 % (2816368)Instructions burned: 14 (million)
% 5.83/1.93 % (2816374)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=987737035:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/16Mi)
% 5.83/1.93 % (2816376)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1667895855:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 5.83/1.93 % (2816374)Also succeeded, but the first one will report.
% 5.83/1.93 % (2816360)Instruction limit reached!
% 5.83/1.93 % (2816360)------------------------------
% 5.83/1.93 % (2816360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.93 % (2816360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.93 % (2816360)CaDiCaL version: 2.1.3
% 5.83/1.93 % (2816360)Termination reason: Instruction limit
% 5.83/1.93 % (2816360)Termination phase: Saturation
% 5.83/1.93 % (2816360)Time elapsed: 0.322 s
% 5.83/1.93 % (2816360)Peak memory usage: 116 MB
% 5.83/1.93 % (2816360)Instructions burned: 307 (million)
% 5.83/1.93 % (2816376)Instruction limit reached!
% 5.83/1.93 % (2816376)------------------------------
% 5.83/1.93 % (2816376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.93 % (2816376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.93 % (2816376)CaDiCaL version: 2.1.3
% 5.83/1.93 % (2816376)Termination reason: Instruction limit
% 5.83/1.93 % (2816376)Termination phase: Saturation
% 5.83/1.93 % (2816376)Time elapsed: 0.029 s
% 5.83/1.93 % (2816376)Peak memory usage: 89 MB
% 5.83/1.93 % (2816376)Instructions burned: 25 (million)
% 5.83/1.93 % (2816379)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=661182422:i=27:canc=cautious:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/27Mi)
% 5.83/1.93 % (2816379)Refutation not found, incomplete strategy
% 5.83/1.93 % (2816379)------------------------------
% 5.83/1.93 % (2816379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.93 % (2816379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.93 % (2816379)CaDiCaL version: 2.1.3
% 5.83/1.93 % (2816379)Termination reason: Refutation not found, incomplete strategy
% 5.83/1.93 % (2816379)Time elapsed: 0.002 s
% 5.83/1.93 % (2816379)Peak memory usage: 89 MB
% 5.83/1.93 % (2816379)Instructions burned: 1 (million)
% 5.83/1.93 % (2816362)Refutation found. Thanks to Tanya!
% 5.83/1.93 % SZS status Theorem for theBenchmark
% 5.83/1.93 % SZS output start Proof for theBenchmark
% See solution above
% 5.83/1.93 % (2816362)------------------------------
% 5.83/1.93 % (2816362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.93 % (2816362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.93 % (2816362)CaDiCaL version: 2.1.3
% 5.83/1.93 % (2816362)Termination reason: Refutation
% 5.83/1.93 % (2816362)Time elapsed: 0.006 s
% 5.83/1.93 % (2816362)Peak memory usage: 89 MB
% 5.83/1.93 % (2816362)Instructions burned: 3 (million)
% 5.83/1.93 % (2816362)------------------------------
% 5.83/1.93 % (2816362)------------------------------
% 5.83/1.93 % (2816354)Success in time 0.684 s
% 5.83/1.93 % Vampire exiting
%------------------------------------------------------------------------------